# SUBGRAPH EXTRACTION AND MEMETIC ALGORITHM FOR THE MAXIMUM CLIQUE PROBLEM

### Duc-Cuong Dang, Aziz Moukrim

#### Abstract

The maximum clique problem involves finding the largest set of pairwise adjacent vertices in a graph. The problem is classic but still attracts much attention because of its hardness and its prominent applications. Our work is based on the existence of an order on all the vertices whereby those belonging to a maximum clique stay close enough to each other. Such an order can be identified via the extraction of a particular subgraph from the original graph. The problem can consequently be seen as a permutation problem that can be addressed efficiently with an evolutionary-like algorithm, here we use a memetic algorithm (MA). Computational experiments conducted on DIMACS benchmark instances clearly show our MA which not only outperforms existing genetic approaches, but also compares very well to state-of-the-art algorithms.

#### References

- Balas, E. and Yu, C. (1986). Finding a maximum clique in an arbitary graph. SIAM Journal of Computing, 15:1054-1068.
- Battiti, R. and Protasi, M. (2001). Reactive local search for the maximum clique problem. Algorithmica, 29:610- 637.
- Bomze, I., Budinich, M., Pardalos, P., and Pelillo, M. (1999). Handbook of Combinatorial Optimization, chapter The maximum clique problem. Kluwer Academic Publishers.
- Bui, T. N. and Eppley, P. H. (1995). A hybrid genetic algorithm for the maximum clique problem. In Proceed-

#### Paper Citation

#### in Harvard Style

Dang D. and Moukrim A. (2010). **SUBGRAPH EXTRACTION AND MEMETIC ALGORITHM FOR THE MAXIMUM CLIQUE PROBLEM** . In *Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)* ISBN 978-989-8425-31-7, pages 77-84. DOI: 10.5220/0003081000770084

#### in Bibtex Style

@conference{icec10,

author={Duc-Cuong Dang and Aziz Moukrim},

title={SUBGRAPH EXTRACTION AND MEMETIC ALGORITHM FOR THE MAXIMUM CLIQUE PROBLEM},

booktitle={Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)},

year={2010},

pages={77-84},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003081000770084},

isbn={978-989-8425-31-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Evolutionary Computation - Volume 1: ICEC, (IJCCI 2010)

TI - SUBGRAPH EXTRACTION AND MEMETIC ALGORITHM FOR THE MAXIMUM CLIQUE PROBLEM

SN - 978-989-8425-31-7

AU - Dang D.

AU - Moukrim A.

PY - 2010

SP - 77

EP - 84

DO - 10.5220/0003081000770084