DPO: Dynamic-Programming Optimization on Hybrid Constraints

Abstract

In Bayesian inference, the most probable explanation (MPE) problem requests a variable instantiation with the highest probability given some evidence. Since a Bayesian network can be encoded as a literal-weighted CNF formula ϕ, we study Boolean MPE, a more general problem that requests a model τ of ϕ with the highest weight, where the weight of τ is the product of weights of literals satisfied by τ . It is known that Boolean MPE can be solved via reduction to (weighted partial) MaxSAT. Recent work proposed DPMC, a dynamic-programming model counter that leverages graph-decomposition techniques to construct project-join trees. A project-join tree is an execution plan that specifies how to conjoin clauses and project out variables. We build on DPMC and introduce DPO, a dynamic-programming optimizer that exactly solves Boolean MPE. By using algebraic decision diagrams (ADDs) to represent pseudo-Boolean (PB) functions, DPO is able to handle disjunctive clauses as well as XOR clauses. (Cardinality constraints and PB constraints may also be compactly represented by ADDs, so one can further extend DPO's support for hybrid inputs.) To test the competitiveness of DPO, we generate random XOR-CNF formulas. On these hybrid benchmarks, DPO significantly outperforms MaxHS, UWrMaxSat, and GaussMaxHS, which are state-of-the-art exact solvers for MaxSAT.

DPER: Dynamic Programming for Exist-Random Stochastic SAT

“…We introduce DPER, an exact ER-SSAT solver that employs dynamic programming on graded project-join trees, based on a WPMC solver [Dudek et al, 2021]. DPER also adapts an iterative procedure to find maximizers from MaxSAT [Kyrillidis et al, 2022] and Boolean MPE [Phan and Vardi, 2022]. Our experiments show that DPER contributes to the portfolio of state-of-the-art ER-SSAT solvers (DC-SSAT [Majercik and Boots, 2005] and erSSAT [Lee et al, 2018]) through competitiveness on low-width instances.…”

“…To find maximizers for ER-SSAT, we leverage the following idea, which originated from the basic algorithm for PB programming [Crama et al, 1990] then was adapted for MaxSAT [Kyrillidis et al, 2022] and Boolean MPE [Phan and Vardi, 2022].…”

“…Here, we build on the approach of ProCount to develop an exact solver for ER-SSAT. To find a maximizing truth assignment (maximizer) for ER-SSAT, we leverage an iterative technique that was recently proposed to solve maximum satisfiability (MaxSAT) [Kyrillidis et al, 2022] and Boolean MPE [Phan and Vardi, 2022]. MaxSAT is an optimization version of SAT and requests a truth assignment that maximizes the number of satisfied clauses of an unsatisfiable CNF formula [Krentel, 1988].…”

“…MaxSAT is an optimization version of SAT and requests a truth assignment that maximizes the number of satisfied clauses of an unsatisfiable CNF formula [Krentel, 1988]. By building on techniques from WPMC [Dudek et al, 2021], Boolean MPE [Phan and Vardi, 2022], and MaxSAT [Kyrillidis et al, 2022], we construct DPER, a dynamic-programming ER-SSAT framework. We then compare DPER to state-of-the-art solvers (DC-SSAT [Majercik and Boots, 2005] and erSSAT [Lee et al, 2018]).…”