efficient techniques for searching the temporal csp lin xu and berthe y. choueiry
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
Temporal networksSimple Temporal Problem• Floyd-Warshall algorithm [Dean 85, Dechter et al. 91]
• STP [Time 03]
Disjunctive Temporal Problem• Search + heuristics [S&K 00, O&C 00, Tsa&P 03]
• Some of our results are applicable
Temporal Constraint Satisfaction Problem• Search + ULT [Schwalb & Dechter 97]
• Our contribution [this talk, CP 03]
Solving TCSP TCSP is NP-hard, solved with BT [DM&P 91]
Contributions1. 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)
2. Combination with previous results – AC, a preprocessing step [this morning]
– STP [Time 03]
3. Extensive evaluation on random problems
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
New Cycle Check: NewCyc
Check presence of new cycles O(|E|) Check consistency (STP) only in a cycle is
added to the graph
Advantages of NewCyc Fewer consistency checking operations Operations restricted to new bi-connected
component
Does not affect # of nodes visited in search
EdgeOrd heuristic
Order edges using triangle adjacency Priority list is a by product of triangulation
Advantages of EdgeOrd Localized backtracking Automatic decomposition of the constraint graph
no need for explicit AP
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
Cumulative improvementBefore, after AP, after NewCyc,… … and now (AC, STP, NewCyc, EdgeOrd)
Max on y-axis 5.000.000 Max on y-axis 18.000, 2 orders of magnitude improvement