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- W4283163752 abstract "Holant problems provide a novel framework to study the complexity of counting problems. It is a refinement to counting constraint satisfaction problems (#CSP) with a more explicit role for the constraint functions. Both graph homomorphisms and #CSP can be viewed as special cases of Holant problems. For approximation algorithms on Holant problems, the attention is focused on proving zero-freeness of the partition functions and establishing fully polynomial-time approximation schemes (FPTAS) using the Taylor expansion method. In this paper, we study the Holant problems defined by a real constraint function satisfying a generalized second-order recurrence. We present fully polynomial-time (deterministic or randomized) approximation schemes for the Holant problems except for a couple of cases. Our algorithms are established in two ways: 1) we construct holographic transformations from the Holant problems to the Ising model, and obtain the algorithms using the approaches with respect to the Ising model; 2) we prove the zero-freeness of the Holant problems, and present an algorithm based on the Taylor expansion method. In addition, for most of the other cases, there exist approximation-preserving reductions between the Holant problems and the problem of counting perfect matchings, which is a central open problem in approximate counting." @default.
- W4283163752 created "2022-06-21" @default.
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- W4283163752 date "2022-05-01" @default.
- W4283163752 modified "2023-10-13" @default.
- W4283163752 title "Zero-freeness and approximation of real Boolean Holant problems" @default.
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- W4283163752 doi "https://doi.org/10.1016/j.tcs.2022.03.009" @default.
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