A sufficient condition for backtrack-bounded search

Authors:
Eugene C. Freuder
Affiliations:
Univ. of New Hampshire, Durham
Venue:
Journal of the ACM (JACM)
Year:
1985

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Abstract

Backtrack search is often used to solve constraint satisfaction problems. A relationship involving the structure of the constraints is described that provides a bound on the backtracking required to advance deeper into the backtrack tree. This analysis leads to upper bounds on the effort required for solution of a class of constraint satisfaction problems. The solutions involve a combination of relaxation preprocessing and backtrack search. The bounds are expressed in terms of the structure of the constraint connections. Specifically, the effort is shown to have a bound exponential in the size of the largest biconnected component of the constraint graph, as opposed to the size of the graph as a whole.