Dichotomy result on 3-regular bipartite non-negative functions

We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function f=[x0,x1,x2,x3], we prove that the bipartite Holant problem Holant(f|(=3)) is either computable in polynomial time or #P-hard. T...

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Bibliographic Details
Published inTheoretical computer science Vol. 949; p. 113745
Main Authors Fan, Austen Z., Cai, Jin-Yi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 09.03.2023
Subjects
Bipartite graph
Dichotomy theorem
Holant problem
Dichotomy theorem
Holant problem
Bipartite graph
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Summary:We prove a complexity dichotomy theorem for a class of Holant problems on 3-regular bipartite graphs. Given an arbitrary nonnegative weighted symmetric constraint function f=[x0,x1,x2,x3], we prove that the bipartite Holant problem Holant(f|(=3)) is either computable in polynomial time or #P-hard. The dichotomy criterion on f is explicit.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2023.113745