TY - JOUR
T1 - GO-MOCE
T2 - Greedy Order Method of Conditional Expectations for Max Sat
AU - Berend, Daniel
AU - Golan, Shahar
AU - Twitto, Yochai
N1 - Funding Information:
This research was partially supported by the Milken Families Foundation Chair in Mathematics, by the Lynne and William Frankel Foundation for Computer Science, and by the Israeli Council for Higher Education (CHE) via the Data Science Research Center, Ben-Gurion University of the Negev.
Publisher Copyright:
© 2022 Elsevier B.V.
PY - 2022/2/1
Y1 - 2022/2/1
N2 - In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson's Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS. We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%. We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.
AB - In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson's Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS. We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%. We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.
KW - Analysis of algorithms
KW - Combinatorial Optimization
KW - Maximum Satisfiability
KW - Probabilistic algorithms
KW - The Method of Conditional Expectations
UR - http://www.scopus.com/inward/record.url?scp=85124250743&partnerID=8YFLogxK
U2 - 10.1016/j.disopt.2022.100685
DO - 10.1016/j.disopt.2022.100685
M3 - Article
AN - SCOPUS:85124250743
SN - 1572-5286
VL - 43
JO - Discrete Optimization
JF - Discrete Optimization
M1 - 100685
ER -