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:
-
- Boston University
- University of Central Florida
- Publication Date:
- Research Org.:
- Boston Univ., MA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1574034
- Alternate Identifier(s):
- OSTI ID: 1800383
- Grant/Contract Number:
- FG02-06ER46316
- Resource Type:
- Published Article
- Journal Name:
- SciPost Physics
- Additional Journal Information:
- Journal Name: SciPost Physics Journal Volume: 7 Journal Issue: 5; Journal ID: ISSN 2542-4653
- Publisher:
- Stichting SciPost
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Physics
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. https://doi.org/10.21468/SciPostPhys.7.5.060
Kourtis, Stefanos, Chamon, Claudio, Mucciolo, Eduardo, and Ruckenstein, Andrei. Tue .
"Fast counting with tensor networks". Netherlands. https://doi.org/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},
number = 5,
volume = 7,
place = {Netherlands},
year = {Tue Nov 12 00:00:00 EST 2019},
month = {Tue Nov 12 00:00:00 EST 2019}
}
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https://doi.org/10.21468/SciPostPhys.7.5.060
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