1 / 37

Dynamic Ordering for Asynchronous Backtracking on DisCSPs

Dynamic Ordering for Asynchronous Backtracking on DisCSPs. Roie Zivan and Amnon Meisels Dept. of Computer Science Ben-Gurion University. A Distributed Constraint Network. Agents’ local network. V 1. [0,1,2,3]. V 6. V 4. [0,1]. [0,1,2]. Agent 1. A “realistic” example.

iwanda
Download Presentation

Dynamic Ordering for Asynchronous Backtracking on DisCSPs

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Dynamic Ordering for Asynchronous Backtracking on DisCSPs Roie Zivan and Amnon Meisels Dept. of Computer Science Ben-Gurion University

  2. A Distributed Constraint Network Dynm Ordr ABT - CP-2005

  3. Agents’ local network V1 [0,1,2,3] V6 V4 [0,1] [0,1,2] Agent1 Dynm Ordr ABT - CP-2005

  4. A “realistic” example • Two wards in a Hospital. • Nurses – ward 1: Dina, Ela, Flora ward 2: Aviva, Bila, Gila • Aviva, Bila, Dina are ‘Senior’ nurses. • In every shift there should be at least one senior nurse. Local Constraint Inter Constraint One senior nurse S1 S1 S2 S2 S3 S3 First ward Second ward Dynm Ordr ABT - CP-2005

  5. Solving DisCSPs A2 A1 V1 = 2 V2 = ? Dynm Ordr ABT - CP-2005

  6. Sequential (synchronous) BT An A2 A3 An-1 A1 [V1=2],[V2=1],[V3=?]… Current Partial Assignment (CPA) Dynm Ordr ABT - CP-2005

  7. Asynchronous Backtracking Motivation: Concurrent computation. Highlights: • Agents always hold an assignment which is consistent with their view of the system. • On backtrack operations, agents change their views by eliminating inconsistent values. Dynm Ordr ABT - CP-2005

  8. Asynchronous Backtracking Simplifying Assumptions: • Each agent holds exactly one variable • Every agent can send messages to any other agent Dynm Ordr ABT - CP-2005

  9. Asynchronous Backtrack (ABT) A3 A2 A1 [A3=1] A4 [A1=2] Dynm Ordr ABT - CP-2005

  10. Backtrack in ABT AgentView of Agent A4: A1=2, A3=1 Nogood Current Assignment A3 A1=2, A3=1 A4=1 Dynm Ordr ABT - CP-2005

  11. Backtracking generates links A3 A2 A1 A4 [A1=2], [A3=1] Dynm Ordr ABT - CP-2005

  12. ABT – Strong Assumption All Agents are ordered by afixed order of Priorities [Yokoo 92-2000] [BesBrMes 2001 – 2005] [Hammadi 98 – 2002] [Gomez et. al 2002 – 2005] Dynm Ordr ABT - CP-2005

  13. Motivation for dynamic reordering Results of recent studies of sequential assigning algorithms for DisCSPs: Nguyen & Faltings 2004 Brito & Meseguer 2004 Dynm Ordr ABT - CP-2005

  14. Why is it a problem? [1] [1] V1 ≠ V2 V1 ≠ V2 A2 A1 V1 = 1 Dynm Ordr ABT - CP-2005

  15. A2 A1 V1 = 1 Why is it a problem? [1] [1] V1 ≠ V2 V1 ≠ V2 Dynm Ordr ABT - CP-2005

  16. Why is it a problem? [1] [1] V1 ≠ V2 V1 ≠ V2 A1 A2 V1 = 1 V2 = 1 Dynm Ordr ABT - CP-2005

  17. A2 A1 V2 = 1 Why is it a problem? [1] [1] V1 ≠ V2 V1 ≠ V2 V1 = 1 Dynm Ordr ABT - CP-2005

  18. A2 A1 Dynamic ordering can be a problem [1] [1] V1 ≠ V2 V1 ≠ V2 V2 = 1 V1 = 1 Dynm Ordr ABT - CP-2005

  19. Reordering Asynchronous Backtracking • Asynchronous Weak Commitment - AWC [Yokoo 95 - 2000] (exponential space) • Hybridizing ABT and AWC into a polynomial space, complete protocol. [Silaghi and Faltings 2001] (complex algorithm with unrewarding results) Dynm Ordr ABT - CP-2005

  20. Reordering – in standard backtracking 1 2 3 4 Dynm Ordr ABT - CP-2005

  21. Reordering – sequential assignments algorithms 1 2 3 4 4 3 Dynm Ordr ABT - CP-2005

  22. Reordering – sequential assignments algorithms 1 2 4 3 4 2 4 3 3 Dynm Ordr ABT - CP-2005

  23. Reordering – standard backtracking Highlights: • Moving forward - choose a desirable order • Backtracking is done in the same order as the forward moves Same idea can be applied in Asynchronous Backtracking Dynm Ordr ABT - CP-2005

  24. Ordering Rules for Agents in ABT • Change order only when changing assignment • Enforce reordering only on Agents with lower priority Dynm Ordr ABT - CP-2005

  25. ABT with Dynamic Ordering [A1,2],[A2,1], [A4,1] A1,A3,A2,A4 A3 ≠ 1 A3 = 1 Dynm Ordr ABT - CP-2005

  26. ABT with Dynamic Ordering [A1,2],[A2,1], [A4,1] A1,A3,A2,A4 A1,A3,A4,A2 A3 = 2 A1,A3,A4,A2 A3 = 2 Dynm Ordr ABT - CP-2005

  27. Which order is most up-to-date? Time-Stamping method of Nguyen & Faltings 2004: • Each order is time-stamped • A time-stamp is an array of integers of size n, all initialized to 0 • Each agent that assigns its variable, updates the time-stamp as follows: • Counters of higher priority agents are untouched • The counter of the assigning agent is incremented by 1 • The counters of lower priority agents are set to zero • Time-stamps are compared lexicographically Dynm Ordr ABT - CP-2005

  28. ABT with Dynamic Ordering [A1,1],[A3,1],[A2,3],[A4,2] A3 ≠ 1 A3 = 1 Dynm Ordr ABT - CP-2005

  29. ABT with Dynamic Ordering [A1,1],[A3,1],[A2,3],[A4,2] [A1,1],[A3,1],[A2,3],[A4,2] [A1,1],[A3,1],[A4,2],[A2,3] [A1,1],[A3,2],[A4,0],[A2,0] [A1,1],[A3,1],[A2,3],[A4,2] A3 = 2 Dynm Ordr ABT - CP-2005

  30. Choosing the right heuristic • Heuristics that work well for sequential assignment algorithms fail for ABT_DO (min-domain) • After each change of order, relevant Nogoodsare discarded • Nogood-triggered heuristic [Ginsberg-93] • Agent changes its current order only when it receives a Nogood which causes an assignment change • The Nogood sender is moved to a place immediately following that of the assigning agent • The only agent that moves up has no conflicts with newly formed lower priority agents  few Nogoods are removed Dynm Ordr ABT - CP-2005

  31. ABT_DO - Different Heuristics(20 Agents p1 = 0.4) Dynm Ordr ABT - CP-2005

  32. ABT_DO - Different Heuristics(20 Agents p1 = 0.4) Dynm Ordr ABT - CP-2005

  33. ABT_DO - Different Heuristics(20 Agents p1 = 0.7) Dynm Ordr ABT - CP-2005

  34. ABT_DO - Different Heuristics(20 Agents p1 = 0.7) Dynm Ordr ABT - CP-2005

  35. Nogoods removed by Different Heuristics( p1 = 0.4) Dynm Ordr ABT - CP-2005

  36. Nogoods removed by Different Heuristics(p1 = 0.7) Dynm Ordr ABT - CP-2005

  37. Conclusions • Dynamic Variable/Agent reordering is a powerful tool in CSP solving algorithms • Most previous studies of asynchronous backtracking used a fixed order of agents • Dynamic reordering for ABT with polynomial space can be achieved and implemented • The heuristic must take into consideration the loss of valid Nogoods • A Nogood-triggered heuristic, avoids Nogoods loss and improves the performance by a large factor • Number of messages decreases also Dynm Ordr ABT - CP-2005

More Related