Abstract
The maximum independent set problem is a classic graph optimization problem. It is well known that it is an NP-Complete problem. In this paper, an improved simulated annealing algorithm is presented for the maximum independent set problem. In this algorithm, an acceptance function is defined for every vertex. This can help the algorithm find a near optimal solution to a problem. Simulations are performed on benchmark graphs and random graphs. The simulation results show that the proposed algorithm provides a high probability of finding optimal solutions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Stinson, D.R.: An Introduction to the Design and Analysis of Algorithms, 2nd edn. The Charles Babbage Research Center, Winnipeg, Manitoba, Canada (1987)
Karp, R.M.: Reducibility among Combinatorial Problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computation, pp. 85–103. Plenum Press, New York (1972)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979)
Johnson, D.: Approximate Algorithms for Combinatorial Problems. Journal of Computer and System Sciences 9, 256–278 (1974)
Abello, J., Pardalos, P.M., Resende, M.G.C.: On the Maximum Clique Problems in very Large Graphs. In: Abello, J., Vitter, J.S. (eds.) External Memory Algorithms and Visualization. DIMACS series on discrete mathematics and theoretical Computer Science, vol. 50, pp. 119–130. American Mathematical Society, Providence (1999)
Avondo-Bodeno, G.: Economic Applications of the Theory of Graphs. Gordon and Breach Science, New York (1962)
Berge, C.: The Theory of Graphs and Its Applications. John Wiley and Sons, New York (1962)
Bomze, I.M., Budinich, M., Pardalos, P.M., Pelillot, M.: The maximum clique problem. In: Du, D.Z., Pardalos, P.M. (eds.) Handbook of Combinatorial Optimization, pp. 1–74. Kluwer Academic Publishers, Dordrecht (1999)
Karp, R.M., Wigderson, A.: A Fast Parallel Algorithm for the Maximal Independent Set Problem. Journal of the ACM 32(4), 762–773 (1985)
Alon, N., Babai, L., Itai, A.: A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem. Journal of Algorithms 7, 567–583 (1986)
Goldberg, M., Spencer, T.: A New Parallel Algorithm for the Maximal Independent Set Problem. SIAM Journal on Computing 18, 419–427 (1989)
Goldberg, M., Spencer, T.: Constructing a Maximal Independent Set in Parallel. SIAM Journal on Discrete Mathematics 2, 322–328 (1989)
Goldberg, M., Spencer, T.: An Efficient Parallel Algorithm that Finds Independent Sets of Guaranteed Size. SIAM Journal on Discrete Mathematics 6, 443–459 (1993)
Takefuji, Y., Chen, L., Lee, K., Huffman, J.: Parallel Algorithm for Finding a Near Maximum Independent Set of the Circle Graph. IEEE Transaction on Neural Networks 1, 263–267 (1990)
Bäck, T., Khuri, S.: An Evolutionary Heuristic for the Maximum Independent Set Problem. In: Michalewicz, Z., Schaffer, J.D., Schwefel, H.P., Fogel, D.B., Kitano, H. (eds.) Proceeding of the First IEEE Conference on Evolutionary Computation, pp. 531–535. IEEE Press, New York (1994)
Busygin, S., Butenko, S., Pardalos, P.: A Heuristic for the Maximum Independent Set Problem Based on Optimization of a Quadratic over a Sphere. Journal of Combinatorial Optimization 6, 287–297 (2002)
Berman, P., Fujito, T.: On Approximation Properties of the Independent Set Problem for Low Degree Graphs. Theory of Computing Systems 32, 115–132 (1999)
Dahlhaus, E., Karpinski, M., Kelsen, P.: An Efficient Parallel Algorithm for Computing a Maximal Independent Set in a Hypergraph of Dimension 3. Information Processing Letters 42, 309–313 (1992)
Pham, D.T., Karaboga, D.: Intelligent Optimisation Techniques: Genetic Algorithm, Tabu Search, Simulated Annealing, and Neural Networks. Springer, Heidelberg (2000)
Halldórsson, M.M., Radhakrishnan, J.: Greed is good: Approximating Independent Sets in Sparse and Bounded-degree Graphs. Algorithmica 18, 145–163 (1997)
Yuan, S.-Y., Kuo, S.-Y.: A New Technique for Optimization Problems in Graph Theory. IEEE Transactions on Computers 47, 190–196 (1998)
Matual, D.W.: On the Complete Subgraph of a Random Graph”. In: Bose, R., Dowling, T. (eds.) Proceeding of the Second Chapel Hill Conference on Combinatory Mathematics and its Applications, pp. 356–369. Chapel Hill, North Carolina (1970)
Bertoni, A., Campadelli, P., Grossi, G.: A Neural Algorithm for the Maximum Clique Problem: Analysis, Experiments, and Circuit Implementation. Algorithmica 33, 71–88 (2002)
Jagota, S.: Approximating Maximum Clique with a Hopfield Network. IEEE Transactions on Neural Networks 6, 724–735 (1995)
Funabiki, N., Nishikawa, S.: Comparisons of Energy-descent Optimization Algorithms for Maximum Clique Problems. IEICE Transactions on Fundamentals E79-A(4), 452–460 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, X., Ma, J., Wang, H. (2006). An Improved Simulated Annealing Algorithm for the Maximum Independent Set Problem. In: Huang, DS., Li, K., Irwin, G.W. (eds) Intelligent Computing. ICIC 2006. Lecture Notes in Computer Science, vol 4113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11816157_99
Download citation
DOI: https://doi.org/10.1007/11816157_99
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37271-4
Online ISBN: 978-3-540-37273-8
eBook Packages: Computer ScienceComputer Science (R0)