Reactive and dynamic local search for Max-Clique, does the complexity pay off?

This paper presents some preliminary results of an ongoing investigation about how different algorithmic building blocks contribute to solving the Maximum Clique problem. In detail, we consider greedy constructions, plateau searches, and more complex schemes based on dynamic penalties and/or prohibitions, in particular the recently proposed technique of Dynamic Local Search and the previously proposed Reactive Local Search. The experimental results consider both the empirical hardness, measured by the iterations needed to reach empirical maxima, and the CPU time per iteration.

[1]  Panos M. Pardalos,et al.  The maximum clique problem , 1994, J. Glob. Optim..

[2]  Roberto Battiti,et al.  The Reactive Tabu Search , 1994, INFORMS J. Comput..

[3]  J. Håstad.  Clique is hard to approximate within n 1-C , 1996 .

[4]  Roberto Battiti,et al.  Greedy, Prohibition, and Reactive Heuristics for Graph Partitioning , 1999, IEEE Trans. Computers.

[5]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[6]  Lars Engebretsen,et al.  Clique Is Hard To Approximate Within , 2000 .

[7]  Mark K. Goldberg,et al.  Discovering Optimization Algorithms Through Automated Learning , 2001, Graphs and Discovery.

[8]  Roberto Battiti,et al.  Reactive Local Search for the Maximum Clique Problem1 , 2001, Algorithmica.

[9]  G. Stormo,et al.  A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences. , 2004, Bioinformatics.

[10]  Xing Xu,et al.  A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences , 2004, Bioinform..

[11]  Federico Della Croce,et al.  Combining Swaps and Node Weights in an Adaptive Greedy Approach for the Maximum Clique Problem , 2004, J. Heuristics.

[12]  Ulrik Brandes,et al.  Efficient generation of large random networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Frank Hutter,et al.  Parameter Adjustment Based on Performance Prediction: Towards an Instance-Aware Problem Solver , 2005 .

[14]  Wilbert E. Wilhelm,et al.  Clique-detection models in computational biochemistry and genomics , 2006, Eur. J. Oper. Res..

[15]  Wayne J. Pullan,et al.  Dynamic Local Search for the Maximum Clique Problem , 2011, J. Artif. Intell. Res..

[16]  Teofilo F. Gonzalez,et al.  Reactive Search: Machine Learning for Memory-Based Heuristics , 2007 .

[17]  J. Jeffry Howbert,et al.  The Maximum Clique Problem , 2007 .