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Efficient Techniques for Searching the Temporal CSP Lin Xu and Berthe Y. Choueiry

Efficient Techniques for Searching the Temporal CSP Lin Xu and Berthe Y. Choueiry Constraint Systems Laboratory Department of Computer Science and Engineering University of Nebraska-Lincoln { lxu | choueiry }@cse.unl.edu. Outline. Temporal networks Contributions Results

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Efficient Techniques for Searching the Temporal CSP Lin Xu and Berthe Y. Choueiry

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  1. Efficient Techniques for Searching the Temporal CSP Lin Xu and Berthe Y. Choueiry Constraint Systems Laboratory Department of Computer Science and Engineering University of Nebraska-Lincoln { lxu | choueiry }@cse.unl.edu

  2. Outline • Temporal networks • Contributions • Results • 2 order of magnitude improvement on TCSP

  3. Temporal networks • Simple Temporal Problem • Floyd-Warshall algorithm [Dean 85, Dechter et al. 91] • STP [Time 03] • Temporal Constraint Satisfaction Problem • Search + ULT [Schwalb & Dechter 97] • Our contribution [this talk, CP 03] • Disjunctive Temporal Problem • Search + heuristics [S&K 00, O&C 00, Tsa&P 03] • Some of our results are applicable

  4. Solving TCSP • TCSP is NP-hard, solved with BT [DM&P 91] • Contributions • Techniques that exploit structure • Show effectiveness of Articulation Points (AP) • NewCyc avoids unnecessary consistency checking • EdgeOrd is a variable ordering heuristic • Localized backtracking • Implicit decomposition according to Articulation Points (AP) • Combination with previous results • AC, a preprocessing step [this morning] • STP [Time 03] • Extensive evaluation on random problems

  5. TCSP as a meta-CSP • Preprocessing with AC reduces size of TCSP, especially for dense networks • Using STP solves individual STPs efficiently, especially for sparse networks •  requires triangulation: Plan A, Plan B

  6. New Cycle Check: NewCyc • Check presence of new cycles O(|E|) • Check consistency (STP) only in a cycle is added to the graph

  7. Advantages of NewCyc • Fewer consistency checking operations • Operations restricted to new bi-connected component • Does not affect # of nodes visited in search

  8. Edge Ordering in BT-TCSP

  9. EdgeOrd heuristic • Order edges using triangle adjacency • Priority list is a by product of triangulation

  10. Advantages of EdgeOrd • Localized backtracking • Automatic decomposition of the constraint graph  no need for explicit AP

  11. Experimental evaluations With/without: Explicit decomposition using AP,AC, STP, NewCyc, EdgeOrd

  12. Expected (direct) effects • Number of nodes visited (#NV) • AC reduces the size of TCSP • EdgeOrd localizes BT • Consistency checking effort (#CC) • AP, STP, NewCyc, reduce number of consistency checking at each node

  13. Effect of AC on #nodes visited

  14. Cumulative improvement Before, after AP, after NewCyc,… … and now (AC, STP, NewCyc, EdgeOrd) Max on y-axis 18.000, 2 orders of magnitude improvement Max on y-axis 5.000.000

  15. Future work • Investigate incremental triangulation for • dynamic edge-ordering • using NewCyc in Disjunctive Temporal Problem • Plan B, heuristic [G. Noubir], algorithm [A. Berry] • Test with dynamic bundling [AusJCAI 01, SARA 02]

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