Total Ordering Problem
Abstract
The problem of finding a total ordering of a finite set satisfying a given set of in-between restrictions is considered. It is shown that the problem is $NP$-complete.
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References
1.
Alfred V. Aho, John E. Hopcroft, Jeffrey D. Ullman, The design and analysis of computer algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1975x+470
2.
S. A. Cook, The complexity of theorem-proving procedures, Third Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 1971, 151–158
3.
V. Chvatal, G. Thomassen, Distances in orientations of graphs, Research report, STAN-CS-75-511, Stanford University, Stanford, CA, 1975
4.
Richard M. Karp, R. E. Miller, J. W. Thatcher, Reducibility among combinatorial problemsComplexity of computer computations (Proc. Sympos., IBM Thomas J. Watson Res. Center, Yorktown Heights, N.Y., 1972), Plenum, New York, 1972, 85–103
5.
D. E. Knuth, The Art of Computer Programming, Vol. 1, Addison-Wesley, Reading, MA, 1968
6.
L. Lovász, Coverings and coloring of hypergraphs, Proceedings of the Fourth Southeastern Conference on Combinatorics, Graph Theory, and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1973), Utilitas Math., Winnipeg, Man., 1973, 3–12
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Copyright © 1979 © Society for Industrial and Applied Mathematics.
History
Submitted: 15 September 1977
Published online: 31 July 2006
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