Abstract
The maximum weight k-independent set problem has applications in many practical problems like k-machines job scheduling problem, k-colourable subgraph problem, VLSI design layout and routing problem. Based on DAG (Directed Acyclic Graph) approach, an O(kn 2) time sequential algorithm is designed in this paper to solve the maximum weight k-independent set problem on weighted trapezoid graphs. The weights considered here are all non-negative and associated with each of the n vertices of the graph.
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References
D.G. Corneil and P.A. Kamula, “Extensions of permutation and interval graphs, ” in Proc. 18th Southeast Conf. on Combinatorics, Graph Theory and Computing, Congr. Numer., 1987, pp. 267–276.
I. Dagan, M.C. Golumbic, and R.Y. Pinter, “Trapezoid graphs and their coloring, ” Discrete Applied Mathematics, vol. 21, pp. 35–46, 1988.
F. Cheah and D.G. Corneil, “On the structure of trapezoid graphs, ” Discrete Applied Mathematics, vol. 66, pp. 109–133, 1996.
R.K. Ahuja, K. Mehlhorn, J.B. Orlin, and R.E. Tarjan, “Faster algorithms for the shortest path problem, ” J. ACM, vol. 37, pp. 213–223, 1990.
M.S. Chang and F.-H. Wang, Efficient algorithms for the maximum weight clique and maximum weight independent set problems on permutation graphs, Information Processing Letters, vol. 43, pp. 293–295, 1992.
J. Edmonds and R.M. Karp, “Theoretical improvements in algorithmic efficiency for network flow problems, ” J. ACM, vol. 19, 248–264, 1972.
M.R. Garey and D.S. Johnson, Computer and Intractability: A Guide to the Theory of NP-Completeness, Freeman: San Francisco, CA, 1979.
M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press: New York, 1980.
M. Hota, M. Pal, and T.K. Pal, “An efficient algorithm to generate all maximal independent sets on trapezoid graphs, ” Intern. J. Computer Mathematics, vol. 70, pp. 587–599, 1999.
J.Y. Hsiao, C.Y. Tang, and R.S. Chang, “Solving the single step graph searching problem by solving the maximum two-independent set problem, ” Information Processing Letters, vol. 40, pp. 283–287, 1991.
J.Y. Hsiao, C.Y. Tang, and R.S. Chang, “An efficient algorithm for finding a maximum weight 2-independent set on interval graphs, ” Information Processing Letters, vol. 43, pp. 229–235, 1992.
W.L. Hsu and K.H. Tsai, “A linear time algorithm for the two-track assignment problem, ” in Proceedings of 27th Allerton Conf. on Communication, Control and Computing, 1989, pp. 291–300.
D.S. Johnson, “The NP-completeness column: An on going guide, ” J. Algorithms, vol. 6, pp. 434–451, 1985.
R.D. Lou, M. Sarrafgadeh, and D.T. Lee, “An optimal algorithm for the maximum two-chain problem, ” SIAM J. Discrete Math., vol. 5, pp. 285–304, 1992.
T.H. Ma and J.P. Spinrad, “On the 2-chain subgraph cover and related problems, ” J. Algorithms, vol. 17, pp. 251–268, 1994.
M. Pal and G.P. Bhattacharjee, “A sequential algorithm for finding a maximum weight k-independent set on interval graphs, ” Intern. J. Comput. Math., vol. 60, pp. 205–214, 1996.
M. Sarrafgadeh and D.T. Lee, “A new approach to topological via minimization, ” IEEE Trans. Computer Aided Design, vol. 8, pp. 890–900, 1989.
M. Yannakakis and F. Gavril, “The maximum k-colourable subgraph problem for chordal graphs, ” Information Processing Letters, vol. 24, pp. 133–137, 1987.
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Hota, M., Pal, M. & Pal, T.K. An Efficient Algorithm for Finding a Maximum Weight k-Independent Set on Trapezoid Graphs. Computational Optimization and Applications 18, 49–62 (2001). https://doi.org/10.1023/A:1008791627588
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DOI: https://doi.org/10.1023/A:1008791627588