Abstract
We present anO(n log logn) time algorithm for finding a maximum matching in a permutation graph withn vertices, assuming that the input graph is represented by a permutation.
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References
C. Berge: Two theorems in graph theory. Proceeding of National Academy of Science43 (1957) 842–844
J. Edmonds: Paths, trees and flowers. Canadian J.17 (1965) 449–467
P. van Emde Boas: Preserving order in a forest in less than logarithmic time and linear space. Information Processing Letters6 (1977) 80–82
S. Even, O. Kariv: AnO(n 2.5) algorithm for finding maximum matching in general graphs. Proceeding of 16th IEEE Sympo. on Foundations of Computer Science (1975) 100–112
H. Gabow: An efficient implementation of Edmonds' maximum matching algorithm. TR 31, Stan-CS (1972) 72–328
M.C. Golumbic: Algorithmic graph theory and perfect graphs. Academic Press, New York, 1980
M.C. Hopcroft, R.M. Karp: AnO(n 2.5) algorithm for maximum matching in bipartite graphs. SIAM J. on Computing2 (1973) 225–231
V. Kamakoti, C. Pandu Rangan: Efficient transitive reduction on permutation graphs with applications. SCI J. of Computer Science and Informatics (INDIA, 1994)
Y. Liang, C. Rhee: Finding a maximum matching in a circular-arc graph. Information Processing Letters45 (1993) 185–190
S. Micali, V. Vazirani: AnO(√nm) algorithm for finding maximum matching in general graphs. 21th Annual IEEE Sympo. on the Foundations of Software Technology and Theoretical Computer Science (1980)
A. Pnueli, A. Lempel, S. Even: Transitive orientation of graphs and identification of permutation graphs. Can. J. Math.23 (1971) 160–175
J. Spinrad: On comparability and permutation graphs. SIAM J. Computing14 (1985) 658–670
M.S. Yu, C.H. Yang: AnO(n) time algorithm for maximum matching on cographs. Information Processing Letters47 (1993) 89–93
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Rhee, C., Liang, Y.D. Finding a maximum matching in a permutation graph. Acta Informatica 32, 779–792 (1995). https://doi.org/10.1007/BF01178659
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DOI: https://doi.org/10.1007/BF01178659