Abstract
The Bandwidth Minimization Problem for Graphs (BMPG) can be defined as finding a labeling for the vertices of a graph, where the maximum absolute difference between labels of each pair of connected vertices is minimum. The most used measure for the BMPG algorithms isβ, that indicates only the maximum of all absolute differences.
After analyzing some drawbacks of β, a measure, calledγ, which uses a positional numerical system with variable base and takes into account all the absolute differences of a graph is given.
In order to test the performance of γ and β a stochastic search procedure based on a Simulated Annealing (SA) algorithm has been applied to solve the BMPG. The experiments show that the SA that uses γ has better results for many classes of graphs than the one that uses β.
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References
Kosko, E.: Matrix Inversion by Partitioning. The Aeronautical Quart. 8 (1956) 157
Livesley, R.R.: The Analysis of Large Structural Systems. Computer J. 3 (1960)34
Chinn, P.Z., Chvátalová, J., Dewdney, A.K., Gibbs, N.E.: The Bandwidth Problem for Graphs and Matrices-A Survey. J. of Graph Theory 6 (1982) 223–254
Harper, L.H.: Optimal assignment of numbers to vertices. J. of SIAM 12 (1964) 131–135
Harary, F.: Theory of graphs and its aplications. Czechoslovak Academy of Science, Prague (1967) 161
Torres-Jiménez, J.: Minimización del Ancho de Banda de un Grafo Usando un Algoritmo Genético. Ph. D. ITESM-Mor., México (1997)
Papadimitriou, C.H.: The NP-Completeness of the bandwidth minimization problem. J. of Comp. 16 (1976) 263–270
Garey, M.R., Graham, R.L., Johnson, D.S., Knuth, D.E.: Complexity results for bandwidth minimization. SIAM J. of App. Math. 34 (1978) 477–495
Gurari, E.M., Sudborough, I.H.: Improved dynamic programming algorithms for bandwidth minimization and the min-cut linear arrangement problem. J. of Algorithms 5 (1984) 531–546
Cuthill, E., McKee, J.: Reducing the bandwidth of sparse symmetric matrices. Proceedings 24th National of the ACM (1969) 157–172
Gibbs, N.E., et. al.: An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J. on Numerical Analysis 13 (1976) 235–251
George, A., Liu, W.: Computer Solution of Large Sparse Positive Definite Systems. Prentice Hall, Englewood Cliffs, NJ (1981)
Haralambides, J., Makedon, F., Monien, B.: An aproximation algorithm for cater-pillars. J. of Math. Systems Theory 24 (1991) 169–177
Dueck, G., Jeffs, J.: A Heuristic Bandwidth Reduction Algorithm. J. of Comb. Math. and Comp. 18 (1995)
Esposito, A., Fiorenzo, S., Malucelli, F., Tarricone, L.: A wonderful bandwidth matrix reduction algorithm. Submitted to Operations Research Letters
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220 (1983) 671–680
Spears, W.M.: Simulated Annealing for hard satisfiability problems. AI Center, Naval Research Laboratory, Washington, DC 20375 AIC-93-015 (1993)
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Torres-Jimenez, J., Rodriguez-Tello, E. (2000). A New Measure for the Bandwidth Minimization Problem. In: Monard, M.C., Sichman, J.S. (eds) Advances in Artificial Intelligence. IBERAMIA SBIA 2000 2000. Lecture Notes in Computer Science(), vol 1952. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44399-1_49
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DOI: https://doi.org/10.1007/3-540-44399-1_49
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