Sofya Raskhodnikova

Transcription

1 Sofya Raskhodnikova Work: Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot, Israel sofya/ Home: Neve Metz 16 Rehovot, Israel RESEARCH INTERESTS Design and analysis of sublinear-time algorithms, approximation and randomized algorithms, computational complexity, coding theory, computational geometry CITIZENSHIP Citizen of the USA EDUCATION EXPERIENCE Cambridge, MA Ph.D. in Computer Science, 2003 Thesis: Property Testing: Theory and Applications Advisor: Michael Sipser Readers: Shafi Goldwasser, Madhu Sudan M.S. in Computer Science, 1999 Thesis: Monotonicity Testing Advisor: Michael Sipser B.S. in Mathematics and Computer Science, 1997 Faculty of Mathematics and Computer Science Weizmann Institute of Science 10/2004 current Postdoctoral Fellow supported by the Feinberg Graduate School. Research in sublinear-time algorithms, combinatorics, string compression. Developed and taught a graduate course on sublinear-time algorithms with 15 registered students, supervised a teaching assistant. School of Computer Science The Hebrew University of Jerusalem 8/2003 9/2004 Postdoctoral Fellow supported by the Lady Davis Fellowship. Academic sponsor: Prof. Alex Samorodnitsky Research in sublinear-time algorithms, coding, combinatorics, vision. Theory of Computation Group, LCS, MIT 1/98 06/2003 Research Assistant, supervised by Prof. Michael Sipser. Research in algorithms, computational geometry, complexity.

2 MIT EECS department Fall semesters of Teaching Assistant for the Theory of Computation course, taught by Prof. Sipser. Led a weekly recitation section, prepared handouts, graded tests, supervised homework graders and held tutoring sessions. NEC Research Institute Summers Research Assistant, supervised by Prof. Ronitt Rubinfeld. Research in sublinear-time algorithms. RSA Labs, part of Security Dynamics 06/99 08/99 Research Assistant, supervised by Dr. Ari Juels. Designed and implemented a graphical Java simulation of a protocol protecting against denial of service attacks. Worked on cryptographic protocols for lending computational resources. InterSystems 06/97 8/97 Software Engineer. Implemented a new namespace mapping syntax for the Cache database management system. Autonomous Agents group at MIT Media Laboratory 06/96 05/97 Worked on Project Yenta with the goal to implement a privacy-protected, distributed matchmaking and coalition-building system. Amorphous Computing Group at LCS, MIT 06/95 12/95 Worked on designing a computer system based on multiple tiny processors communicating with each other by electric field interactions. PUBLICATIONS (available on my web page) S. Raskhodnikova, Property Testing: Theory and Applications, Ph.D. Thesis,, Cambridge, MA, S. Raskhodnikova, D. Ron, R. Rubinfeld, A. Shpilka, and A. Smith, Sublinear Algorithms for Approximating String Compressibility and the Distribution Support Size, Electronic Colloquium on Computational Complexity, TR05-125, E. Ben-Sasson, P. Harsha, and S. Raskhodnikova, 3CNF Properties are Hard to Test, SIAM Journal on Computing, 35(1):1-21, Preliminary version appeared in Proceedings of the 35th ACM STOC, , S. Raskhodnikova, Approximate Testing of Visual Properties, Proceedings of the 7 th RANDOM, Springer-Verlag, T. Batu, F. Ergun, J. Kilian, A. Magen, S. Raskhodnikova, R. Rubinfeld, and R. Sami, A Sublinear Algorithm for Weakly Approximating Edit Distance, Proceedings of the 35 th ACM STOC, A. Andoni, M. Deza, A. Gupta, P. Indyk, and S. Raskhodnikova, Lower Bounds for Embedding of Edit Distance into Normed Spaces, Proceedings of the 14 th ACM-SIAM SODA, E. Fischer, E. Lehman, I. Newman, S. Raskhodnikova, R. Rubinfeld, and A. Samorodnitsky, Monotonicity Testing Over General Poset Domains, Proceedings of the 34 th ACM STOC, , 2002.

3 Y. Dodis, O. Goldreich, E. Lehman, S. Raskhodnikova, D. Ron, and A. Samorodnitsky, Improved Testing Algorithms for Monotonicity, Proceedings of the 3 rd RANDOM, , S. Raskhodnikova, Monotonicity Testing, Master s Thesis, Massachusetts Institute of Technology, Cambridge, MA, TALKS Dagstuhl Seminar on Sublinear Algorithms, Schloss Dagstuhl, Germany, Ben Gurion University Computer Science Seminar, Beer Sheva, Israel, Tayota Technological Institute Seminar, Chicago, University of Waterloo Theory of Computation Seminar, Canada, HUJI Theory of Computation Seminar, Jerusalem, Tel Aviv University Theory of Computation Seminar, Haifa University Theory of Computation Seminar, Weizmann Institute Theory of Computation Seminar, Rehovot, th International Workshop on Randomization, Princeton, Microsoft Research, Redmond, th ACM Symposium on Theory of Computing, Montreal, MIT Complexity Seminar, NYU Theory of Computation Seminar, DIMACS Workshop on Sublinear Algorithms, New Jersey, rd International Workshop on Randomization, Berkeley, AWARDS Lady Davis Postdoctoral Fellowship, 2003; Award for Excellent Work at RSA, 1999; NY Governor s Citation for Academic Excellence, 1994; 1st place in Belorussian Republican Math Olympiad, 1992 REFERENCES Professor Michael Sipser Department of Mathematics 77 Mass Ave, Room Cambridge MA Phone: sipser@math.mit.edu Professor Ronitt Rubinfeld Department of Computer Science 32 Vassar Street, Room 32-G698 Cambridge MA Phone: ronitt@csail.mit.edu Professor Madhu Sudan Department of Computer Science 32 Vassar Street, Room 32-G640 Cambridge MA Phone: madhu@csail.mit.edu Professor Dana Ron Department of Electrical Engineering Systems Tel Aviv University, Ramat Aviv Tel Aviv Israel Phone: danar@eng.tau.ac.il DESCRIPTION OF PUBLICATIONS S. Raskhodnikova, Property Testing: Theory and Applications, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge, MA, 2003.

4 Property testers are algorithms that distinguish inputs with a given property from those that are far from satisfying the property. Far means that many characters of the input must be changed before the property arises in it. The query complexity of a property tester is the number of input characters it reads. The thesis is a detailed investigation of properties that are and are not testable with sublinear query complexity. We begin by characterizing properties of strings over the binary alphabet in terms of their formula complexity. Every such property can be represented by a CNF formula. We show that properties of n-bit strings defined by 2CNF formulas are testable with O( n) queries, whereas there are 3CNF formulas for which the corresponding properties require Ω(n) queries. We show that testing properties defined by 2CNF formulas is equivalent to other testing problems, such as testing monotonicity of functions over partial orders. We give upper and lower bounds for the general problem and for specific partial orders. In the final part of the thesis, we initiate an investigation of property testing as applied to images and obtain very efficient algorithms for several basic properties: being a half-plane, connectedness and convexity. S. Raskhodnikova, D. Ron, R. Rubinfeld, A. Shpilka, and A. Smith, Sublinear Algorithms for Approximating String Compressibility and the Distribution Support Size, ECCC, TR05-125, We raise the question of approximating compressibility of a string with respect to a fixed compression scheme, in sublinear time. We study this question in detail for two popular lossless compression schemes: run-length encoding (RLE) and Lempel-Ziv (LZ), and present algorithms and lower bounds for approximating compressibility with respect to both schemes. While we obtain much stronger results for RLE in terms of the efficiency of the algorithms, our investigation of LZ yields results whose interest goes beyond the initial questions we set out to study. In particular, we prove combinatorial structural lemmas that relate compressibility of a string with respect to Lempel-Ziv to the number of distinct short substrings contained in it. We also show that compressibility with respect to LZ is related to approximating the support size of a distribution. This problem has been considered under different guises in the literature. We prove a strong lower bound for it, at the heart of which is a construction of two positive integer random variables, X and Y, with very different expectations and the following condition on the moments up to k: E[X]/E[Y ] = E[X 2 ]/E[Y 2 ] =... = E[X k ]/E[Y k ]. E. Ben-Sasson, P. Harsha, S. Raskhodnikova, 3CNF Properties are Hard to Test, SIAM Journal on Computing, 35(1):1-21, For a Boolean formula φ on n variables, the associated property P φ is the collection of n- bit strings that satisfy φ. We study the query complexity of tests that distinguish (with high probability) between strings in P φ and strings that are far from P φ in Hamming distance. We prove that there are 3CNF formulae (with O(n) clauses) such that testing for the associated property requires Ω(n) queries, even with adaptive tests. This contrasts with 2CNF formulae, whose associated properties are always testable with O( n) queries. Notice that for every negative instance (i.e., an assignment that does not satisfy φ) there are three bit queries that witness this fact. Nevertheless, finding such a short witness requires reading a constant fraction of the input, even when the input is very far from satisfying the formula that is associated with the property.

5 A property is linear if its elements form a linear space. We provide sufficient conditions for linear properties to be hard to test, and in the course of the proof include the following observations which are of independent interest: 1. In the context of testing for linear properties, adaptive two-sided error tests have no more power than nonadaptive one-sided error tests. Moreover, without loss of generality, any test for a linear property is a linear test. A linear test verifies that a portion of the input satisfies a set of linear constraints, which define the property, and rejects if and only if it finds a falsified constraint. A linear test is by definition nonadaptive and, when applied to linear properties, has a one-sided error. 2. Random low density parity check codes (which are known to have linear distance and constant rate) are not locally testable. In fact, testing such a code of length n requires Ω(n) queries. S. Raskhodnikova, Approximate Testing of Visual Properties, Proceedings of the 7 th RANDOM, We apply property testing to visual properties of images. Image analysis is potentially very well suited to the property testing paradigm. Image representations are typically very large, and slight modifications to the representation do not significantly affect the image. Some salient features of an image may be tested by examining only a small part thereof. Indeed, one motivation for this study is the observation that the eye focuses on relatively few places within an image during its analysis. The analogy is not perfect due to the eye s peripheral vision, but it suggests that property testing may give some insight into the visual system. We study visual properties of discretized images represented by matrices of binary pixel values. We obtain algorithms for several basic properties: being a half-plane, connectedness and convexity. All our algorithms have complexity independent of the image size, and therefore work well even for huge images. T. Batu, F. Ergun, J. Kilian, A. Magen, S. Raskhodnikova, R. Rubinfeld, and R. Sami, A Sublinear Algorithm for Weakly Approximating Edit Distance, Proceedings of the 35 th ACM STOC, We show how to determine in sublinear time whether the edit distance between two strings is small. Edit distance is the number of single character insertions, deletions and substitutions needed to transform one string into another. We present a sublinear algorithm that, given two strings of length n, accepts if the edit distance between the strings is O(n α ) and rejects with high probability if it is Ω(n), for any fixed α < 1. Our algorithm works by recursively subdividing the input strings into smaller substrings and looking for pairs of substrings with small edit distance. We query both strings at random places and use a special technique for recycling our samples so that the overall query complexity, as well as the running time, stays low. The test runs in time Õ(n max{ α 2,2α 1} ) for any fixed α < 1. Our algorithm is a first step for trading off accuracy for efficiency for edit distance computation. We also show that Ω(n α/2 ) queries are required to distinguish pairs of string with edit distance at most n α from those with edit distance at least n/6.

6 A. Andoni, M. Deza, A. Gupta, P. Indyk, and S. Raskhodnikova, Lower Bounds for Embedding of Edit Distance into Normed Spaces, Proceedings of the 14 th ACM-SIAM SODA, We present the first non-trivial lower bound for embedding the edit distance metric into l p norms. The edit distance between two strings is the minimum number of insertions, deletions and character substitutions needed to transform one string into another. Lowdistortion embeddings of this metric would allow us to adapt approximation algorithms for problems over better-understood metrics to work over edit distance. We show that this metric cannot be embedded into the square of the l 2 norm (with arbitrary dimension) with distortion better than 3/2. This implies the same lower bound for embedding into l 1. For the latter norm, we present another (much shorter) proof using hypermetric inequalities. We also show that for our approach, the factor 3/2 is tight, even for embeddings into the l 1 norm. We give some experimental evidence that the only known technique for obtaining super-constant lower bounds for embeddings into shortest path metrics over a graph showing that the graph is an expander is not applicable here. E. Fischer, E. Lehman, I. Newman, S. Raskhodnikova, R. Rubinfeld, and A. Samorodnitsky, Monotonicity Testing Over General Poset Domains, Proceedings of the 34 th ACM STOC, , We show that in its most general setting, testing that boolean functions are close to monotone is equivalent, with respect to the number of required queries, to several other testing problems in logic and graph theory. These problems include: testing that a boolean assignment of variables is close to an assignment that satisfies a specific 2CNF formula, testing that a set of vertices is close to one that is a vertex cover of a specific graph, and testing that a set of vertices is close to a clique. We then investigate the query complexity of monotonicity testing of both boolean and integer functions over general partial orders. We give algorithms and lower bounds for the general problem, as well as for some interesting special cases. In proving a general lower bound, we construct graphs with many edge-disjoint induced matchings of linear size. Y. Dodis, O. Goldreich, E. Lehman, S. Raskhodnikova, D. Ron, and A. Samorodnitsky, Improved Testing Algorithms for Monotonicity, Proceedings of the 3 rd RANDOM, , We present improved algorithms for testing monotonicity of functions f : Σ d A, where Σ and A are finite ordered sets. A function is monotone if increasing an input character does not decrease the output. For example, a function f : {1,..., n} A is monotone if f(1),..., f(n) are sorted. For any distance parameter ɛ, the query complexity of our test is O((d/ɛ) log Σ log A ). The previous best known bound was Õ((d 2 /ɛ) Σ 2 A ). For the boolean range (A = {0, 1}), we present an alternative test whose query complexity, O(d 2 /ɛ 2 ), is independent of the alphabet size Σ. S. Raskhodnikova, Monotonicity Testing, Master s Thesis,, Cambridge, MA, The thesis contains a more detailed exposition of the results in Improved Testing Algorithms for monotonicity.