Abstract
We tackle the maximum clique problem by reformulating it in terms of a standard quadratic program, which derives from a theorem of Motzkin and Straus. A heuristic is then obtained by solving with Lemke’s method the linear complementarity problem that arises from the KKT conditions of the QP. We have added a pivoting rule that exploits degeneracy to reach good suboptimal solutions. Very positive results have been obtained on the DIMACS benchmark graphs.
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Massaro, A., Pelillo, M. (2001). A Pivoting-Based Heuristic for the Maximum Clique Problem. In: Hadjisavvas, N., Pardalos, P.M. (eds) Advances in Convex Analysis and Global Optimization. Nonconvex Optimization and Its Applications, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0279-7_23
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DOI: https://doi.org/10.1007/978-1-4613-0279-7_23
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-7923-6942-4
Online ISBN: 978-1-4613-0279-7
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