Abstract
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.
This research was supported by the ESPRIT BRA Program of the EC under contract no. 3075, Project ALCOM.
Preview
Unable to display preview. Download preview PDF.
References
D. Adolphson and T.C. Hu. Optimal linear ordering. SIAM J. on Applied Mathematics, 25(3):403–423, Nov 1973.
J. Diaz. The δ-operator. In L. Budach, editor, Fundamentals of Computation Theory, pages 105–111. Akademie-Verlag, 1979.
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.
M.R. Garey and D.S. Johnson. Some simplified NP-complete graph problems. Theoretical Computer Science, 1:237–267, 1976.
M.R. Garey and D.S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, 1979.
A. Gibbons and W. Rytter. Efficient Parallel Algorithms. Cambridge University Press, Cambridge, 1988.
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.
A. Gibbons and W. Rytter. Optimal edge-colouring outerplanar graphs is in NC. Theoretical Computer Science, 71:401–411, 1990.
L.H. Harper. Stabilization and the edgesum problem. Ars Combinatoria, 4:225–270, Dec. 1977.
M. Nanan and M. Kurtzberg. A review of the placement and quadratic assignment problems. SIAM Review, 14(2):324–341, April 1972.
Yossi Shiloach. A minimum linear arrangement algorithm for undirected trees. SIAM J. on Computing, 8(1):15–31, February 1979.
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.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Díaz, J., Gibbons, A.M., Paterson, M.S., Torán, J. (1991). The MINSUMCUT problem. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028251
Download citation
DOI: https://doi.org/10.1007/BFb0028251
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-54343-5
Online ISBN: 978-3-540-47566-8
eBook Packages: Springer Book Archive