Using Recursive Decomposition to Construct Elimination Orders, Jointrees, and Dtrees

Abstract

Darwiche has recently proposed a graphical model for driving conditioning algorithms, called a dtree, which specifies a recursive decomposition of a directed acyclic graph (DAG) into its families. A main property of a dtree is its width, and it was shown previously how to convert a DAG elimination order of width w into a dtree of width ≤ w. The importance of this conversion is that any algorithm for constructing low-width elimination orders can be directly used for constructing low-width dtrees. We propose in this paper a more direct method for constructing dtrees based on hypergraph partitioning. This new method turns out to be quite competitive with existing methods in minimizing width. We also present methods for converting a dtree of width w into elimination orders and jointrees of no greater width. This leads to a new class of algorithms for generating elimination orders and jointrees (via recursive decomposition).