Impact of Community Structure on SAT Solver Performance

Newsham, Zack; Ganesh, Vijay; Fischmeister, Sebastian; Audemard, Gilles; Simon, Laurent

doi:10.1007/978-3-319-09284-3_20

Cited by 53 publications

(58 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As was mentioned earlier, it has been found empirically that modularity correlates with CDCL performance [23]. This is a claim about the average behavior of CDCL over a wide variety of industrial benchmarks, not about its behavior on any specific instance.…”

Section: Sat and Community Structurementioning

confidence: 75%

On the Hardness of SAT with Community Structure

Mull

Fremont

Seshia

2016

Theory and Applications of Satisfiability Testing – SAT 2016

View full text Add to dashboard Cite

Abstract. Recent attempts to explain the effectiveness of Boolean satisfiability (SAT) solvers based on conflict-driven clause learning (CDCL) on large industrial benchmarks have focused on the concept of community structure. Specifically, industrial benchmarks have been empirically found to have good community structure, and experiments seem to show a correlation between such structure and the efficiency of CDCL. However, in this paper we establish hardness results suggesting that community structure is not sufficient to explain the success of CDCL in practice. First, we formally characterize a property shared by a wide class of metrics capturing community structure, including "modularity". Next, we show that the SAT instances with good community structure according to any metric with this property are still NP-hard. Finally, we study a class of random instances generated from the"pseudo-industrial" community attachment model of Giráldez-Cru and Levy. We prove that, with high probability, instances from this model that have relatively few communities but are still highly modular require exponentially long resolution proofs and so are hard for CDCL. We also present experimental evidence that our result continues to hold for instances with many more communities. This indicates that actual industrial instances easily solved by CDCL may have some other relevant structure not captured by the community attachment model.

show abstract

Section: Sat and Community Structurementioning

confidence: 75%

On the Hardness of SAT with Community Structure

Mull

Fremont

Seshia

2016

Theory and Applications of Satisfiability Testing – SAT 2016

View full text Add to dashboard Cite

show abstract

“…Community structure is a property exhibited in many real-world graphs, particularly in social networks, where the graph can be partitioned into groups of vertices, called communities, such that each group is densely connected within itself but sparsely connected with other groups. Recent research has shown that the community structure quality of the SAT input correlates with faster solving time [38]. We show that bridge variables connecting distinct communities in the community structure of a SAT instance [21] are high priority targets for both the branching heuristic and clause-learning, which suggests one possible explanation for this correlation.…”

Section: Introductionmentioning

confidence: 63%

Understanding VSIDS Branching Heuristics in Conflict-Driven Clause-Learning SAT Solvers

Jia

Zulkoski

Zaman

et al. 2015

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Conflict-Driven Clause-Learning (CDCL) SAT solvers crucially depend on the Variable State Independent Decaying Sum (VSIDS) branching heuristic for their performance. Although VSIDS was proposed nearly fifteen years ago, and many other branching heuristics for SAT solving have since been proposed, VSIDS remains one of the most effective branching heuristics. Despite its widespread use and repeated attempts to understand it, this additive bumping and multiplicative decay branching heuristic has remained an enigma. In this paper, we advance our understanding of VSIDS by answering the following key questions. The first question we pose is "what is special about the class of variables that VSIDS chooses to additively bump?" In answering this question we showed that VSIDS overwhelmingly picks, bumps, and learns bridge variables, defined as the variables that connect distinct communities in the community structure of SAT instances. This is surprising since VSIDS was invented more than a decade before the link between community structure and SAT solver performance was discovered. Additionally, we show that VSIDS viewed as a ranking function correlates strongly with temporal graph centrality measures. Putting these two findings together, we conclude that VSIDS picks high-centrality bridge variables. The second question we pose is "what role does multiplicative decay play in making VSIDS so effective?" We show that the multiplicative decay behaves like an exponential moving average (EMA) that favors variables that persistently occur in conflicts (the signal) over variables that occur intermittently (the noise). The third question we pose is "whether VSIDS is temporally and spatially focused." We show that VSIDS disproportionately picks variables from a few communities unlike, say, the random branching heuristic. We put these findings together to invent a new adaptive VSIDS branching heuristic that solves more instances than one of the best-known VSIDS variants over the SAT Competition 2013 benchmarks.

show abstract

“…The variables inside a community have strong relations, but the relations among the variables in different communities are much weaker [1]. In [9], it is shown that LBD can be strongly related to the community structure of the initial formula, which explains why clauses with smaller LBD are more probably used in unit propagations.…”

Section: Lbd: a Measure Of The Usefulness Of A Learnt Clausementioning

confidence: 96%

On Reducing Clause DataBase in Glucose

Li¹,

Fan²,

Xu³

EPiC Series in Computing

View full text Add to dashboard Cite

Modern CDCL SAT solvers generally save the variable value when backtracking. We present a measure called nbSAT based on the saved assignment to predict the usefulness of a learnt clause when reducing clause database in Glucose 3.0. Roughly speaking, the nbSAT value of a learnt clause is equal to the number of literals satisfied by the current partial assignment plus the number of other literals that would be satisfied by the saved assignment. The nbSAT measure is similar to a previous measure called psm which is not implemented in Glucose 3.0. We study the nbSAT measure by empirically showing that it may be more accurate than the LBD measure originally used in Glucose. Based on this study, we implement an improvement in Glucose 3.0 to remove half of learnt clauses with large nbSAT values instead of half of clauses with large LBD values. This improvement, together with a resolution method to keep the learnt clauses or resolvents produced using a learnt clause that subsume an original clause, makes Glucose 3.0 more effective for the application and hard combinatorial instances from the SAT 2014 competition.

show abstract

Impact of Community Structure on SAT Solver Performance

Cited by 53 publications

References 8 publications

On the Hardness of SAT with Community Structure

On the Hardness of SAT with Community Structure

Understanding VSIDS Branching Heuristics in Conflict-Driven Clause-Learning SAT Solvers

On Reducing Clause DataBase in Glucose

Contact Info

Product

Resources

About