A. Baker. Intelligent backtracking on the hardest constraint problems. Journal of Articial Intelligence Research, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....when checking the K consistency of an assignment. As we said in Section 4, in all the tests we have set sat GH as to jar.tex; 31 08 1999; 11:10; p.27 28 E. Giunchiglia, F. Giunchiglia and A. Tacchella use the early pruning strategy. Dlp GH instead implements a backjumping schema in the spirit of (Baker, 1995): when an assignment is discovered to be not K consistent, backtracking to a point which does not lead to the same contradiction is enforced. While implementing early pruning does not introduce overheads, this is not the case for backjumping, where a dependency set of each derived clause has to be ....

A. Baker. Intelligent backtracking on the hardest constraint problems. Journal of Articial Intelligence Research, 1995.

....since any subproblem created by further variable instantiations within the insoluble subproblem is also insoluble, FC CBJ does sometimes manage to jump straight out of subsubproblems that FC spends a very long time on. This can be the case even when the original subproblem is arc consistent. Baker [1] suggests that all exceptionally hard problems can be defeated by a search strategy which uses a sufficiently intelligent backtracker. He presents experiments on graph colouring problems using dependency directed backtracking, which records all the nogoods it discovers during search and uses these ....

A. B. Baker. Intelligent Backtracking on the Hardest Constraint Problems. Technical report, CIRL, University of Oregon, Feb. 1995.

....problems are consistently hard to solve due to subtle interactions between constraints. Under constrained problems on the other hand, while generally easy to solve, can also prove extremely difficult in a small number of cases due to a phenomenon called thrashing [ Gent and Walsh, 1996; Baker, 1996 ] Thrashing occurs when the order in which nondeterministic constraints are expanded results in large amounts of unproductive backtracking. This problem is exaggerated in tableaux algorithms as inherent unsatisfiability caused by a disjunctive expansion choice may be concealed in a sub problem ....

....performed by recursively testing satisfiability with the chosen term added as a positive or negated constraint the heuristic also determines in which order the two possibilities are explored. 4. 3 Intelligent backtracking The thrashing problem can be addressed by using a form of backjumping [ Baker, 1996; Ginsberg, 1993 ] to return rapidly to a branching point where a different choice could remove the source of the conflict. In backjumping constraints are labeled to indicate the disjunctive expansion choices from which they were derived. The initial x : C constraint is labeled f0g, a constraint ....

A. B. Baker. Intelligent backtracking in the hardest constraint problems. Journal of Artificial Intelligence Research, 1996. To appear.

....the mean cost; it is for this reason that authors reporting phase transition behaviour have often used the median rather than the mean as a measure of average difficulty. To date no complete 1 search method has been shown to be completely immune from ehps, although studies of various algorithms [40, 41, 7, 1] have shown that their incidence and magnitude varies greatly between search methods. It is clearly important, therefore, to consider relative ehp behaviour when comparing algorithm performance. 1 To date, no exceptionally hard soluble problems have been reported in studies of incomplete local ....

....higher level of consistency could be maintained during search, while more elaborate backjumping algorithms have been described. Although maintaining a higher level of consistency would very likely further reduce ehp incidence, the probable overheads involved would be prohibitively expensive. Baker [1] suggests that all exceptionally hard problems can be eliminated by a search strategy employing a sufficiently intelligent backtracker, and presents experiments using dependency directed backtracking [18] which records nogoods during search. However, Baker admits that this algorithm has an ....

A. B. Baker. Intelligent backtracking on the hardest constraint problems. Technical report, CIRL and DCIS, University of Oregon, United States, 1995.

....choice led immediately to a solution. Based on the same idea, Bayardo and Schrag [2] show how to create exceptionally hard satisfiability problems by embedding an insoluble subproblem within a larger problem: in this case, the overall problem is unsatisfiable. In 3 colouring problems, Baker [1] similarly points out that a backtracking algorithm can find an algorithm exceptionally hard if the graph is disconnected and the algorithm attempts to assign colours last to a component which has no solutions. He claims that similar behaviour can also occur in soluble problems, but presents ....

....of FC and CBJ encountered far fewer ehps than FC by itself, but they did still occur. We suggested that this happens when either the proof of arc inconsistency in the subproblem is complex or a higher level of inconsistency is involved: CBJ cannot then jump out of the subproblem. Even so, Baker [1] suggests, based on experiments with graph colouring problems, that a sufficiently intelligent backtracker will avoid ehps altogether. Hence, in random binary CSPs, there are a number of available strategies for avoiding the insoluble subproblems occurring in ehps: looking ahead to detect the ....

A. B. Baker. Intelligent Backtracking on the Hardest Constraint Problems. Technical report, CIRL, University of Oregon, Feb. 1995.

....Somewhere in the middle is the crossover point at which half of the problems are solvable and half are unsolvable. One important lesson is that the transition from the underconstrained region to the overconstrained region is often very abrupt [13, 15, 23] 1 This chapter is a revised version of [6]. CHAPTER 2. BACKTRACKING ON THE HARDEST PROBLEMS 24 For sufficiently large problems, increasing the number of constraints by even a few percent will drastically reduce the probability of there being a solution. The second important lesson concerns the difficulty of the problems for a search ....

Andrew B. Baker. Intelligent backtracking on the hardest constraint problems. Journal of Artificial Intelligence Research, 1995. To appear.

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