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

Gocht, S. , McBride, R. , McCreesh, C. , Nordström, J. , Prosser, P. and Trimble, J. (2020) Certifying Solvers for Clique and Maximum Common (Connected) Subgraph Problems. In: 26th International Conference on Principles and Practice of Constraint Programming, Louvain-la-Neuve, Belgium, 07-11 Sep 2020, pp. 338-357. ISBN 9783030584740 (doi:10.1007/978-3-030-58475-7_20)

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Abstract

An algorithm is said to be certifying if it outputs, together with a solution to the problem it solves, a proof that this solution is correct. We explain how state of the art maximum clique, maximum weighted clique, maximal clique enumeration and maximum common (connected) induced subgraph algorithms can be turned into certifying solvers by using pseudo-Boolean models and cutting planes proofs, and demonstrate that this approach can also handle reductions between problems. The generality of our results suggests that this method is ready for widespread adoption in solvers for combinatorial graph problems.

Item Type:Conference Proceedings
Additional Information:The first and fourth authors were funded by the Swedish Research Council (VR) grant 2016-00782. The fourth author was also supported by the Independent Research Fund Denmark (DFF) grant 9040-00389B. The third, fifth and sixth authors were supported by the Engineering and Physical Sciences Research Council [grant numbers EP/P026842/1 and EP/M508056/1]. Some code development used resources provided by the Swedish National Infrastructure for Computing (SNIC).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Trimble, Mr James and Prosser, Dr Patrick and Mccreesh, Dr Ciaran
Authors: Gocht, S., McBride, R., McCreesh, C., Nordström, J., Prosser, P., and Trimble, J.
College/School:College of Science and Engineering > School of Computing Science
ISSN:0302-9743
ISBN:9783030584740
Copyright Holders:Copyright © Springer Nature Switzerland AG 2020
First Published:First published in International Conference on Principles and Practice of Constraint Programming CP 2020: Principles and Practice of Constraint Programming (LNCS, volume 12333)
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300525Modelling and Optimisation with GraphsPatrick ProsserEngineering and Physical Sciences Research Council (EPSRC)EP/P026842/1Computing Science
190906EPSRC 2015 DTPMary Beth KneafseyEngineering and Physical Sciences Research Council (EPSRC)EP/M508056/1Research and Innovation Services