an:00006335
Zbl 0747.57006
Jaeger, Fran??ois; Vertigan, D. L.; Welsh, D. J. A.
On the computational complexity of the Jones and Tutte polynomials
EN
Math. Proc. Camb. Philos. Soc. 108, No. 1, 35-53 (1990).
00155989
1990
j
57M25 57M15 68Q25 68R10
computing the Jones polynomial of a link; Alexander-Conway polynomial; \(\#P\)-hard; Tutte polynomial of a matroid
From the introduction: ``The original problem motivating this paper is to decide whether or not computing the Jones polynomial of a link is, in general, a feasible computation. To put this question into perspective, it is well known that computation of the Alexander-Conway polynomial of a link is `easy' (that is, can be done in time polynomial in the size of the input) being just the expansion of a one-variable determinant, but that the computations of the Homfly and Kauffman polynomials of a link are \(NP\)-hard. The Jones polynomial could be regarded as lying somewhere between the Alexander-Conway polynomial and these two other link polynomials in terms of computational difficulty. However, as we shall see, it turns out to be computationally intractable in a very strong sense, even for the special case of alternating links.'' ``We show that determining the Jones polynomial of an alternating link is \(\#P\)-hard. This is a special case of a wide range of results on the general intractability of the evaluation of the Tutte polynomial of a matroid''.
B.Zimmermann (Trieste)