SciPost Submission Page
Fast counting with tensor networks
by Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Stefanos Kourtis |
| Submission information | |
|---|---|
| Preprint Link: | scipost_201908_00005v1 (pdf) |
| Date submitted: | Aug. 5, 2019, 2 a.m. |
| Submitted by: | Stefanos Kourtis |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2019-10-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_201908_00005v1, delivered 2019-10-17, doi: 10.21468/SciPost.Report.1238
Strengths
1- The paper is well-organized and well-written. 2- The paper is perfectly understandable for the tensor-network expert who is not familiar with CSPs, and (I assume) the other way around. 3- The benchmarks or "numerical experiments" are sound and the comparison with other state-of-the-art methods is convincing.
Weaknesses
Report
Requested changes
none