Hybrid backtracking bounded by tree-decomposition of constraint networks

(No)good Recording and ROBDDs for Solving Structured (V)CSPs

“…Note that Tree-Clustering does not provide interesting results in practical cases. So, an alternative approach, called BTD and also based on tree-decomposition of graphs, was proposed in [13]. It seems to provide empirical results among the best ones obtained by structural methods.…”

“…Such a space complexity is an important drawback which surely explains why most of performed works remains theoretical. Indeed, except [13,10], no practical results have been provided. Even for implemented methods, the amount of required memory may be problematic.…”

“…Even for implemented methods, the amount of required memory may be problematic. For instance, the BTD method (for Backtracking with Tree-Decomposition [13]), which records structural goods and nogoods in hash tables, requires sometimes more memory than available for solving some instances. A priori, this memory problem is even more delicate for optimization problems modeled as Valued CSPs (VCSPs [19]).…”

An Extension of Complexity Bounds and Dynamic Heuristics for Tree-Decompositions of CSP

“…This paper deals with the question of an efficient use of the considered decompositions. We focus on the BTD method (Backtracking on tree-decomposition [5]) which seems to be the most effective method proposed until now within the framework of these structural methods. Indeed, most of works based on this approach only present theoretical results, except [6,5].…”

“…We focus on the BTD method (Backtracking on tree-decomposition [5]) which seems to be the most effective method proposed until now within the framework of these structural methods. Indeed, most of works based on this approach only present theoretical results, except [6,5]. BTD proceeds by an enumerative search guided by a static pre-established partial order induced by a tree-decomposition of the constraint graph.…”