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• W2474151873 abstract "In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach works for the Tutte polynomial and independence polynomial, as well as partition functions of complex-valued spin and edge-coloring models. More specifically, we define a large class of graph polynomials $mathcal C$ and show that if $pin cal C$ and there is a disk $D$ centered at zero in the complex plane such that $p(G)$ does not vanish on $D$ for all bounded degree graphs $G$, then for each $z$ in the interior of $D$ there exists a deterministic polynomial-time approximation algorithm for evaluating $p(G)$ at $z$. This gives an explicit connection between absence of zeros of graph polynomials and the existence of efficient approximation algorithms, allowing us to show new relationships between well-known conjectures. Our work builds on a recent line of work initiated by. Barvinok, which provides a new algorithmic approach besides the existing Markov chain Monte Carlo method and the correlation decay method for these types of problems." @default.
• W2474151873 created "2016-07-22" @default.
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• W2474151873 date "2017-01-01" @default.
• W2474151873 modified "2023-10-18" @default.
• W2474151873 title "Deterministic Polynomial-Time Approximation Algorithms for Partition Functions and Graph Polynomials" @default.
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• W2474151873 doi "https://doi.org/10.1137/16m1101003" @default.
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