Certifying Solvers for Clique and Maximum Common (Connected) Subgraph Problems

Gocht, Stephan; McBride, Ross; McCreesh, Ciaran; Nordström, Jakob; Prosser, Patrick; Trimble, James

doi:10.1007/978-3-030-58475-7_20

Cited by 15 publications

(20 citation statements)

References 60 publications

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“…Only algorithms that show a significant improvement over state‐of‐the‐art get to be published in the top CO journals. In addition, it has been argued that exact algorithms should also be certifying , that is, provide an easily verifiable proof that the solution is correct (Gocht et al., 2020).…”

Section: Discussionmentioning

confidence: 99%

Research trends in combinatorial optimization

Weinand

Sörensen

Segundo

et al. 2021

Int Trans Operational Res

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Real‐world problems are becoming highly complex and therefore have to be solved with combinatorial optimization (CO) techniques. Motivated by the strong increase in publications on CO, 8393 articles from this research field are subjected to a bibliometric analysis. The corpus of literature is examined using mathematical methods and a novel algorithm for keyword analysis. In addition to the most relevant countries, organizations, and authors as well as their collaborations, the most pertinent CO problems, solution methods, and application areas are presented. Publications on CO focus mainly on the development or enhancement of metaheuristics like genetic algorithms. The increasingly problem‐oriented studies deal particularly with real‐world applications within the energy sector, production sector, or data management, which are of increasing relevance due to various global developments. The demonstration of global research trends in CO can support researchers in identifying the relevant issues regarding this expanding and transforming research area.

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Section: Discussionmentioning

confidence: 99%

Research trends in combinatorial optimization

Weinand

Sörensen

Segundo

et al. 2021

Int Trans Operational Res

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“…So, although a full proof-logging constraint solver does not yet exist, we can confidently claim that symmetries no longer block this goal. Gocht et al [2020a] showed how VeriPB can be used to implement proof logging for a wide range of maximum clique algorithms, observing that the cutting planes proof system is rich enough to justify a wide range of bound and inference functions used by various solvers (despite cutting planes not knowing what a graph or clique is). However, there is one clique-solving technique in the literature that is not amenable to cutting planes reasoning.…”

Section: Symmetries In Constraint Programmingmentioning

confidence: 99%

“…To provide proof logging for this, we must instead be able to introduce vertex dominance constraints precisely when they are used. It is hard to see how to achieve this with the redundance rule, but it is possible using dominance-based strengthening: we have implemented this in the proof logging maximum clique solver in [Gocht et al, 2020a], as discussed in more detail in Appendix E.…”

Section: Lazy Global Domination In Maximum Cliquementioning

confidence: 99%

“…For this reason, if the condition |C curr | + j > |C best | fails to hold, we know that the current clique candidate cannot possibly be extended to a clique that is larger than what we have already found in C best . At the end of the first call MaxCliqueSearch(G, V, C curr = ∅, C best = ∅), after completion of all recursive subcalls, the vertex set C best will be a clique of maximum size in G. A certifying version of essentially this algorithm with VeriPB proof logging was presented by Gocht et al [2020a]. It might be worth noting in this context that one quite interesting challenge is to justify the backtracking performed when the condition |C curr | + j > |C best | fails, and this is one place where the strength of the pseudo-Boolean reasoning in the cutting planes proof system is very helpful (as opposed to the clausal reasoning in, e.g., DRAT).…”

Section: E Technical Appendix On Proof Logging For Vertex Dominance I...mentioning

confidence: 99%

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Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Bogaerts¹,

Gocht²,

McCreesh³

et al. 2022

Preprint

Self Cite

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Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking are easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

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“…Current SAT techniques are not easily extendable, as CP considers optimisation problems, possibly using integer variables, and complex constraints that may require an exponential number of clauses when encoding into SAT. There has been progress in this direction using cutting planes reasoning, but only for specific problems or constraints [7,11,12]. For similar reasons, the machine learning features used in SAT may not directly translate to (LCG-based) CP.…”

Section: Introductionmentioning

confidence: 99%

Learning Variable Activity Initialisation for Lazy Clause Generation Solvers

Driel

Demirović

Yorke-Smith

2021

Integration of Constraint Programming, Artificial Intelligence, and Operations Research

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Contemporary research explores the possibilities of integrating machine learning (ML) approaches with traditional combinatorial optimisation solvers. Since optimisation hybrid solvers, which combine propositional satisfiability (SAT) and constraint programming (CP), dominate recent benchmarks, it is surprising that the literature has paid limited attention to machine learning approaches for hybrid CP-SAT solvers. We identify the technique of minimal unsatisfiable subsets as promising to improve the performance of the hybrid CP-SAT lazy clause generation solver Chuffed. We leverage a graph convolutional network (GCN) model, trained on an adapted version of the MiniZinc benchmark suite. The GCN predicts which variables belong to an unsatisfiable subset on CP instances; these predictions are used to initialise the activity score of Chuffed's Variable-State Independent Decaying Sum (VSIDS) heuristic. We benchmark the ML-aided Chuffed on the MiniZinc benchmark suite and find a robust 2.5% gain over baseline Chuffed on MRCPSP instances. This paper thus presents the first, to our knowledge, successful application of machine learning to improve hybrid CP-SAT solvers, a step towards improved automatic solving of CP models.

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Certifying Solvers for Clique and Maximum Common (Connected) Subgraph Problems

Cited by 15 publications

References 60 publications

Research trends in combinatorial optimization

Research trends in combinatorial optimization

Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Learning Variable Activity Initialisation for Lazy Clause Generation Solvers

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