A novel parallel local search algorithm for the maximum vertex weight clique problem in large graphs

  • Ender Sevinc
  • Tansel DokerogluEmail author
Methodologies and Application


This study proposes a new parallel local search algorithm (Par-LS) for solving the maximum vertex weight clique problem (MVWCP) in large graphs. Solving the MVWCP in a large graph with millions of edges and vertices is an intractable problem. Parallel local search methods are powerful tools to deal with such problems with their high-performance computation capability. The Par-LS algorithm is developed on a distributed memory environment by using message passing interface libraries and employs a different exploration strategy at each processor. The Par-LS introduces new operators parallel(\(\omega \),1)-swap and parallel(1,2)-swap, for searching the neighboring solutions while improving the current solution through iterations. During our experiments, 172 of 173 benchmark problem instances from the DIMACS, BHOSLIB and Network Data Repository graph libraries are solved optimally with respect to the best/optimal reported results. A new best solution for the largest problem instance of the BHOSLIB benchmark (frb100-40) is discovered. The Par-LS algorithm is reported as one of the best performing algorithms in the literature for the solution of the MVWCP in large graphs.


Maximum clique problem Parallel search Vertex weight MPI 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Human and animals participants

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

There is no individual participant included in the study.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer EngineeringTED UniversityAnkaraTurkey
  2. 2.Department of Computer EngineeringTHK UniversityAnkaraTurkey

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