ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
ACM Transactions on Mathematical Software (TOMS)
Edge-selection heuristics for computing Tutte polynomials
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
A space-time tradeoff for permutation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Exponential time complexity of the permanent and the Tutte polynomial
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Covering and packing in linear space
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The complexity of the cover polynomials for planar graphs of bounded degree
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Deterministic parameterized connected vertex cover
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Information Processing Letters
Approximating the Tutte polynomial of a binary matroid and other related combinatorial polynomials
Journal of Computer and System Sciences
Fast monotone summation over disjoint sets
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Space---Time tradeoffs for subset sum: an improved worst case algorithm
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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The deletion–contraction algorithm is perhapsthe most popular method for computing a host of fundamental graph invariants such as the chromatic, flow, and reliability polynomials in graph theory, the Jones polynomial of an alternating link in knot theory, and the partition functions of the models of Ising, Potts, and Fortuin–Kasteleyn in statistical physics. Prior to this work, deletion–contraction was also the fastest known general-purpose algorithm for these invariants, running in time roughly proportional to the number of spanning trees in the input graph.Here, we give a substantially faster algorithm that computes the Tutte polynomial—and hence, all the aforementioned invariants and more—of an arbitrary graph in time within a polynomial factor of the number of connected vertex sets. The algorithm actually evaluates a multivariate generalization of the Tutte polynomial by making use of an identity due to Fortuin and Kasteleyn. We also provide a polynomial-space variant of the algorithm and give an analogous result for Chung and Graham's cover polynomial.