Computing the Tutte polynomial of a graph of moderate size
The problem of computing the Tutte polynomial of a graph is #P-hard in general, and any known algorithm takes exponential time at least. This paper presents a new algorithm by exploiting a fact that many 2-isomorphic minors appear in the process of computation. The complexity of the algorithm is analyzed in terms of Bell numbers and Catalan numbers. This algorithm enables us to compute practically the Tutte polynomial of any graph with at most 14 vertices and 91 edges, and that of a planar graph such as 12×12 lattice graph with 144 vertices and 264 edges.
- Akers, S. B. (1978) Binary Decision Diagrams. IEEE Trans. on Computers C-27: pp. 509-516
- N. Alon, A. Frieze and D. J. A. Welsh: Polynomial Time Randomised Approximation Schemes for the Tutte Polynomial of Dense Graphs. Proceedings of the IEEE Annual Symposium on Foundations of Computer Science, 1994, pp.24–35.
- Bryant, R. E. (1986) Graph Based Algorithms for Boolean Function Manipulation. IEEE Trans. on Computers C-35: pp. 677-691
- D. R. Karger. A Randomized Fully Polynomial Time Approximation Scheme for the All Terminal Network Reliability Problem. Proceedings of the 27th Annual ACM Symposium on Theory of Computing, 1995, pp.11–17.
- A. Shioura, A. Tamura and T. Uno: An Optimal Algorithm for Scanning All Spanning Trees of Undirected Graphs. SIAM Journal on Computing, to appear.
- S. Tani: An Extended Framework of Ordered Binary Decision Diagrams for Combinatorial Graph Problems. Master's Thesis, Department of Information Science, University of Tokyo, 1995.
- Thistlethwaite, M. B. (1987) A Spanning Tree Expansion of the Jones Polynomial. Topology 26: pp. 297-309
- Tutte, W. T. (1954) A Contribution to the Theory of Chromatic Polynomials. Canadian Journal of Mathematics 6: pp. 80-91
- D. J. A. Welsh: Complexity: Knots, Colourings and Counting. London Mathematical Society Lecture Note Series, Vol.186, Cambridge University Press, 1993.
- H. S. Wilf: Algorithms and Complexity. Prentice-Hall, 1986.
- Computing the Tutte polynomial of a graph of moderate size
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- Algorithms and Computations
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- 6th International Symposium, ISAAC '95 Cairns, Australia, December 4–6, 1995 Proceedings
- pp 224-233
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- Lecture Notes in Computer Science
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- Springer Berlin Heidelberg
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