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Point-width and Max-CSPs
[article]

2020
*
arXiv
*
pre-print

The two most general hypergraph properties known to ensure tractability of

arXiv:1904.07388v2
fatcat:efn7yqggmzd5tlx26u35xhrkjm
*Max*-*CSPs*, β-acyclicity*and*bounded (incidence) MIM-*width*, are incomparable*and*lead to very different algorithms. ... We introduce the framework of*point*decompositions for hypergraphs*and*use it to derive a new sufficient condition for the tractability of (structurally restricted)*Max*-*CSPs*, which generalises both bounded ... Acknowledgements We would like to thank the anonymous referees of both the conference [9]*and*this full version of the paper. ...##
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Complexity and Approximability of Parameterized MAX-CSPs

2017
*
Algorithmica
*

We consider

doi:10.1007/s00453-017-0310-8
fatcat:ofab3wvgwjg75kehvxwaecmytm
*Max*-*CSPs*with the constraint types*AND*, OR, PARITY,*and*MAJORITY,*and*with various parameters k,*and*we attempt to fully classify them into the following three cases: 1. ... The parameters we investigate are structural measures, such as the treewidth or the clique-*width*of the variable-constraint incidence graph of the*CSP*instance. ... There exists an FPT-AS which, given > 0*and*an instance φ of*MAX*-THRESHOLD, computes a (1 − )-approximate solution*and*runs in time f (fvs * , ) · poly(n), where fvs * is the size of the smallest feedback ...##
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Using Blocks for Constraint Satisfaction
[chapter]

1998
*
Lecture Notes in Computer Science
*

Third, we s h o w that the

doi:10.1007/3-540-49481-2_45
fatcat:qk73xylfr5arrh6f4m7veh43hq
*width*k of a graph is bounded by kmax k kmax + 1 where kmax is the maximum*width*of the block induced subgraphs. fseybold, ... In this paper, we analyze the impact of a further graph concept on*CSPs*: biconnected components (blocks). ... Meyer auf'm Hofe*and*A. Below for reading an earlier version of this paper. We w ould also like to thank Th. Raschle*and*N. Galli for many fruitful comments on graph-related topics. ...##
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New Search Heuristics for Max-CSP
[chapter]

2000
*
Lecture Notes in Computer Science
*

This approach w as presented

doi:10.1007/3-540-45349-0_20
fatcat:wqqojwcmlne3vpvgrl374r23z4
*and*evaluated rst in the context of optimization in belief networks. In this paper we extend this work to*Max*-*CSP*. ... The heuristics are used to guide Branch-*and*-Bound*and*Best-First search, whose performance are compared on a number of constraint problems. ... When formulated as a*Max*-*CSP*problem, its solution satis es all but one constraint. Given the ordering d = A;E;D;C;B of the graph, the*width**and*induced-*width*of the ordered graph is 3. ...##
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Counting Homomorphisms via Hypergraph-Based Structural Restrictions
[chapter]

2012
*
Lecture Notes in Computer Science
*

approaches to combinatorial optimization problems on bounded treewidth graphs, but basing the decompositions on various hypergraph

doi:10.1007/978-3-642-32147-4_34
fatcat:ir6ffm3qzzecfo4qrudun7u6me
*width*measures from the literature on plain*CSPs*. ... Our ability to solve this problem has several applications in artificial intelligence, statistical physics,*and*more recently in guiding backtrack search heuristics to find solutions to*CSPs*[20] . ... The sets C t are called the guards*and*the*width*of (T, (B t ) t∈V (T ) , (C t ) t∈V (T ) ) is*max*{|C t | | t ∈ V (T )}. ...##
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Statistical Modelling of CSP Solving Algorithms Performance
[chapter]

2005
*
Lecture Notes in Computer Science
*

The goal of this work is to try to create a statistical model, based only on easily computable parameters from the

doi:10.1007/11564751_99
fatcat:gogah33qkncftny36zs2decwza
*CSP*problem to predict runtime behaviour of the solving algorithms,*and*let us choose ... For the vertices of the graph, we calculate the node degree statistics (mean, standard deviation, min*and**max*). ... )) vertex degree statistics (mean, stdev,*max*, min)*and*their inverse values (43-58) constraint ((43 − 50))*and*nogood graph ((51 − 58)) vertex clustering coefficient statistics*and*their inverse values ...##
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Optimization-based heuristics for maximal constraint satisfaction
[chapter]

1995
*
Lecture Notes in Computer Science
*

For

doi:10.1007/3-540-60299-2_7
fatcat:njddhkqepvfnjc646dnnqknray
*MAX*-*CSP*, we have developed two heuristics for dynamic variable*and*value ordering, called highest weight*and*lowest support respectively, to be used inside the extended forward checking algorithm ( ... We present a new heuristic approach for maximal constraint satisfaction of overconstrained problems (*MAX*-*CSP*). ... Luisa Romanillos*and*Romero Donlo for their collaboration on writing this paper. ...##
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Streaming and Sketching Complexity of CSPs: A survey
[article]

2022
*
arXiv
*
pre-print

In this survey we describe progress over the last decade or so in understanding the complexity of solving constraint satisfaction problems (

arXiv:2205.02744v1
fatcat:mzmpbufhxbaulf2pkel5htkiii
*CSPs*) approximately in the streaming*and*sketching models of ... After surveying some of the results we give some sketches of the proofs*and*in particular try to explain why there is a tight dichotomy result for sketching algorithms working in subpolynomial space regime ... I want to thank her*and*all other co-authors -Chi-Ning Chou, Sasha Golovnev, Noah Singer, Raghuvansh Saxena, Amirbehshad Shahrasbi*and*Ameya Velingker -for the collaborations*and*discussions which informed ...##
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Research problems

2006
*
Discrete Applied Mathematics
*

has three operations,

doi:10.1016/j.dam.2005.09.001
fatcat:c3n5otty6vagde7ejc3rtlnczi
*and*C*max*denotes the makespan objective. ... Following the standard three-field notation for machine scheduling problems, we denote the problem as RF2| = 3|C*max*, where RF2 indicates a two-machine reentrant flow shop, = 3 describes that each job ... In the*CSP*notation, a knapsack capacity is the*width*of a stock item that should be cut into smaller, customer specified,*widths*. ...##
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Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination

2010
*
Artificial Intelligence
*

The Constraint Satisfaction Problem (

doi:10.1016/j.artint.2010.03.002
fatcat:emwukrqjlfdphcydgqzrdcecsq
*CSP*) is a central generic problem in artificial intelligence. ... We show that the broken-triangle property is conservative (i.e., it is preserved under domain reduction*and*hence under arc consistency operations)*and*that there is a polynomial-time algorithm to determine ... Acknowledgements We would like to thank Chris Jefferson for*pointing*out Theorem 7.6. ...##
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An Extension of Complexity Bounds and Dynamic Heuristics for Tree-Decompositions of CSP
[chapter]

2006
*
Lecture Notes in Computer Science
*

k))), with w the "tree-

doi:10.1007/11889205_62
fatcat:f6moovshdzgc7kiptm3ikwu6qi
*width*" of a*CSP**and*k a constant. ... We consider here the practical efficiency of these approaches by defining five classes of variable orders more*and*more dynamic which guarantee time complexity bounds from O(exp(w + 1)) to O(exp(2(w + ...*CSP*solving,*points*up the importance of a dynamic variable ordering. ...##
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Page 9259 of Mathematical Reviews Vol. , Issue 2001M
[page]

2001
*
Mathematical Reviews
*

We then introduce a new class of tractable

*CSPs*based on the concept of hypertree decomposition recently developed in database theory,*and*analyze the cost of solving*CSPs*having bounded hypertree-*width*... Then a clustering algorithm is created for the*max*-t similarity-relation matrix. Three critical*max*-t compositions of*max*-min,*max*-prod*and**max*-A are compared. ...##
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On Regularity of Max-CSPs and Min-CSPs
[article]

2020
*
arXiv
*
pre-print

In particular, we show that for any

arXiv:2004.08374v1
fatcat:d4wro5qsfrcgdajar6ga3dzd6a
*CSP*Λ, existence of an α approximation algorithm for unweighted regular*Max*-*CSP*Λ implies existence of an α-o(1) approximation algorithm for weighted*Max*-*CSP*Λ in which ... We also give an analogous result for Min-*CSPs*,*and*therefore show that up to arbitrarily small error it is sufficient to conduct the study of approximability of*CSPs*only on regular unweighted instances ... Acknowledgments I am indebted to Per Austrin for*pointing*out the reduction in [22] to me. ...##
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Dynamic algorithms for classes of constraint satisfaction problems

2001
*
Theoretical Computer Science
*

Many fundamental tasks in artiÿcial intelligence

doi:10.1016/s0304-3975(00)00013-x
fatcat:opeg2rqoifhv7m75omvahabreu
*and*in combinatorial optimization can be formulated as a Constraint Satisfaction Problem (*CSP*). ... In general, the problem of ÿnding a solution to a*CSP*is NP-complete, but in some cases it has shown to be polynomially solvable. ... The total time required for maintaining the properties of d-arc consistency*and**width*1 for a binary*CSP*under a sequence of arc insertions*and*pair deletions is O(nk(k + log n)). ...##
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Proof Complexity Meets Algebra

2018
*
ACM Transactions on Computational Logic
*

the proof complexity of the

doi:10.1145/3265985
fatcat:hhamzk75vfhrbj4vuf7eo5lzmm
*CSP*. ... We hence ask for the existence of a natural proof system with good behaviour with respect to reductions*and*simultaneously small size refutations beyond bounded*width*. ... We want to close by*pointing*out that another proof system that can efficiently solve*CSPs*of bounded*width*,*and*that at the same time goes beyond bounded*width*, is the proof system that operates with ...
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