All roads lead to Rome---New search methods for the optimal triangulation problem
International Journal of Approximate Reasoning
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We demonstrate that certain large-clique graph triangulations can be useful for reducing computational requirements when making queries on mixed stochastic/deterministic graphical models. This is counter to the conventional wisdom that triangulations that minimize clique size are always most desirable for use in computing queries on graphical models. Many of these large-clique triangulations are non-minimal and are thus unattainable via the popular elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs needs to be considered when searching for state space optimal triangulations in such graphs. Empirical results on random and real world graphs are given. We also present an algorithm and correctness proof for determining if a triangulation can be obtained via elimination, and we show that the decision problem associated with finding optimal state space triangulations in this mixed setting is NP-complete.