AND/OR search spaces and the semantic width of constraint networks

Abstract

The primary contribution of this paper consists in using the AND/OR search paradigm [1,2] to define the new concept of semantic width of a constraint network. The well known parameter tree-width is graph based, and cannot capture context sensitive information. This often results in a very loose upper bound on the actual complexity of the problem. A typical example is the compact result of a compilation schemes such as ordered binary decision diagram (OBDD), in spite of a large tree-width (and path-width). The semantic width is based on the notion of equivalent constraint networks. The idea is to capture the intrinsic hardness of a problem by the smallest width equivalent network. This paper specializes the AND/OR formalism to constraint networks and elaborates the properties of AND/OR search graphs. The semantic width characterizes the size of the minimal AND/OR graph and it is clearly hard to compute. Nevertheless, the semantic width can explain why sometimes the minimal AND/OR graph or tree are much smaller than the upper bounds exponential in tree-width or path-width. © Springer-Verlag Berlin Heidelberg 2005.