Fig. 4. Example of Predicted Workers. Fig. 3. A Framework for Tackling the MQA Problem.

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1 217 IEEE 33rd International Conference on Data Engineering Prediction-Based Task Assignment in Satial Crowdsourcing Peng Cheng #, Xiang Lian, Lei Chen #, Cyrus Shahabi # Hong Kong University of Science and Technology, Hong Kong, China {chengaa, leichen}@cse.ust.hk Kent State University, Ohio, USA xlian@kent.edu University of Southern California, California, USA shahabi@usc.edu Abstract With the raid advancement of mobile devices and crowdsourcing latforms, satial crowdsourcing has attracted much attention from various research communities. A satial crowdsourcing system eriodically matches a number of locationbased workers with nearby satial tasks (e.g., taking hotos or videos at some secific locations). Previous studies on satial crowdsourcing focus on task assignment strategies that maximize an assignment score based solely on the available information about workers/tasks at the time of assignment. These strategies can only achieve local otimality by neglecting the workers/tasks that may join the system in a future time. In contrast, in this aer, we aim to imrove the global assignment, by considering both resent and future (via redictions) workers/tasks. In articular, we formalize a new otimization roblem, namely maximum quality task assignment (MQA). The otimization objective of MQA is to maximize a global assignment quality score, under a traveling budget constraint. To tackle this roblem, we design an effective grid-based rediction method to estimate the satial distributions of workers/tasks in the future, and then utilize the redictions to assign workers to tasks at any given time instance. We rove that the MQA roblem is NPhard, and thus intractable. Therefore, we roose efficient heuristics to tackle the MQA roblem, including MQA greedy and MQA divide-and-conquer aroaches, which can efficiently assign workers to satial tasks with high quality scores and low budget consumtions. Through extensive exeriments, we demonstrate the efficiency and effectiveness of our aroaches on both real and synthetic datasets. I. INTRODUCTION Mobile devices not only bring convenience to our daily life, but also enable eole to easily erform location-based tasks in their vicinity, such as taking hotos/videos (e.g., street view of Google Mas [2]), reorting traffic conditions (e.g., Waze [4]), and identifying the status of dislay shelves at neighborhood stores (e.g., Gigwalk [1]). Recently, to exloit these henomena, a new framework, namely satial crowdsourcing [18], for requesting workers to erform satial tasks, has drawn much attention from both academia (e.g., MediaQ [19]) and industry (e.g., TaskRabbit [3]). A tyical satial crowdsourcing system (e.g., gmission [7]) utilizes a number of dynamically moving workers to accomlish satial tasks (e.g., taking hotos/videos), which requires workers to hysically go to the secified locations to comlete these tasks. We first rovide the following motivating examle. Examle 1 (The Satial Crowdsourcing Problem with Multile Time Instances) Consider a scenario of satial (a) assignment at timestam (b) assignment at timestam ( +1) Fig. 1. Locally Otimal Worker-and-Task Assignments in the Satial Crowdsourcing System. crowdsourcing in Figure 1, where satial tasks, t 1 t 3,are reresented by red circles, and workers, w 1 w 3, are denoted by blue triangles. In articular, Figure 1(a) shows a worker, w 1, and two tasks, t 1 and t 2, which join the system at a timestam (denoted by markers with solid border). Figure 1(b) deicts two more workers, w 2 and w 3, and one more task, t 3, which arrive at the system at a future timestam ( +1) (denoted by markers with the dashed border). Each worker w i (1 i 3) has a articular exertise to erform different tyes of satial tasks t j (1 j 3). Thus, we assume that the cometence of a worker w i to erform task t j can be catured by a quality score q ij (as shown in Table I). Furthermore, each worker, w i, is rovided with some reward (e.g., monetary or oints) to cover the traveling cost from w i to t j, which is roortional to the traveling distance, dist(w i,t j ) (as deicted in Table I), where dist(x, y) is a distance function from x to y. Thus, workers are ersuaded to erform tasks even if they are far away from the tasks locations, which imroves the task comletion rate, esecially for workers/tasks with unbalanced location distributions. Given a maximum reward budget at each time instance, a satial crowdsourcing roblem is to assign workers to tasks at both current and future timestams, and (+1), resectively, such that the overall quality score of assignments is maximized while the reward for workers is under an allocated budget. In Examle 1, the traditional satial crowdsourcing aroaches [1], [19] considered the worker-and-task assignments only based on workers/tasks that are available in the system at each time instance. For examle, in the first time instance,, of Figure 1(a), only t 1, t 2, and w 1 exist. Therefore, we assign worker w 1 to task t 1 (rather than task t 2 ), since X/17 $ IEEE DOI 1.119/ICDE

2 TABLE I. DISTANCES AND QUALITY SCORES OF WORKER-AND-TASK PAIRS worker-and-task air, w i,t j distance, dist(w i,t j) quality score, q ij w 1,t w 1,t w 1,t w 2,t w 2,t w 2,t w 3,t w 3,t w 3,t it holds that dist(w 1,t 1 ) < dist(w 1,t 2 ) and q 11 > q 12 (i.e., worker w 1 can accomlish task t 1 with lower budget consumtion and higher quality, comared with task t 2,as given in Table I). Next, in the second time instance of Figure 1(b), two new tasks, t 2 and t 3, and two new workers, w 2 and w 3, become available in the system at timestam ( +1). Traditional satial crowdsourcing aroaches would create assignment airs w 2,t 2 and w 3,t 3 at this time instance (see lines in Figure 1(b)). As a result, such an assignment strategy at two searate time instances leads to the overall traveling cost 5 (= 1+3+1) and overall quality score 7 (= 3+2+2). Note that the assignment strategy above does not take into account future workers/tasks that may join the system at a later time instance. In [18], it is shown that an otimal assignment strategy exists for a single time instance but this local otimality may not yield a global otimal assignment across all time instances. In our running examle, at timestam, a clairvoyant algorithm that knows the future workers/tasks that arrive at timestam ( +1), may rovide a better global assignment strategy (i.e., with lower overall traveling cost and higher overall quality score). Based on this observation, in this aer, we will formulate a new otimization roblem, namely maximum quality task assignment (MQA) with the goal of assigning moving workers to satial tasks under a budget constraint to achieve a better global assignment across multile time instances. Examle 2 (The Maximum Quality Task Assignment Problem) In the examle of Figure 1, the MQA roblem is to maximize the overall quality score of assignments under traveling cost budget constraints across multile time instances. As shown in Figure 2, at timestam, we can have the rediction-based assignments: w 2,t 1, w 1,t 2, and w 3,t 3, which can achieve a better global assignment with smaller traveling cost 4(=1+2+1)and higher quality score 8 (= 4+2+2), comared to locally otimal assignments (without rediction) in Figure 1 with the traveling cost, 5, and the quality score 7. As shown in [18] and from the examle above, we can see that even an otimal local assignment based on the currently available tasks/workers at each time instance may not lead to a global otimal solution. In [18], some heuristics based on ast worker/task distributions (e.g., based on location entroy) were roosed to address this challenge. Here, instead, we strive to redict/estimate future task/worker distributions to rovide a better global assignment strategy. Moreover, in [18], the objective was to maximize the number of assigned tasks without considering the traveling budget constraint and the quality score of task assignment. In contrast, the otimization objective of MQA is to maximize the assignment quality score under budget constraints. Different from rior studies in satial crowdsourcing, the MQA roblem requires designing an accurate rediction aroach for estimating future location distributions of tasks and workers (and the quality distributions of worker- Fig. 2. Globally Otimal Assignments for the Maximum Quality Task Assignment (MQA) Problem. and-task assignment airs as well), and considering the assignments over the estimated location/quality variables of future tasks/workers, which is quite challenging. Furthermore, in this aer, we rove that the MQA roblem is NP-hard for any given time instance, by reducing it from the -1 Knasack roblem [26]. As a result, the MQA roblem is not tractable. Therefore, in order to efficiently tackle the MQA roblem, we will roose effective heuristics, including MQA greedy and MQA divide-and-conquer aroaches, over both current and redicted workers/tasks, which can efficiently comute a better global assignment with high quality scores under the budget constraints. Secifically, we make the following contributions. We formally define the maximum quality task assignment (MQA) roblem in Section II. We rove that the MQA roblem is NP-hard in Section II-D. We roose an effective grid-based rediction aroach to estimate location/quality distributions/statistics for future tasks /workers in Section III. We design an efficient MQA greedy algorithm to iteratively select one best assignment air each time over current/future tasks/workers in Section IV. We illustrate a novel MQA divide-and-conquer algorithm to recursively divide the roblem into subroblems and merge assignment results in subroblems in Section V. We verify the effectiveness and efficiency of our roosed MQA aroaches with extensive exeriments on real and synthetic data sets in Section VI. In addition to the contributions listed above, in this aer, we review revious works in satial crowdsourcing in Section VII, and conclude in Section VIII. II. PROBLEM DEFINITION A. Dynamically Moving Workers Definition 1: (Dynamically Moving Workers) Let W = {w 1,w 2,..., w n } be a set of n moving workers at timestam. Each worker w i (1 i n) is located at osition l i () at timestam, and freely moves with velocity v i. In Definition 1, worker w i can dynamically move with seed v i in any direction. At each timestam, worker w i are located at ositions l i (). Workers can freely join or leave the satial crowdsourcing system. B. Time-Constrained Satial Tasks Definition 2: (Time-Constrained Satial Tasks) Let T = {t 1,t 2,..., t m } be a set of time-constrained satial tasks at timestam. Each satial task t j (1 j m) is located at a secific location l j, and workers are exected to reach the location of task t j before the deadline e j. In Definition 2, a task requester creates a time-constrained satial task t j (e.g., taking a hoto), which requires workers to be hysically at the secific location l j before the deadline e j. In this aer, we assume that each satial task can be erformed by a single worker

3 C. The Maximum Quality Task Assignment Problem In this section, we will formalize the roblem of maximum quality task assignment (MQA), which assigns timeconstrained satial tasks to satially scattered workers with the objective of maximizing the overall quality score of assignments under the traveling budget constraint. Task Assignment Instance Set. Before we resent the MQA roblem, we first introduce the notion of the task assignment instance set. Definition 3: (Task Assignment Instance Set, I ) At timestam, given a worker set W and a task set T, a task assignment instance set, I, is a set of valid worker-andtask assignment airs in the form w i,t j, where each worker w i W is assigned to at most one task t j T, and each task t j T is accomlished by at most one worker w i W. Intuitively, I in Definition 3 is one ossible (valid) workerand-task assignment between worker set W and task set T. A valid assignment air w i,t j is in I, if and only if this air satisfies the condition that worker w i can reach the location l j of task t j before the deadline e j. The Reward of the Worker-and-Task Assignment Pair. As discussed earlier in Section I, we assume that each workerand-task assignment air w i,t j is associated with a traveling cost, c ij, which corresonds to the reward (e.g., monetary or oints) to cover the transortation fee from l i () to l j (e.g., cost of gas or ublic transortation). Without loss of generality we assume that the reward, c ij, is comuted by: c ij = C dist(l i (),l j ), where C is the unit cost er mile, and dist(l i (), l j ) is the distance between locations of worker w i and task t j. For simlicity, we will use the Euclidean distance function dist(l i (), l j ) in this aer. The Quality Score of the Worker-and-Task Assignment Pair. Each worker-and-task assignment air w i,t j is also associated with a quality score, denoted as q ij ( [, 1]), which indicates the quality of the task t j that is comleted by worker w i. Due to different tyes of tasks with various difficulty levels (e.g., taking hotos vs. reairing houses) and different exertise or cometence of workers in erforming tasks, we assume that different worker-and-task airs w i,t j may be associated with diverse quality scores q ij. The MQA Problem. Next, we rovide the definition of our maximum quality task assignment (MQA) roblem. Definition 4: (Maximum Quality Task Assignment (MQA) ) Given a set of time instances P and a maximum reward budget B for each time instance, the roblem of maximum quality task assignment (MQA) is to assign the available workers in W to tasks in T to rovide a task assignment instance set, I, at timestam P, such that: 1) at any timestam P, each worker w i W is assigned to at most one satial task t j T such that his/her arrival time at location l j is before deadline e j ; 2) at timestam P, the total reward (i.e., the traveling cost) of all the assigned workers does not exceed budget B, that is, w i,t j I c ij B; and 3) the overall quality score of the assigned tasks of all timestams in P is maximized, that is, maximize q ij. (1) P w i,t j I Intuitively, the MQA roblem (given in Definition 4) assigns workers to tasks at multile time instances in P, such Symbol T W ŵ i (or ˆt j) w i (or t j) I e j l i() l j v i c ij q ij B C P w TABLE II. SYMBOLS AND DESCRIPTIONS. Descrition a set of m time-constrained satial tasks t j at timestam a set of n dynamically moving workers w i at timestam the redicted worker (or task) the worker (or task) in either current or next time instance the task assignment instance set at timestam the deadline of arriving at the location of task t j the osition of worker w i at timestam the osition of task t j the velocity of worker w i the traveling cost from the location of worker w i to that of task t j the quality score of assigning worker w i to erform task t j the maximum reward budget (i.e., traveling cost) at each time instance the unit rice of the traveling cost by workers a set of time instances the size of the sliding window to do the rediction that (1) at each time instance, an assignment air w i,t j is valid (i.e., satisfying the time constraints, e j ); (2) at each time instance, the total reward of assignment airs is less than or equal to the maximum budget B; and (3) the overall quality score of assignments of all the time instances is maximized. As discussed earlier in Section I, it may not be globally otimal to simly otimize the assignments at each individual time instance searately. The MQA aroaches aim to rovide a better global assignment by taking into account tasks/workers not only at the current timestam, but also at the future timestam ( + i) P. Table II summarizes the commonly used symbols. D. Hardness of the MQA Problem In order to give a sense on the size of the solution sace, with n dynamically moving workers and m time-constrained satial tasks, in the worst case, there are an exonential number of ossible worker-and-task assignment strategies, which leads to high time comlexity (i.e., O((m +1) n )). Then, we rove that the MQA roblem is NP-hard, by reducing it from a wellknown NP-hard roblem, -1 Knasack roblem [26]. Lemma 2.1: (Hardness of the MQA Problem) The maximum quality task assignment (MQA) roblem is NP-hard. Proof: Please refer to Aendix A of technical reort [9]. From Lemma 2.1, we can see that the MQA roblem is NPhard, and thus intractable. Alternatively, we will later design efficient heuristics to tackle the MQA roblem and achieve better global assignment strategies. E. Framework Figure 3 illustrates a general framework, namely rocedure MQA Framework, for solving the MQA roblem, which assigns workers with satial tasks at multile time instances in P, based on the redicted location/quality distributions of workers/tasks. Secifically, at timestam, we first retrieve a set, T,of available satial tasks, and a set, W, of available workers (lines 1-3). Here, the task set T (or worker set W ) contains both tasks (or workers) that have not been assigned at the last time instance and the ones that newly arrive at the system after the last time instance (note: those workers who finished tasks in revious time instances are also treated as new workers that join the system, thus the workers can continuously contribute to the latform). In order to achieve better global assignments, we need to redict workers and tasks at a future timestam ( +1) that newly join the system, and obtain two sets W +1 and T +1, resectively (line 4). Subsequently, with both current and future sets of tasks/workers (i.e., T /W and T +1 /W +1, resectively), we

4 TABLE III. EXAMPLE OF GRID-BASED PREDICTION Cell Previous Worker Numbers Predicted Worker Number C 1 [4, 3, 4] 4 C 2 [2, 3, 3] 3 C 3 [, 1, ] C 4 [1, 1, 1] 1 can aly our roosed algorithms in this aer (including MQA greedy and MQA divide-and-conquer), and retrieve better assignment airs in assignment instance set I (line 5). Finally, we notify each worker w i to do his/her task t j (lines 6-7). Procedure MQA Framework { Inut: a set of time instances P Outut: a worker-and-task assignment strategy across the time instances in P (1) for time instance P (2) retrieve all the available satial tasks in set T (3) retrieve all the available workers in set W (4) redict new future tasks/workers in T +1 and W +1 at the next time instance (5) aly the MQA greedy or MQA divide-and-conquer aroach to obtain a assignment instance set, I, w.r.t. T, W, T +1 and W +1 (6) for each air w i,t j in I (7) inform worker w i to erform task t j} Fig. 3. A Framework for Tackling the MQA Problem. III. THE GRID-BASED WORKER/TASK PREDICTION APPROACH In order to achieve better global assignments in our MQA roblem, we need to accurately redict the future status of workers/tasks that newly join the satial crowdsourcing system. Secifically, in this section, we will introduce a gridbased worker/task rediction aroach, which can efficiently and effectively estimate the number of future workers/tasks, location distributions of future workers/tasks, and quality score distributions w.r.t. future worker-and-task airs (and their existence robabilities as well). A. The Grid-Based Prediction Algorithm In this section, we discuss how to redict the number of tasks /workers, and their location distributions in a 2- dimensional data sace U =[, 1] 2. In articular, we consider a grid index, I, over tasks and workers, which divides the data sace U into γ 2 cells, each with the side length 1/γ, where the selection of the best γ value can be guided by a cost model in [1]. Next, we estimate the otential workers/tasks that may fall into each cell at a future timestam, which is inferred from historical data of the most recent sliding window of size w. In articular, our grid-based rediction algorithm first redicts the future numbers of workers/tasks from the latest w worker/task sets in each cell, then generates ossible worker (or task) samles in W +1 (or T +1 ) for each cell of the grid index I. First, we initialize a worker set W +1 and a task set T +1 at the future time instance with emty sets. Subsequently, within each cell cell i, we can obtain its w latest worker counts, W (i) (i) (i) w+1, W w+2,..., and W, which form a sliding window of a time series (with size w). Due to the temoral correlation of worker counts in the sliding window, in this aer, we utilize the linear regression [2] over these w worker counts to redict the future number, W (i) +1, of workers in cell, cell i, that newly join the system at timestam (+1). Note that other rediction methods can be also lugged into our gridbased rediction framework, which we lan to study in our future work. Similarly, we can estimate the number, T (i) +1,of tasks in cell i at timestam ( +1). According to the redicted numbers of workers/tasks, we can uniformly generate W (i) (i) +1 worker samles (or T +1 task samles) within each cell cell i, and add them to the redicted worker set W +1 (or task set T +1 ). We use samling with Fig. 4. Examle of Predicted Workers. relacement to generate worker/task samles, which means two samles can be generated at the same location. For the seudo code of the MQA rediction algorithm, lease refer to Aendix B of our technical reort [9]. Examle 3 (The Grid-Based Prediction) Consider that a sace is divided into 4 cells, C 1 to C 4, as shown in Figure 4. Based on the historical records on the number of workers in each cell C i, we want to redict the workers that will aear in C i at the next time instance. Table III resents the number of workers for each cell in current time instance and revious two time instances 1 and 2. For examle, there 4 workers at time 2, 3 workers at time 1 and 4 workers at time in cell C 1. Then, we redict the number of workers in cell C 1 at time +1 is 4. We uniformly generate 4 worker samles. After generating redicted workers for each cell, we can cature the distribution of workers as shown in Figure 4. Location Distributions of the Predicted Workers/Tasks. As each cell is small, from the global view, the distributions of tasks/workers in the entire sace are aroximately catured. However, in each cell, discrete samles may be of small samle sizes, which may lead to low rediction accuracy. For examle, if the samle size is only 1, then different ossible locations of this one single samle (generated in the cell) may dramatically affect our MQA assignment results. Insired by this, instead of using discrete samles redicted, in this aer, we will alternatively consider continuous robability density function (df) for location distributions of workers/tasks. Secifically, we aly the kernel density estimation over samles in each cell to describe the distributions of samles locations. That is, centered at each samle s i generated in cell i, we can obtain the continuous df function of this worker/task samle, f(x) = ( ( 2 1 r=1 h r K x[r] s[r] h r )), where h r ( (, 1)) is the bandwidth on the r-th dimension, and function K( ) is a uniform kernel function [15], given by K(u) = 1 2 1( u 1). Here, 1( u 1)=1, when u 1holds. Note that the choice of the kernel function is not significant for aroximation results [15], thus, in this aer, we use uniform kernel function K( ). From the df function f(x) of each samle s i cell i, each dimension r can be bounded by an interval [s i [r] h r,s i [r]+h r ]. Tyically, in the literature [15], we set h r = ˆσC v (k)n 1/(2v+1), where ˆσ is the standard deviation of samles (derived from current worker/task statistics), v is the order of the kernel (v is set to 2 here), and C v (k) = ( ) (= 2 π 1/2 (v!) 3 R(k) 1/(2v+1), 2v(2v)!k for v 2(k) kv (k) =1/3,R(k) =1/2 with Uniform kernel functions). B. Statistics of the Predicted Workers/Tasks For the ease of the resentation, in this aer, we denote those future workers w i and tasks t j that are redicted as ŵ i and t j, resectively. Due to the redicted future workers/tasks, in our PB-SC roblem, we need to consider worker-and-task assignment airs that may involve redicted workers/tasks. That is, we have 3 cases, ŵ i,t j, w i, t j, and ŵ i, t j, where ŵ i and

5 t j are the redicted worker and task samles, resectively, following uniform distributions reresented by kernel functions K( ) (as mentioned in Section III-A). Due to the existence of these redicted workers/tasks, the traveling costs and the quality scores of assignment airs now become random variables (rather than fixed values). In this section, we will discuss how to obtain statistics (e.g., mean and variance) of traveling costs, quality scores, and confidences, associated with assignment airs. The Traveling Cost of Pairs with the Predicted Workers/Tasks. The traveling cost, ĉ ij, of worker-and-task airs involving the redicted workers/tasks (i.e., ŵ i,t j, w i, t j, or ŵ i, t j ) can be given by C dist(ŵ i,t j ), C dist(w i, t j ), or C dist(ŵ i, t j ), resectively. We discuss the general case of comuting statistics of variable ĉ ij = C dist(ŵ i, t j ). Since it is nontrivial to calculate the statistics of the Euclidean distance between variables ŵ i and t j, we alternatively consider statistics (mean and variance) of the squared Euclidean distance variable Z 2 = dist 2 (ŵ i, t j ) (= 2 r=1 (ŵ i[r] t j [r]) 2 ), where ŵ i and t j are two variables uniformly residing in a 2D sace. The Comutation of Mean E(Z 2 ). Let variable Z r = ŵ i [r] t j [r], for r =1, 2, whose mean E(Z r ) and variance Var(Z r ) can be easily comuted (i.e., E(Z r )=s i [r] s j [r] and Var(Z r )= (hr(ŵi[r]))2 +(h r( t j[r])) 2 3 resectively). Then, we have Z 2 = Z1 2 + Z2. 2 Thus, the mean E(Z 2 ) can be given by: E(Z 2 )=E(Z 2 1 )+E(Z2 2 ). (2) The Comutation of Variance Var(Z 2 ). Moreover, for variance Var(Z 2 ), it holds that: Var(Z 2 ) = E(Z 4 ) (E(Z 2 )) 2 (3) = E((Z Z2 2 )2 ) (E(Z 2 )) 2 = E(Z 4 1 )+2 E(Z2 1 ) E(Z2 2 )+E(Z4 2 ) (E(Z2 )) 2. From Eqs. (2) and (3) above, the remaining issues are to comute E(Z 2 r ) and E(Z 4 r ) (for r =1, 2). The Comutation of E(Z 2 r ). For E(Z 2 r ), since Z r = ŵ i [r] t j [r], wehave: E(Z 2 r ) = Var(Zr) +(E(Zr))2 (4) = Var(ŵ i[r]) + Var( t j[r])+(e(ŵ i[r]) E( t j[r])) 2. The Comutation of E(Z 4 r ). For E(Z 4 r ), we can derive that: E(Z 4 r ) = E((ŵi[r] t j[r]) 4 ) = E(ŵ i[r] 4 ) 4 E(ŵ i[r] 3 ) E( t j[r]) +6 E(ŵ i[r] 2 ) E( t j[r] 2 ) 4 E(ŵ i[r]) E( t j[r] 3 ) +E( t j[r] 4 ). (5) In Eq. (5), variable ŵ i [r] follows the uniform distribution within bound [lb w, ub w] (for the r-th dimension of uniform kernel function K( ) in Section III-A). We can thus infer that: E(ŵ i[r] 4 ) = E(ŵ i[r] 3 ) = E(ŵ i[r] 2 ) = ub w lb w ub w lb w ub w lb w x 4 1 ub w lb w dx = ub w5 lb w 5 5(ub w lb w), x 3 1 ub w lb w dx = ub w4 lb w 4 4(ub w lb w), x 2 1 ub w lb w dx = ub w3 lb w 3 3(ub w lb w), where [lb w, ub w] =[s i [r] h r (ŵ i [r]),s i [r]+h r (ŵ i [r])]. Similarly, we can also obtain E( t j [r] 4 ), E( t j [r] 3 ), and E( t j [r] 2 ) for task t j [r]. We omit it here. This way, by substituting Eqs. (4) and (5) into Eqs. (2) and (3), we can obtain mean E(Z 2 ) and variance Var(Z 2 ) of the squared Euclidean distance between two Uniform distributions. Quality Scores of Pairs with the Predicted Workers/Tasks. We consider the three cases to comute statistics of quality score distributions. Case 1: ŵ i,t j. In this case, at the current timestam, we can obtain all the n i workers w i that can reach task t j. Then, we use quality scores, q ij, of their corresonding worker-and-task airs w i,t j as samles (each with robability 1/n i ), which can describe/estimate future distributions of quality scores. Corresondingly, with these samles, we can obtain mean and variance of quality scores between the redicted worker ŵ i and the current task t j. Case 2: w i, t j. Similar to Case 1, we can obtain m j satial tasks t j that can be reached by worker w i. Then, we obtain m j quality score samles from valid airs w i,t j (each samle with robability 1/m j ), whose mean and variance can be used to cature the quality score distribution between the current worker w i and a redicted task t j. Case 3: ŵ i, t j. Since both worker ŵ i and task t j have redicted distributions, we cannot directly obtain quality score distributions. Thus, our basic idea is to infer future quality scores by existing workers w i and tasks t j at the current timestam. That is, at the current time instance, we collect quality scores q ij of all airs w i,t j as samles, and use them to reresent robabilistic distributions of quality scores of both worker ŵ i and task t j at the future time instance. Existence Probabilities of Pairs with the Predicted Workers/Tasks. Some assignment airs that involve the redicted worker/task may not be valid, due to the time constraints of satial tasks t j or t j (i.e., deadline e j ). Thus, we will associate each air (with either worker or task in future) with an existence robability, ij. For air ŵ i,t j,welet ij = min{ ni W, 1}, where n i is the number of valid workers who can reach task t j at the current timestam, and W is the total number of (estimated) workers at timestam. Similarly, for air w i, t j, we can obtain: ij = min{ mj T, 1}, where m j is the number of valid tasks that worker w i can reach before the deadlines, and T is the total number of (estimated) tasks at timestam. For air ŵ i, t j, let u ij be the total number of valid airs between W and T at timestam. Then, we can estimate the existence robability of air ŵ i, t j by: ij = uij W. T IV. THE MQA APPROACH In this section, we roose an efficient MQA greedy algorithm () to solve the MQA roblem, which iteratively finds one best worker-and-task assignment air, w i,t j, each time, with the highest increase of the quality score and under the budget constraint of high confidences. Here, in order to achieve high total quality scores, is alied over both current and redicted future workers/tasks. After all assignment airs (involving current/future workers/tasks) are selected, we will only insert into the set I those airs, w i,t j, with both workers and tasks at current timestam (i.e., w i W and t j T )

6 A. The Comarisons of the Quality Score Increases / Traveling Cost Increases Since MQA greedy algorithm needs to select one workerand-task assignment air, w i, t j, at a iteration with the highest increase of the total quality score, in this section, we will first formalize the increase of the quality score, Δ q ( w i, t j ), for a air w i, t j, and then comare the increases of overall quality scores between two airs w i, t j and w a, t b, where w i, t j, w a, and t b can be either current or redicted workers/tasks. The Calculation of the Quality Score Increase, Δ q ( w i, t j ). Based on Eq. (1), the overall quality score is given by summing u all quality scores of the selected assignment airs. Thus, when we choose a new assignment air w i, t j, the increase of the quality score, Δ q ( w i, t j ), is exactly equal to the quality score of this new air w i, t j, denoted as q ij. That is, Δ q( w i, t j) = q ij, (6) where q ij is a fixed value, if both w i and t j are current worker and task, resectively; otherwise, q ij is a random variable whose distribution can be given by samles discussed in Section III-B. The Comarisons of the Quality Score Increase Between Two Pairs w i, t j and w a, t b. Next, we discuss how to decide which worker-and-task assignment air is better, in terms of the quality score increase, between two airs w i, t j and w a, t b. Secifically, if both airs have workers/tasks at current timestam, then the quality score increases, q ij and q ab (given in Eq. (6)), are fixed values. In this case, the air with higher quality score increase is better. On the other hand, in the case that either of the two airs involves the redicted workers/tasks, their corresonding quality score increases, that is, q ij and/or q ab, are random variables. To comare the two quality score increases, we can comute the robability, Pr Δq( w i, t, that air w j) i, t j has the increase greater than that of the other one. That is, by alying the central limit theorem (CLT) [14], [16], we have: Pr Δq ( wi, t j ) = Pr{Δ q( w i, t j) > Δ q( w a t b)} (7) = Pr{ q ij > q ab} = 1 Pr{ q ij q ab} { qij q ab (E( q ij) E( q ab)) = 1 Pr Var( q ij) +Var( q ab) (E( qij) E( } Var( q ij) +Var( q ab) ( (E( qij) E( q ab)) = 1 Φ Var( q ij) +Var( q ab) where Φ( ) is the cumulative density function (cdf) of a standard normal distribution. With Eq. (7), we can comute the robability, Pr Δq( w i, t, j) that air w i, t j is better than (i.e., with higher score than) air w a, t b. If it holds that Pr Δq( w i, t j) >.5, then we say that air w i, t j is exected to have higher quality score increase; otherwise, air w a, t b has higher quality score increase. The Comarisons of the Traveling Cost Increase Between Two Pairs w i, t j and w a, t b. Similar to the quality score, we can also comute the robability, Pr Δc( w i, t j), that the increase of the traveling cost for air w i, t j is smaller than that of air w a, t b. That is, we can obtain: ), Pr Δc( wi, t j ) = Pr{Δ c( w i, t j) Δ c( w a, t b)} (8) = Pr{ c ij c ab} ( (E( cij) E( c ab)) = Φ Var( c ij) +Var( c ab) B. The Pruning Strategy As discussed in Section IV-A, one straightforward method for selecting a good assignment air at a iteration is as follows. We sequentially scan each valid worker-andtask air w i, t j, and comare its quality score increase, Δ q ( w i, t j ), with that of the best-so-far air w a, t b, in terms of the robability Pr Δq( w i, t. If the air w j) i, t j exects to have higher quality score (and moreover satisfy the budget constraint), then we consider it as the new best-so-far air. The straightforward method mentioned above considers all ossible valid assignment airs, and comutes their comarison robabilities, which requires high time comlexity, that is, O(m n ), where m and n are the numbers of tasks and workers at both current and future time instances, resectively. Therefore, in this section, we will roose effective runing methods to quickly discard those false alarms of assignment airs, with both high traveling costs and low quality scores. Pruning with Bounds of Quality and Traveling Cost. Without loss of generality, for each air w i, t j, assume that we can obtain its lower and uer bounds of the traveling cost, c ij, and quality score, q ij, where c ij and q ij are either fixed values (if w i and t j are worker/task at the current time instance) or random variables (if worker and/or task are from the future time instance). That is, we denote c ij [lb c ij,ub c ij ] and q ij [lb q ij,ub q ij ]. This way, in a 2D quality-and-travel-cost sace, each worker-and-task assignment air, w i, t j, corresonds to a rectangle, [lb q ij,ubq ij ] [lb c ij,ub c ij ]. Then, based on the idea of the skyline query [5], we can safely rune those airs that are dominated by candidate airs, in terms of the traveling cost and quality score. Lemma 4.1: (The Dominance Pruning) Given a candidate air w a, t b, a valid worker-and-task air w i, t j can be safely runed, if and only if it holds that: (1) ub c ab <lb c ij, and (2) lb q ab >ub q ij. Proof: Since it holds that c ij [lb c ij,ub c ij ] and q ij [lb q ij,ub q ij ], by lemma assumtions and inequality transition, we have: c ab ub c ab <lb c ij c ij, and q ab lb q ab >ub q ij q ij. As a result, we can see that, comared to air w a, t b, air w i, t j has both higher traveling cost c ij and lower quality score q ij. Since our algorithm only selects one best air each iteration (which can maximally increase the quality score and minimally increase the traveling cost), air w i, t j is definitely worse than w a, t b in both quality and traveling cost dimensions, and thus can be safely runed. Pruning with the Increase Probability. Lemma 4.1 utilizes the lower/uer bounds of the quality score and traveling cost to enable the dominance runing. If a air cannot be simly runed by Lemma 4.1, we will further consider a more costly runing method, by consider the robabilistic information. Lemma 4.2: (The Increase Probability Pruning) Given a candidate air w a, t b, a valid air w i, t j can be safely )

7 Procedure MQA Greedy { Inut: current and redicted workers w i in W, current and redicted tasks t j in T, and the maximum ossible budget B max Outut: a worker-and-task assignment instance set, I (1) I = ; (2) obtain a list, L, of valid worker-and-task airs for w i W and t j T (3) for k =1to min{ W, T } (4) S = ; (5) for each valid assignment air w i, t j L (6) if w i, t j has lb c ij greater than the remaining budget, then continue; (7) if air w i, t j cannot be runed w.r.t. S by Lemma 4.1 (8) if air w i, t j cannot be runed w.r.t. S by Lemma 4.2 (9) add w i, t j to S (1) rune other candidate airs in S with w i, t j (11) select one best assignment air w i, t j in S satisfying the budget constraint B max in Eq. (9) and with the highest robability Pr q,max( w i, t j ) in Eq. (1) (12) add the selected air w i, t j to I (13) remove all those valid airs w i, or, t j from L (14) remove those worker-and-task airs with the redicted workers/tasks from I (15) return I } Fig. 5. The MQA Greedy Algorithm. runed, if and only if it holds that: (1) Pr Δq( w i, t (w.r.t. j) w a, t b ) is greater than.5, and (2) Pr Δc( w i, t j) (w.r.t. candidate air w a, t b ) is greater than.5, where Pr Δq( w i, t j) and Pr Δc( w i, t j) are given by Eqs. (7) and (8), resectively. Intuitively, Lemma 4.2 filters out those airs w i, t j that have higher robabilities to be inferior to other candidate airs w a, t b, in terms of both traveling cost and quality score. Based on Lemmas 4.1 and 4.2, we can obtain a set, S,of candidate airs that cannot be dominated by other airs. Selection of the Best Pair Among Candidate Pairs. Given a number of candidate airs in set S, still needs to identify one best air with a high quality score and under the budget constraint. Secifically, we will first filter out those false alarms in S with high traveling costs (i.e., violating the budget constraint), and then return one air with the highest robability to have larger quality score than others in S. Assume that in, we have so far selected L airs, denoted as w a, t b. Then, with a new assignment air w i, t j S, if it holds that: Pr wa, t b lb c ab + c ij B max δ, (9) then air w i, t j S can be safely ruled out from candidate set S, where δ is a user-secified confidence level that the selected assignment satisfies the budget constraint B max for both (remaining) current- and next- time instance budgets. Eq. (9) can be comuted via CLT [14], [16]. Next, in the remaining candidate airs in S, we will select one air w i, t j with the highest robability, Pr q,max ( w i, t j ), of having the largest high quality. That is, we have: Pr q,max( w i, t j ) = wa, t b Pr Δq ( wi, t j ) ( wa, t b ) (1) where Pr Δq( w i, t ( w j) a, t b ) is the robability of quality score increase, comared with air w a, t b, given by Eq. (7). Finally, among all the remaining candidate airs in set S, we will choose the one, w i, t j, with the highest robability Pr q,max ( w i, t j ), which will be included as a selected best assignment air in. C. The MQA Greedy Algorithm In this subsection, we roose MQA greedy algorithm, which iteratively assigns a worker to a satial task greedily that can obtain a high the overall quality score under the budget constraint each iteration. Figure 5 resents the seudo code of our MQA greedy algorithm, namely MQA Greedy, which obtains one best worker-and-task assignment air each time over both current and redicted future workers and tasks, where the selected air satisfies the budget constraint B max and has the largest quality score with high confidence, where B max is the available budget in both current and next time instances. We first initialize the worker-and-task assignment instance set I with an emty set (line 1). Then, we obtain a list, L, of valid worker-and-task assignment airs, which may involve either current or future workers/tasks, that is, w i W and t j T (line 2). Next, for each iteration, we find one best assignment air with high quality score and low traveling cost (satisfying the budget constraint) (lines 3-13). In articular, we check each valid assignment air w i, t j in the list L (line 5). If this air has the lower bound, lb c ij, of the traveling cost greater than (the uer bound of) the remaining budget (w.r.t. I and B max ), then it does not satisfy the budget constraint, and we can continue to check the next assignment air (line 6). Then, if the air w i, t j cannot be runed by dominance and increase robability runing methods in Lemmas 4.1 and 4.2, resectively, then w i, t j is a candidate air, and we include in an initially emty candidate set S (lines 7-9). In addition, we can also use candidate air w i, t j to rune other airs in set S (line 1). After that, we can insert the best air from the candidate set S into set I (lines 11-12), such that the budget constraint B max is satisfied in Eq. (9) and the robability Pr q,max ( w i, t j ) in Eq. (1) is maximized. Since each worker can be assigned with at most one task and each task is accomlished by at most one worker, we remove those valid airs from L that contains either worker w i or task t j (line 13). Finally, we remove those worker-and-task airs involving future workers/tasks from I, and return the set I as the solution of the MQA greedy algorithm (lines 14-15). V. THE MQA DIVIDE-AND-CONQUER APPROACH In this section, we roose an efficient MQA divide-andconquer algorithm (), which artitions the MQA roblem into g subroblems, recursively conquers the subroblems, and merges assignment results from subroblems. In this aer, we will divide the MQA roblem with m current/future tasks into g subroblems, each involving m /g tasks. The rocess continues, until the subroblem sizes become 1 (i.e., with one single satial task in subroblems, which can be easily solved by ). We will later discuss how to utilize a cost model to estimate the best g value that can achieve low MQA rocessing cost. A. The Decomosition of the MQA Problem Decomosing the MQA Problem. Secifically, assume that the original MQA roblem involves m current/future satial tasks for both current and next time instances. Our goal is to divide this roblem into g subroblems M s (for 1 s g), such that each subroblem M s involves a disjoint subgrou of m /g satial tasks, t j, each of which is associated with otentially valid worker(s) w i (i.e., with valid worker-and-task assignment airs w i, t j ). After the decomosition, each subroblem M s contains all valid airs, w i, t j, w.r.t. the decomosed m /g tasks. Since tasks in different subroblems may be reachable by the same workers, different subroblems may involve the same (conflicting) workers, whose conflictions should be resolved

8 (a) The MQA Problem (b) The Decomosed Subroblems Fig. 6. Illustration of Decomosing the MQA Problem. when we merge solutions (the selected assignment airs) to these subroblems (as discussed in Section V-B). Examle 4 (The MQA Problem Decomosition) Figure 6 shows an examle of decomosing the MQA roblem (as shown in Figure 6(a)) into 3 subroblems (as deicted in Figure 6(b)), where each subroblem contains one single satial task (i.e., subroblem size = 1), associated with its related valid workers. Here, the dashed border indicates the redicted future workers (i.e., w 4 and w 5 ) or task (i.e., t 3 ). In this examle, the first subroblem in Figure 6(b) contains task t 1, which can be reached by workers w 1 and w 4. Different tasks may have conflicting workers, for examle, tasks t 1 and t 2 from subroblems M 1 and M 2, resectively, share the same (conflicting) worker w 1. The MQA Decomosition Algorithm. Figure 7 illustrates the seudo code of our MQA decomosition algorithm, namely MQA Decomosition, which decomoses the MQA roblem (with m tasks), and returns g MQA subroblems, M s (each having m /g tasks). Secifically, we first initialize g emty subroblems, M s, where 1 s g (lines 1-2). Then, we find all valid worker-and-task assignment airs w i, t j for both current and redicted workers/tasks in sets W and T, resectively (line 3). Next, we want to iteratively retrieve g subroblems, M s, from the original MQA roblem (lines 4-8). That is, for the s th iteration, we first obtain an anchor task t j and its ( m/g 1) nearest tasks, and add them to set T (s) (line 5), where anchor tasks t j are chosen in a sweeing style (starting with the smallest longitude, or mean of the longitude for future tasks; in the case that multile tasks have the same longitude, we choose the one with smallest latitude). For each task t j T (s), we obtain all its related workers w i who can reach task t j, and add airs w i, t j to subroblem M s (lines 6-8). Finally, we return the g decomosed subroblems M s (for 1 s g) (line 9). B. The MQA Merge Algorithm As mentioned earlier, we can execute the decomosition algorithm to recursive divide the MQA roblem, until each subroblem only involves one single task (which can be easily rocessed by the greedy algorithm). After we obtain solutions to the decomosed MQA subroblems (i.e., a number of selected assignment airs in subroblems), we need to merge these solutions into the one to the original MQA roblem. Resolving Worker-and-Task Assignment Conflicts. During the merge rocess, some workers are conflicting, that is, they are assigned to different tasks in the solutions to distinct subroblems at the same time. This contradicts with the requirement that each worker can only be assigned with at most one satial task at each time instance. Thus, to merge solutions of these conflicting subroblems, we resolve the conflicts. Procedure MQA Decomosition { Inut: n current/future workers w i in W, m current/future satial tasks t j in T, and the number of subroblems g Outut: the decomosed MQA subroblems, M s (for 1 s g) (1) for s =1tog (2) M s = (3) comute all valid worker-and-task airs w i, t j from W and T (4) for s =1to g (5) add an anchor task t j and find its ( m /g 1) nearest tasks to set T (s) // the task, t j, whose longitude (or mean of the longitude) is the smallest (6) (7) for each current/future task t j T (s) obtain all valid workers w i that can reach task t j (8) add these airs w i, t j to subroblem M s (9) return subroblems M 1, M 2,..., and M g} Fig. 7. The MQA Problem Decomosition Algorithm. Next, we use an examle to illustrate how to resolve the conflicts between two (or multile) airs w i, t j and w i, t b (w.r.t. the conflicting worker w i ), by selecting one best air with low traveling cost and high quality score. Examle 5 (The Merge of Subroblems) In the examle of Figure 6(b), assume that in subroblems M 1 and M 2,we selected airs w 1,t 1 and w 1,t 2 as the best assignment, resectively, which contains the conflicting worker w 1. When we merge the two subroblems M 1 and M 2, we need to resolve such a conflict by deciding which task should be assigned to the conflicting worker w 1. By using Lemmas 4.1 and 4.2, we can first rune airs that are not dominated by others. Then, among the remaining candidate airs, we can select one best air satisfying Eq. (9) and maximizing Eq. (1). In this examle, assume that air w 1,t 1 dominates air w 1,t 2 by Lemma 4.1. Then, we will assign worker w 1 with task t 1 (since w 1,t 1 is the best air), and find another worker (e.g., w 2 ) with the largest quality score under the budget constraint to do task t 2. This way, after solving conflicts, we obtain two udated airs w 1,t 1 and w 2,t 2 for subroblems M 1 and M 2, resectively. The MQA Merge Algorithm. Figure 8 illustrates the MQA merge algorithm, namely MQA Merge, which resolves the conflicts between the current assignment instance set I (that we have merged subroblems M) and that, I (s), of subroblem M s, and returns a merged set without conflicts. First, we obtain a set, W c, of conflicting workers between I and I (s) (line 1), which are assigned with different tasks in different subroblems, M and M s. Then, in each iteration, we select one conflicting worker w i W c with the highest traveling cost in I (s), and choose one best air between w i, t j I and w i, t k I (s), in terms of budget and quality score (which can be achieved by checking Lemmas 4.1 and 4.2, and finding the one that satisfies Eq. (9) and maximizes Eq. (1) (lines 2-4). When w i, t k in subroblem M s is selected as the best air, we can resolve the conflicts by relacing w i, t j with w i, t j in I ; otherwise, we can relace w i, t k with w i, t k in I (s) (lines 5-8). Then, we remove worker w i from set W c (line 9). After resolving all conflicting workers in W c between I and I (s), we can merge them together, and return an udated merged set I (lines 1-11). C. The Algorithm U to now, we have discussed how to decomose and merge subroblems. In this section, we will illustrate the detailed MQA divide-and-conquer () algorithm, which artitions the original MQA roblem into subroblems, recursively solves each subroblem, and merges assignment

9 Procedure MQA Merge { Inut: the current assignment instance set, I, of the merged subroblems M, and the assignment instance set, I (s), of subroblem Ms Outut: a merged worker-and-task assignment instance set, I (1) let W c be a set of conflicting workers between I and I (s) (2) while W c (3) choose a worker w i W c with the highest traveling cost in I (s) // assume w i is assigned to t j in I and to t k in I (s) (4) select one best air between w i, t j I and w i, t k I (s) // by using Lemmas 4.1 and 4.2, and finding the one satisfying // Eq. (9) and maximizing Eq. (1) (5) if air w i, t k in subroblem M s is selected (6) find another best worker w i in M and substitute w i, t j in I (7) else (8) find another best worker w i in Ms and substitute w i, t k in I (s) (9) W c = W c { w i} (1) I = I I (s) (11) return I } Fig. 8. The Merge Algorithm. results of subroblems by resolving conflicts and adjusting the assignments under the budget constraint. Figure 9 shows the seudo code of our algorithm, namely rocedure MQA. We first initialize an emty set rlt, which is used for store candidate airs chosen by our algorithm (line 1). Then, we utilize a novel cost model (discussed in Aendix C to estimate the best number of the decomosed subroblems, g, with resect to current/future sets, W and T, of workers and tasks, resectively (line 2). With this arameter g, we can invoke the MQA Decomosition algorithm (as mentioned in Figure 7), and obtain g subroblems M s (line 3). For each subroblem M s, if M s involves more than 1 task, then we can recursively call rocedure MQA ( ) to obtain the best assignment airs from subroblem M s (lines 4-6). Otherwise, if subroblem M s only contains one single satial task t j, then we aly the greedy algorithm (in Figure 5) to select one best worker for task t j (lines 7-8). Here, the best worker means, the corresonding air has the highest quality score under the budget constraint B max. After that, the selected assignment airs in the s-th subroblem are ket in set rlt (s), where 1 s g. Then, we can invoke rocedure MQA Merge ( ) to merge these g sets rlt (s) into a set rlt, by resolving the conflicts (lines 9-11). Due to the budget constraint B max, we may still need to adjust assignment airs in set rlt such that the total traveling cost is below the maximum budget B max. If the uer bound of the traveling cost in set rlt does not exceed budget B max, then we can directly return rlt as I (lines 12-13). Otherwise, similar to, we need to select best assignment airs from set rlt that are under the budget constraint B max (maximizing the total quality score), and add them to the set I, by calling rocedure MQA Budget Constrained Selection (lines 14-15). In articular, to adjust the budget, we select a best air from set rlt each time that satisfies the budget constraint B max and with the highest quality score. Please refer to details of rocedure MQA Budget Constrained Selection in lines of Figure 9. Discussions on Estimating the Best Number, g, of the Decomosed Subroblems. In order to reduce the comutation cost in our algorithm, we aim to select a best g value that minimizes the rocessing cost, in light of our roosed cost model. Secifically, we formally model the comutation cost, cost, of the algorithm, with resect to g, take the derivative of cost over g, and then Procedure MQA { Inut: n current/future workers in W, and m current/future satial tasks in T, and a maximum budget B max Outut: an assignment instance set, I, with current/future workers/tasks (1) rlt = (2) estimate the best number of subroblems, g, w.r.t. W and T (3) invoke MQA Decomosition(W, T, g), and obtain g subroblems M s (4) for s =1to g (5) if the number of tasks in subroblem M s is greater than 1 (6) rlt (s) = MQA (W (M s), T (M s), B max) (7) else (8) rlt (s) = MQA Greedy(W (M s), T (M s), B max) (9) for s =1to g (1) find the next subroblem, M s (11) rlt = MQA Merge (rlt, rlt (s) ) (12) if the uer bound of the traveling cost of rlt B max (13) return rlt (14) else (15) I = MQA Budget Constrained Selection (rlt, B max) (16) return I } Procedure MQA Budget Constrained Selection { Inut: candidate airs in rlt and a maximum budget B max Outut: a worker-and-task assignment instance set, I, under the budget constraint (17) I = ; (18) for k =1to rlt (19) S = (2) for each assignment air w i, t j rlt (21) if w i, t j has lb c ij greater than the remaining budget, then continue; (22) if air w i, t j cannot be runed w.r.t. S by Lemma 4.1 (23) if air w i, t j cannot be runed w.r.t. S by Lemma 4.2 (24) add w i, t j to S (25) rune other candidate airs in S with w i, t j (26) select one best assignment air w i, t j in S satisfying the budget constraint B max in Eq. (9) and with the highest robability M q,max( w i, t j ) in Eq. (1) (27) add the selected air w i, t j to I (28) return I } Fig. 9. The Divide-and-Conquer Algorithm. let the derivative be. This way, we can find the best g value that minimizes the cost of the algorithm. For details, lease refer to Aendix B of our technical reort [9]. VI. EXPERIMENTAL STUDY Real/Synthetic Data Sets. We tested our roosed MQA rocessing algorithms over both real and synthetic data sets. Secifically, for real data sets, we used two check-in data sets, Gowalla [11] and Foursquare [21]. In the Gowalla data set, there are 196,591 nodes (users), with 6,442,89 checkin records. In the Foursquare data set, there are 2,153,471 users, 1,143,92 venues, and 1,21,97 check-ins, extracted from the Foursquare alication through the ublic API. Since most assignments haen in the same cities, we extract checkin records within the area of San Francisco (with latitude from to and longitude from to ), which has 8,481 Foursquare check-ins, and 149,683 Gowalla check-ins for 6,143 users. We use check-in records of Foursquare to initialize the location and arrival time of tasks in the satial crowdsourcing system, and configure workers using the check-ins records from Gowalla. In other words, we have 6,143 workers and 8,481 satial tasks in the exeriments over real data. For simlicity, we first linearly ma check-in locations from Gowalla and Foursquare into a [, 1] 2 data sace, and then scale the arrival times of workers/tasks in the real data accordingly. In order to generate workers/tasks for each time instance, we evenly divide the entire time san of check-ins from two real data sets into R subintervals ( P ), and utilize check-ins in each subinterval to initialize workers/tasks for the corresonding time instance. For synthetic data sets, we generate workers/tasks that join the satial crowdsourcing system for every time instance in the time instance set P as follows. We randomly roduce locations