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Title: Fast counting with tensor networks

Abstract

We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.

Authors:
 [1];  [1];  [2];  [1]
  1. Boston University
  2. University of Central Florida
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1574034
Grant/Contract Number:  
FG02-06ER46316
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 7 Journal Issue: 5; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, and Ruckenstein, Andrei. Fast counting with tensor networks. Netherlands: N. p., 2019. Web. doi:10.21468/SciPostPhys.7.5.060.
Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, & Ruckenstein, Andrei. Fast counting with tensor networks. Netherlands. doi:10.21468/SciPostPhys.7.5.060.
Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, and Ruckenstein, Andrei. Tue . "Fast counting with tensor networks". Netherlands. doi:10.21468/SciPostPhys.7.5.060.
@article{osti_1574034,
title = {Fast counting with tensor networks},
author = {Kourtis, Stefanos and Chamon, Claudio and Mucciolo, Eduardo and Ruckenstein, Andrei},
abstractNote = {We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #P-hard counting boolean satisfiability (#SAT) problems, namely monotone #1-in-3SAT and #Cubic-Vertex-Cover, and find that they outperform state-of-the-art solvers by a significant margin.},
doi = {10.21468/SciPostPhys.7.5.060},
journal = {SciPost Physics Proceedings},
number = 5,
volume = 7,
place = {Netherlands},
year = {2019},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.7.5.060

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