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Approximating partition functions of bounded-degree Boolean counting Constraint Satisfaction Problems [article]

Andreas Galanis, Leslie Ann Goldberg, Kuan Yang
2020 arXiv   pre-print
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting.  ...  Specifically, given a Boolean constraint language Γ and a degree bound Δ, we study the complexity of #CSP_Δ(Γ), which is the problem of counting satisfying assignments to CSP instances with constraints  ...  Introduction Constraint Satisfaction Problems (CSPs), which originated in Artificial Intelligence [21] provide a general framework for modelling decision, counting and approximate counting problems.  ... 
arXiv:1610.04055v3 fatcat:r6ltgsttvbfi7hxs64iiyt7wbi

Approximating Partition Functions of Bounded-Degree Boolean Counting Constraint Satisfaction Problems * †

Andreas Galanis, Leslie Goldberg, Kuan Yang
unpublished
We study the complexity of approximate counting Constraint Satisfaction Problems (#CSPs) in a bounded degree setting.  ...  Specifically, given a Boolean constraint language Γ and a degree bound ∆, we study the complexity of #CSP ∆ (Γ), which is the problem of counting satisfying assignments to CSP instances with constraints  ...  Introduction Constraint Satisfaction Problems (CSPs), which originated in Artificial Intelligence [18] provide a general framework for modelling decision, counting and approximate counting problems.  ... 
fatcat:mtjczinhprexba2e3jtubpfvza

The Constraint Satisfaction Problem: Complexity and Approximability (Dagstuhl Seminar 15301)

Andrei A. Bulatov, Venkatesan Guruswami, Andrei Krokhin, Dániel Marx, Marc Herbstritt
2016 Dagstuhl Reports  
The Dagstuhl Seminar 15301 "The Constraint Satisfaction Problem: Complexity and Approximability" was aimed at bringing together researchers using all the different techniques in the study of the CSP, so  ...  combinatorics, have been used to analyze both the computational complexity and approximabilty of algorithmic tasks related to the constraint satisfaction problem (CSP), as well as the applicability/limitations  ...  Approximating Bounded-Degree Boolean Counting CSPs Leslie Ann Goldberg (University of Oxford, GB) The talk introduced some work on the complexity of approximately counting satisfying assignments of Boolean  ... 
doi:10.4230/dagrep.5.7.22 dblp:journals/dagstuhl-reports/BulatovGKM15 fatcat:lcyvfsxsbzbrfe27irlpxepxoi

The complexity of approximately counting in 2-spin systems on k-uniform bounded-degree hypergraphs

Andreas Galanis, Leslie Ann Goldberg
2015 Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms  
Nevertheless, we show that for every non-trivial symmetric k-ary Boolean function f there exists a degree bound ∆0 so that for all ∆ ≥ ∆0 the following problem is NP-hard: given a k-uniform hypergraph  ...  One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems  ...  The counting constraint satisfaction problem #CSP(Γ) is the problem of computing the CSP partition function Z Γ,I where I is a CSP instance consisting of a set V of variables and a set S 1 of constraints  ... 
doi:10.1137/1.9781611974331.ch34 dblp:conf/soda/GalanisG16 fatcat:5pzrnnozs5cs5gavh5xkbwikja

Constraint satisfaction: a personal perspective [article]

Tomás Feder
2006 Electronic colloquium on computational complexity  
Representative of this logic class is the class CSP of constraint satisfaction problems.  ...  When the general approach to the classification of constraint satisfaction problems is restricted to graphs and digraphs, one finds that the chordality of graphs plays a crucial role both for the structure  ...  the Boolean constraint satisfaction problem in the case where each variable occurs twice, once in each of two sets of allowed constraints.  ... 
dblp:journals/eccc/Feder06 fatcat:hdzo2lc6kzconfuzlooaceyiyi

The Complexity of Approximating Bounded-Degree Boolean #CSP (Extended Abstract) [article]

Martin E. Dyer, Leslie Ann Goldberg, Markus Jalsenius, David Richerby
2010 arXiv   pre-print
We consider the approximate counting problem for Boolean CSPs with bounded-degree instances, for constraint languages containing the two unary constant relations 0 and 1.  ...  For lower degree bounds, additional cases arise in which the complexity is related to the complexity of approximately counting independent sets in hypergraphs.  ...  Our result We consider the complexity of approximately solving Boolean #CSP problems when instances have bounded degree.  ... 
arXiv:1001.4987v2 fatcat:4tpnzyirivbjfglxnj7koxf2ky

Fast counting with tensor networks [article]

Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein
2018 arXiv   pre-print
We introduce tensor network contraction algorithms for the counting of satisfying assignments in constraint satisfaction problems (#CSP).  ...  We then implement numerical heuristics for the solution of general #P-hard counting boolean satisfiability (#SAT) problems, focusing on random instances of #Cubic-Vertex-Cover as a concrete example, and  ...  constraint satisfaction problems using tensor networks.  ... 
arXiv:1805.00475v1 fatcat:3zjofkimarb2xjinhvremrxxwu

Fast counting with tensor networks

Stefanos Kourtis, Claudio Chamon, Eduardo Mucciolo, Andrei Ruckenstein
2019 SciPost Physics  
We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs).  ...  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  ...  Parts of the computational work reported on in this paper was performed on the Shared Computing Cluster, which is administered by Boston University's Research Computing Services.  ... 
doi:10.21468/scipostphys.7.5.060 fatcat:hax47tot4jcsplhzjq5iz5xqyi

Computational Counting (Dagstuhl Seminar 18341)

Ivona Bezáková, Leslie Ann Goldberg, Mark R. Jerrum, Marc Herbstritt
2018 Dagstuhl Reports  
This report documents the program and the outcomes of Dagstuhl Seminar 17341 "Computational Counting".  ...  A total of 43 researchers from all over the world, with interests and expertise in different aspects of computational counting, actively participated in the meeting.  ...  Approximating partition functions of bounded-degree Boolean counting Constraint Satisfaction Problems Kuan Yang (University of Oxford, GB) License Creative Commons BY 3.0 Unported license © Kuan Yang  ... 
doi:10.4230/dagrep.7.8.23 dblp:journals/dagstuhl-reports/BezakovaGJ17 fatcat:yp3oqvgo4fal5lbio5yeqt4uje

The Complexity of Approximating Bounded-Degree Boolean CSP [article]

Martin Dyer, Leslie Ann Goldberg, Markus Jalsenius, David Richerby
2011 arXiv   pre-print
We consider the approximate counting problem for Boolean CSP with bounded-degree instances, for constraint languages containing the two unary constant relations 0 and 1.  ...  For lower degree bounds, additional cases arise, where the complexity is related to the complexity of approximately counting independent sets in hypergraphs.  ...  Our classification of the approximation complexity of bounded-degree Boolean counting CSPs follows, in Section 6.  ... 
arXiv:0907.2663v2 fatcat:wywiy6ybmnfcflztiuajewnrsi

Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function

Alexander D. Scott, Gregory B. Sorkin
2009 ACM Transactions on Algorithms  
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP.  ...  This gives the first polynomial-space exact algorithm more efficient than exhaustive enumeration for the well-studied problems of finding a minimum bisection of a graph, and calculating the partition function  ...  It therefore follows that the partition function Z I * = σ I * (σ) = σ z I(σ) is the generating function for the original constraint satisfaction problem.  ... 
doi:10.1145/1597036.1597049 fatcat:rm2wgsxjcrfn5lkhdeslpkmnjm

Polynomial-Time Approximation of Zero-Free Partition Functions [article]

Penghui Yao, Yitong Yin, Xinyuan Zhang
2022 arXiv   pre-print
in bounded-degree graphs.  ...  In this paper, we give a polynomial-time algorithm for estimating classical and quantum partition functions specified by local Hamiltonians with bounded maximum degree, assuming a zero-free property for  ...  A Boolean-variate constraint satisfaction problem (Boolean CSP) is specified by a Φ = ( , , ), where = ( , ) is a hypergraph and = ( ) ∈ such that each : {0, 1} → ℂ is a Boolean-variate complex-valued  ... 
arXiv:2201.12772v1 fatcat:gse36s7fsbaftnfy7araf4xji4

Counting Problems and Clones of Functions

Andrei A. Bulatov
2009 2009 39th International Symposium on Multiple-Valued Logic  
The Counting Constraint Satisfaction Problem (#CSP for short) provides a powerful yet convenient formalism to express counting problems.  ...  In other cases, such as approximate counting, the connection is weaker, allows one to employ only partial functions and co-clones of the corresponding type. In those cases many problems remain open.  ...  graphs with bounded vertex degree [17, 20] .  ... 
doi:10.1109/ismvl.2009.47 dblp:conf/ismvl/Bulatov09 fatcat:4xtyqeumsvbr3lcnfu4ukzfrsy

Certifying solution geometry in random CSPs: counts, clusters and balance [article]

Jun-Ting Hsieh, Sidhanth Mohanty, Jeff Xu
2021 arXiv   pre-print
An active topic in the study of random constraint satisfaction problems (CSPs) is the geometry of the space of satisfying or almost satisfying assignments as the function of the density, for which a precise  ...  In parallel, there has been a recent flurry of work on refuting random constraint satisfaction problems, via nailing refutation thresholds for spectral and semidefinite programming-based algorithms, and  ...  The partition function can be viewed as a weighted (or "permissive") version of the counting problem.  ... 
arXiv:2106.12710v1 fatcat:54qtuux4yrcm5kenh5nbvstyfa

Solving Set Constraint Satisfaction Problems using ROBDDs

P. J. Hawkins, V. Lagoon, P. J. Stuckey
2005 The Journal of Artificial Intelligence Research  
We also show that the ROBDD-based modeling approach can be extended to the modeling of integer and multiset constraint problems in a straightforward manner.  ...  We demonstrate that the ROBDD-based approach provides unprecedented flexibility in modeling constraint satisfaction problems, leading to performance improvements.  ...  Many of these problems are in the CSPLib library of constraint satisfaction problems (Gent, Walsh, & Selman, 2004) .  ... 
doi:10.1613/jair.1638 fatcat:pdk5pibsrjhdlhkisit2pvzcm4
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