The MINSUMCUT problem
In this paper we first present a sequential linear algorithm for a linear arrangement problem on trees, MINSUMCUT, and then an O(log n)-time parallel algorithm for MINSUMCUT on trees, which uses n2/(logn) processors.
KeywordsParallel Algorithm Directed Edge Sequential Algorithm Linear Arrangement Outerplanar Graph
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- [AH73]D. Adolphson and T.C. Hu. Optimal linear ordering. SIAM J. on Applied Mathematics, 25(3):403–423, Nov 1973.Google Scholar
- [Dia79]J. Diaz. The δ-operator. In L. Budach, editor, Fundamentals of Computation Theory, pages 105–111. Akademie-Verlag, 1979.Google Scholar
- [GGJK78]M.R. Garey, R.L. Graham, D.S. Johnson, and D. Knuth. Complexity results for bandwidth minimization. SIAM J on Applied Mathematics, 34:477–495, Sept. 1978.Google Scholar
- [GJ76]M.R. Garey and D.S. Johnson. Some simplified NP-complete graph problems. Theoretical Computer Science, 1:237–267, 1976.Google Scholar
- [GJ79]M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979.Google Scholar
- [GR88]A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, Cambridge, 1988.Google Scholar
- [GR89]A. Gibbons and W. Rytter. Optimal parallel algorithms for dynamic expression evaluation and context free recognition. Information and Computation, 81(1):32–45, April 1989.Google Scholar
- [GR90]A. Gibbons and W. Rytter. Optimal edge-colouring outerplanar graphs is in NC. Theoretical Computer Science, 71:401–411, 1990.Google Scholar
- [Har77]L.H. Harper. Stabilization and the edgesum problem. Ars Combinatoria, 4:225–270, Dec. 1977.Google Scholar
- [NK72]M. Nanan and M. Kurtzberg. A review of the placement and quadratic assignment problems. SIAM Review, 14(2):324–341, April 1972.Google Scholar
- [Shi79]Yossi Shiloach. A minimum linear arrangement algorithm for undirected trees. SIAM J. on Computing, 8(1):15–31, February 1979.Google Scholar
- [Yan83]Mihalis Yannakakis. A polynomial algorithm for the min cut linear arrangement of trees. In IEEE Symp. on Found. of Comp. Sci., volume 24, pages 274–281, Providence RI, Nov. 1983.Google Scholar