Computer Science > Data Structures and Algorithms
[Submitted on 8 May 2019 (v1), last revised 18 Feb 2020 (this version, v3)]
Title:Zeros and approximations of Holant polynomials on the complex plane
View PDFAbstract:We present fully polynomial approximation schemes for a broad class of Holant problems with complex edge weights, which we call Holant polynomials. We transform these problems into partition functions of abstract combinatorial structures known as polymers in statistical physics. Our method involves establishing zero-free regions for the partition functions of polymer models and using the most significant terms of the cluster expansion to approximate them.
Results of our technique include new approximation and sampling algorithms for a diverse class of Holant polynomials in the low-temperature regime and approximation algorithms for general Holant problems with small signature weights. Additionally, we give randomised approximation and sampling algorithms with faster running times for more restrictive classes. Finally, we improve the known zero-free regions for a perfect matching polynomial.
Submission history
From: Philipp Fischbeck [view email][v1] Wed, 8 May 2019 16:25:00 UTC (19 KB)
[v2] Thu, 11 Jul 2019 12:45:50 UTC (33 KB)
[v3] Tue, 18 Feb 2020 13:22:46 UTC (45 KB)
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