Fast compilation of graph substructures for counting and enumeration

Abstract

In this paper, we propose a new compilation method called merging frontier-based search for s–t simple paths on a graph. Recently, Nishino et al. proposed a top-down construction algorithm, which compiles s–t simple paths into a zero-suppressed SDD (ZSDD), and they showed that this method is more efficient than simpath by Knuth. However, since the method of Nishino et al. uses ZSDD as a tractable representation, it requires complicated steps for compilation. In this paper, we propose structured Z-d-DNNF, which is a super set of ZSDD. Though this representation relaxed the restriction of ZSDD, it supports important queries like model counting and model enumeration. Using this representation instead of ZSDD, we show that more efficient compilation can be realized for s–t simple paths.