Year: 2012
Type: preprint
Abstract: The complexity of a reasoning task over a graphical model is tied to the induced width of the underlying graph. It is well-known that the conditioning (assigning values) on a subset of variables yields a subproblem of the reduced complexity where instantiated variables are removed. If the assigned variables constitute a cycle-cutset, the rest of the network is singly-connected and therefore can be solved by linear propagation algorithms. A w-cutset is a generalization of a cycle-cutset defined as a subset of nodes such that the subgraph with cutset nodes removed has induced-width of w or less. In this paper we address the problem of finding a minimal w-cutset in a graph. We relate the problem to that of finding the minimal w-cutset of a treedecomposition. The latter can be mapped to the well-known set multi-cover problem. This relationship yields a proof of NP-completeness on one hand and a greedy algorithm for finding a w-cutset of a tree decomposition on the other. Empirical evaluation of the algorithms is presented.
Source: arXiv (Cornell University)
Authors: Bidyuk, Bozhena, Dechter, Rina
Institution: University of California, Irvine
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1846676416