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Randomised Approximation in the Tutte Plane

Published online by Cambridge University Press:  12 September 2008

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

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
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, 3553.Google Scholar
[2]Jerrum, M. and Sinclair, A. (1990) Polynomial-time approximation algorithms for the Ising model (Extended Abstract). Proc. 17th ICALP, Springer-Verlag, 462475.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, 130135.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, 181187.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