#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region
Computational Complexity
2016-05-30 v4
Abstract
Counting independent sets on bipartite graphs (#BIS) is considered a canonical counting problem of intermediate approximation complexity. It is conjectured that #BIS neither has an FPRAS nor is as hard as #SAT to approximate. We study #BIS in the general framework of two-state spin systems on bipartite graphs. We define two notions, nearly-independent phase-correlated spins and unary symmetry breaking. We prove that it is #BIS-hard to approximate the partition function of any 2-spin system on bipartite graphs supporting these two notions. As a consequence, we classify the complexity of approximating the partition function of antiferromagnetic 2-spin systems on bounded-degree bipartite graphs.
Keywords
Cite
@article{arxiv.1311.4451,
title = {#BIS-Hardness for 2-Spin Systems on Bipartite Bounded Degree Graphs in the Tree Nonuniqueness Region},
author = {Jin-Yi Cai and Andreas Galanis and Leslie Ann Goldberg and Heng Guo and Mark Jerrum and Daniel Stefankovic and Eric Vigoda},
journal= {arXiv preprint arXiv:1311.4451},
year = {2016}
}