Robust Weighted Partial Maximum Satisfiability Problem: Challenge to Σ2P -Complete Problem

Tomoya Sugahara, Kaito Yamashita, Nathanaël Barrot, Miyuki Koshimura, Makoto Yokoo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper introduces a new problem called the Robust Maximum Satisfiability problem (R-MaxSAT), as well as its extension called the Robust weighted Partial MaxSAT (R-PMaxSAT). In R-MaxSAT (or R-PMaxSAT), a problem solver called defender hopes to maximize the number of satisfied clauses (or the sum of their weights) as the standard MaxSAT/partial MaxSAT problem, although she must ensure that the obtained solution is robust (In this paper, we use the pronoun “she” for the defender and “he” for the attacker). We assume an adversary called the attacker will flip some variables after the defender selects a solution. R-PMaxSAT can formalize the robust Clique Partitioning Problem (robust CPP), where CPP has many real-life applications. We first demonstrate that the decision version of R-MaxSAT is Σ2P -complete. Then, we develop two algorithms to solve R-PMaxSAT, by utilizing a state-of-the-art SAT solver or a Quantified Boolean Formula (QBF) solver as a subroutine. Our experimental results show that we can obtain optimal solutions within a reasonable amount of time for randomly generated R-MaxSAT instances with 30 variables and 150 clauses (within 40 s) and R-PMaxSAT instances based on CPP benchmark problems with 60 vertices (within 500 s).

Original languageEnglish
Title of host publicationPRICAI 2022
Subtitle of host publicationTrends in Artificial Intelligence - 19th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2022, Proceedings
EditorsSankalp Khanna, Jian Cao, Quan Bai, Guandong Xu
PublisherSpringer Science and Business Media Deutschland GmbH
Pages17-31
Number of pages15
ISBN (Print)9783031208614
DOIs
Publication statusPublished - 2022
Event19th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2022 - Shangai, China
Duration: Nov 10 2022Nov 13 2022

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13629 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th Pacific Rim International Conference on Artificial Intelligence, PRICAI 2022
Country/TerritoryChina
CityShangai
Period11/10/2211/13/22

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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