Abstract
We present an O(¦ E ¦2¦ V ¦ log ¦ V ¦) algorithm for the construction of the principal partition of a graph. The best known earlier algorithm for this problem is O(¦ E ¦3 log ¦ V ¦). Our approach differs from the earlier approaches in that it is node-partition based rather than edge-set based. We use flow maximisation as our basic subroutine.
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Edmonds, J.: Minimum Partition of a Matroid into independent subsets, J. Res. National Bureau of Standards, vol. 69B, 1965, pp. 67–72.
Imai, H.: Network flow algorithms for lower truncated transversal polymatroids, 31. of the Op. Research Society of Japan, vol. 26, 1983, pp. 186–210.
Iri, M.: A review of recent work in Japan on principal partition of matroids and their applications, Annals of New York Academy of Sciences, vol 319, 1979, pp.306–319.
Iri, M.: Application of matroid theory to engineering systems problems, Proceedings of the Sixth Conference on Probability Theory, (Sept.1979: Bereanu, B., et al, eds.), Editura Academiei Republicii Socialiste Romania, pp.107–127.
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.
Kishi, G. and Kajitani, Y.: Maximally distant trees and principal partition of a linear graph, IEEE Trans. Circuit Theory, CT-16,3,1969,pp.323–330.
Lawler, E. L.: Combinatorial Optimisation: Networks and Matroids, Holt, Rhinehart and Winston, New York, 1976.
Murota, K. and Iri, M.: Matroidal approach to the structural solvability of a system of equations. Eleventh International Symposium on Mathematical Programming, Universitat Bonn, 1982.
Narayanan, H.: Theory of Matroids and Network Analysis, Ph.D. thesis, Department of Electrical Engineering, I.I.T. Bombay, 1974.
Narayanan, H.: The Principal Lattice of Partitions of a Submodular Function, Linear Algebra and its Applications, 144, 1991,pp. 179–216.
Narayanan, H. and Vartak, M. N.: An elementary approach to the principal partition of a matroid, Transactions of the Institute of Electronics and Communication Engineers of Japan, vol. E64, 1981, pp.227–234.
Ohtuski, T., Ishizaki, Y. and Watanabe, H.: Topological degrees of freedom and mixed analysis of electrical networks, IEEE Trans. Circuit Theory, CT-17,4,1970,pp.491–499.
Ozawa, T.: Topological conditions for the solvability of linear active networks, Circuit Theory and Applications, vol. 4, 1976, pp.125–136.
Patkar, S. and Narayanan, H.: Fast algorithms for the Principal Partition of graphs and related problems, Technical Report TR.049.91, I.I.T. Bombay, 1991.
Roskind, J. and Tarjan, R. E.: A note on finding minimum-cost edge disjoint spanning trees, Math. Op. Res.,vol. 10, no. 4,1985, pp.701–708.
Saran, H. and Vazirani, V.V.: Finding the min k-cut within twice the optimal, Preprint, to appear in forthcoming FOCS.
Tomizawa, N.: Strongly Irreducible matroids and principal partition of a matroid into stronly irreducible minors (in Japanese), Transactions of the Institute of Electronics and Communication Engineers of Japan, vol. J59A, 1976, pp. 83–91.
Welsh, D. J. A.: Matroid Theory, Academic Press, New York, 1976.
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Patkar, S., Narayanan, H. (1991). A fast algorithm for the principal partition of a graph. In: Biswas, S., Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1991. Lecture Notes in Computer Science, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54967-6_76
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DOI: https://doi.org/10.1007/3-540-54967-6_76
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