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Randomised Approximation in the Tutte Plane

Published online by Cambridge University Press:  12 September 2008

D. J. A. Welsh
D. J. A. Welsh
Affiliation:
Mathematical Institute and Merton College, University of Oxford
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Abstract

It is shown that unless NP collapses to random polynomial time RP, there can be no fully polynomial randomised approximation scheme for the antiferromagnetic version of the Q-state Potts model.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 137 - 143
Copyright
Copyright © Cambridge University Press 1994

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References

[1]Jaeger, F., Vertigan, D. L. and Welsh, D. J. A. (1990) On the computational complexity of the Jones and Tutte polynomials. Math. Proc. Camb. Phil. Soc. 108, 35–53.Google Scholar
[2]Jerrum, M. and Sinclair, A. (1990) Polynomial-time approximation algorithms for the Ising model (Extended Abstract). Proc. 17th ICALP, Springer-Verlag, 462–475.Google Scholar
[3]Mihail, M. and Winkler, P. (1991) On the number of Eulerian orientations of a graph. Bellcore Technical Memorandum, TM-ARH-018829.Google Scholar
[4]Seymour, P. D. (1981) Nowhere-zero 6-flows. J. Combinatorial Theory (B) 30, 130–135.CrossRefGoogle Scholar
[5]Vertigan, D. L. and Welsh, D. J. A. (1992) The computational complexity of the Tutte plane: the bipartite case. Combinatorics, Probability and Computing 1, 181–187.Google Scholar
[6]Welsh, D. J. A. (1993) Complexity: Knots Colourings and Counting. London Mathematical Society Lecture Note Series 186, Cambridge University Press.Google Scholar