Abstract
In this paper we have shown the utility of the Principal Lattice of Partitions approach to the construction of approximate algorithms for the Min-k-overlap problem. In particular we give an improved performance guarantee in the case of the Min-k-cut problem. An important open problem in this direction is to examine if the PLP can be used to handle the general balanced partition case. A restricted version of this problem is treated in the Appendix.
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References
Ford, L. R. & Fulkerson, D. R.: Flows in Networks, Princeton University Press, Princeton, 1962.
Goldschmidt, O. and Hochbaum, D.S.: Polynomial algorithm for the k-cut problem, Proc. 29 th annual Symp. on the Foundations of Computer Science, 1988,pp. 444–451.
Imai, H.: Network flow algorithms for lower truncated transversal polymatroids, Jl. of the Op. Research Society of Japan, vol. 26, 1983, pp. 186–210.
Iri, M. and Fujishige, S.: Use of matroid theory in operations research, circuits and systems theory, Int. J. Systems Sci., vol. 12, no. 1, 1981, pp. 27–54.
Kozen, D.C.: The Design and Analysis of Algorithms, Springer-Verlag, New York, 1992.
Lawler, E. L.: Combinatorial Optimization: Networks and Matroids, Holt, Reinhart and Winston, New York, 1976.
Lovasz, L.: Submodular Functions and Convexity, Proceedings of XI International Symposium on Mathematical Programming, Bonn, 1982.
Malhotra, V.M., Kumar, M.P., & Maheshwari, S.N.: An O (¦V¦3) Algorithm for Finding Maximum Flows in Networks, Information Processing Letters, 7, no.6, 1978, pp. 277–278.
Narayanan, H.: Theory of Matroids and Network Analysis, Ph.D. thesis, Department of Electrical Engineering, I.I.T. Bombay, 1974.
Narayanan, H.: On the minimum hybrid rank of a graph relative to a partition of its edges and its application to electrical network analysis, Intl. Journal of Circuit Theory and Applications, Vol. 18, 1990, pp. 269–288.
Narayanan, H.: The Principal Lattice of Partitions of a Submodular Function, Linear Algebra and its Applications, 144, 1991,pp. 179–216.
Narayanan, H., Roy, Subir, & Patkar, Sachin: Min k-Cut and the Principal Partition of a Graph, Proceedings of the Second National Seminar on Theoretical Computer Science, Indian Statistical Institute, Calcutta, June 17–19, 1992.
Patkar, S. and Narayanan, H.: Fast algorithm for the Principal Partition of a graph, Proc. 11th Annual Symposium on Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science — 560, 1991, pp. 288–306.
Patkar, S. and Narayanan, H.: Principal Lattice of Partitions of submodular functions on graphs: Fast algorithms for Principal Partition and Generic Rigidity, in Proc. of the 3 rd ann. Int. Symp. on Algorithms and Computation, (ISAAC), Lecture Notes in Computer Science-650, Japan, 1992, pp. 41–50.
Saran, H. and Vazirani, V.V.: Finding a k-Cut within Twice the Optimal, Proc. 32 nd annual Symp. on the Foundations of Computer Science, 1991.
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© 1994 Springer-Verlag Berlin Heidelberg
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Narayanan, H., Roy, S., Patkar, S. (1994). Approximation algorithms for Min-k-overlap problems using the principal lattice of partitions approach. In: Prívara, I., Rovan, B., Ruzička, P. (eds) Mathematical Foundations of Computer Science 1994. MFCS 1994. Lecture Notes in Computer Science, vol 841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58338-6_99
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DOI: https://doi.org/10.1007/3-540-58338-6_99
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