In the Stone Age. Stephan Holzer. Yuval Emek - Technion Roger Wattenhofer - ETH Zürich

Transcription

1 The Power of a Leader In the Stone Age - MIT Yuval Emek - Technion Roger Wattenhofer - ETH Zürich 2nd Workshop on Biological Distributed Algorithms, October 11-12, 2014 in Austin, Texas USA

2 The Power of a Leader In the Stone Age - MIT Yuval Emek - Technion Roger Wattenhofer - ETH Zürich 2nd Workshop on Biological Distributed Algorithms, October 11-12, 2014 in Austin, Texas USA

3 Stone Age Model of Distributed Computing

4 Computational Power of a Cell?

5 Computational Power of a Cell? Finite State Machine

6 Communication?

7 Communication? Transmissions: Same message delivered to all neighbors Constant size message Port for each neighbor Stores the last message delivered

8 Communication? Transmissions: Same message delivered to all neighbors Constant size message Port for each neighbor Stores the last message delivered Can detect if 0, 1 or 2+ ports store message m FSM changes state based on this sends message based on state

9 Stone Age Model of Distributed Computing All nodes run the same FSM (random) Anonymous Weak communication Fully asynchronous Arbitrary network topology (unknown) All features of the protocol are constant!

10 What is known? Can be synchronized Cannot elect a leader Cannot compute shortest paths No Minimum Spanning Tree or Diameter Edsger W. Dijkstra: Actually: I CAN COMPUTE SHORTEST PATHS!

11 Edsger W. Dijkstra: Actually: I CAN COMPUTE SHORTEST PATHS! Actually: Me too! (The slime mold)

12 Physarum polycephalum Nuclei are nodes Tubes / plasma are edges?

13 Computes the Shortest Path Video can be found at:

14 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation E.g. select unique node at random

15 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

16 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

17 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

18 Select Unique Node at Random REPEAT: 1. select Wait: random neighbor Transmissions: 2. Pr[choose yourself]=1/2 - Same message delivered to all neighbors lea der Solution: - Wait until there is a neighbor in a unique state among the neighbors - Detect this via ports - Transmit content of this port

19 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

20 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

21 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

22 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

23 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

24 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

25 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

26 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

27 Select Unique Node at Random REPEAT: 1. select random neighbor 2. Pr[choose yourself]=1/2 lea der

28 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property

29 Check if all nodes up to a certain distance have a certain property Determines the distance (here: 2) lea der

30 Check if all nodes up to a certain distance have a certain property Determines the distance (here: 2) lea der v

31 Check if all nodes up to a certain distance have a certain property Use ping to check properties Determines the distance (here: 2) lea der v

32 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property

33 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property (works for subsets as well)

34 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property (works for subsets as well) Iterate through all nodes (for v V do TASK)

35 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

36 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

37 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

38 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

39 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

40 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

41 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

42 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

43 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

44 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

45 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

46 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

47 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

48 Iterate through all nodes (for v V do) v max leader; while not all nodes at distance dist(leader,v max )+1 are marked do select random node u; // u marks itself if dist(leader,u) > dist(leader, v max ) then v max u; u performs TASK;

49 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property (works for subsets as well) Iterate through all nodes (for u V do TASK)

50 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property (works for subsets as well) Iterate through all nodes (for u V do TASK) Decide dist(u,v) > dist(u,v )

51 Decide dist(u,v) > dist(u,v ) u u Perform BFS v v

52 Decide dist(u,v) > dist(u,v ) u u lea der Acts as synchronizer Perform BFS v v

53 Decide dist(u,v) > dist(u,v ) u u lea der Acts as synchronizer Perform BFS v v

54 Decide dist(u,v) > dist(u,v ) u u lea der Acts as synchronizer Perform BFS v v

55 Decide dist(u,v) > dist(u,v ) u u lea der Acts as synchronizer Perform BFS v v

56 Decide dist(u,v) > dist(u,v ) u u lea der Acts as synchronizer Perform BFS v v

57 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property (works for subsets as well) Iterate through all nodes (for u V do TASK) Decide dist(u,v) > dist(u,v )

58 How a Leader can make a Difference! Symmetry is broken Can coordinate global computation Select unique node at random Check if all nodes up to a certain distance have a certain property (works for subsets as well) Iterate through all nodes (for u V do TASK) Decide dist(u,v) > dist(u,v ) Constant combination of all these

59 Shortest Path INPUT: nodes u,v (assume v is leader) While u v do u marks itself to be on the shortest path for each neighbor w of u do if dist w, v < dist(u, v) then u w; OUTPUT: marked nodes

60 Shortest Path Example:

61 Shortest Path Example:

62 Shortest Path Example:

63 Shortest Path Example:

64 Shortest Path Example:

65 Shortest Path Example:

66 Shortest Path Example:

67 Shortest Path Example:

68 Shortest Path Example:

69 Shortest Path Example:

70 Different Model for the Slime Mold? Keep algorithms simple How does communication work? Strength of flow through tubes indicates length. We assume additional communication through tubes/plasma. Communicate through moving nuclei? Nuclei: How long do they live? Robustness? Do they move? How many are there? Do they communicate / process information?

71 Note These are possibility results - which weak assumptions work - which don t

72 Thanks!