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.
|Title of host publication||2008 IEEE 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS)|
|Publication status||Published - 2008|
|Event||2008 IEEE 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS) - Philadelphia, PA, United States|
Duration: 25 Oct 2008 → 28 Oct 2008
Conference number: 49
|Conference||2008 IEEE 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS)|
|Period||25/10/2008 → 28/10/2008|