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Point-width and Max-CSPs [article]

Clement Carbonnel, Miguel Romero, Stanislav Zivny
2020 arXiv   pre-print
The two most general hypergraph properties known to ensure tractability of 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.  ... 
arXiv:1904.07388v2 fatcat:efn7yqggmzd5tlx26u35xhrkjm

Complexity and Approximability of Parameterized MAX-CSPs

Holger Dell, Eun Jung Kim, Michael Lampis, Valia Mitsou, Tobias Mömke
2017 Algorithmica  
We consider 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  ... 
doi:10.1007/s00453-017-0310-8 fatcat:ofab3wvgwjg75kehvxwaecmytm

Using Blocks for Constraint Satisfaction [chapter]

B. Seybold, F. Metzger, G. Ogan, K. Simon
1998 Lecture Notes in Computer Science  
Third, we s h o w that the 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.  ... 
doi:10.1007/3-540-49481-2_45 fatcat:qk73xylfr5arrh6f4m7veh43hq

New Search Heuristics for Max-CSP [chapter]

Kalev Kask
2000 Lecture Notes in Computer Science  
This approach w as presented 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.  ... 
doi:10.1007/3-540-45349-0_20 fatcat:wqqojwcmlne3vpvgrl374r23z4

Counting Homomorphisms via Hypergraph-Based Structural Restrictions [chapter]

Tommy Färnqvist
2012 Lecture Notes in Computer Science  
approaches to combinatorial optimization problems on bounded treewidth graphs, but basing the decompositions on various hypergraph 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 )}.  ... 
doi:10.1007/978-3-642-32147-4_34 fatcat:ir6ffm3qzzecfo4qrudun7u6me

Statistical Modelling of CSP Solving Algorithms Performance [chapter]

Ramon Béjar, Cèsar Fernández, Carles Mateu
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 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  ... 
doi:10.1007/11564751_99 fatcat:gogah33qkncftny36zs2decwza

Optimization-based heuristics for maximal constraint satisfaction [chapter]

Javier Larrosa, Pedro Meseguer
1995 Lecture Notes in Computer Science  
For 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.  ... 
doi:10.1007/3-540-60299-2_7 fatcat:njddhkqepvfnjc646dnnqknray

Streaming and Sketching Complexity of CSPs: A survey [article]

Madhu Sudan
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 (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  ... 
arXiv:2205.02744v1 fatcat:mzmpbufhxbaulf2pkel5htkiii

Research problems

2006 Discrete Applied Mathematics  
has three operations, 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.  ... 
doi:10.1016/j.dam.2005.09.001 fatcat:c3n5otty6vagde7ejc3rtlnczi

Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination

Martin C. Cooper, Peter G. Jeavons, András Z. Salamon
2010 Artificial Intelligence  
The Constraint Satisfaction Problem (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.  ... 
doi:10.1016/j.artint.2010.03.002 fatcat:emwukrqjlfdphcydgqzrdcecsq

An Extension of Complexity Bounds and Dynamic Heuristics for Tree-Decompositions of CSP [chapter]

Philippe Jégou, Samba Ndojh Ndiaye, Cyril Terrioux
2006 Lecture Notes in Computer Science  
k))), with w the "tree-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.  ... 
doi:10.1007/11889205_62 fatcat:f6moovshdzgc7kiptm3ikwu6qi

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.  ... 

On Regularity of Max-CSPs and Min-CSPs [article]

Aleksa Stankovic
2020 arXiv   pre-print
In particular, we show that for any 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.  ... 
arXiv:2004.08374v1 fatcat:d4wro5qsfrcgdajar6ga3dzd6a

Dynamic algorithms for classes of constraint satisfaction problems

Daniele Frigioni, Alberto Marchetti-Spaccamela, Umberto Nanni
2001 Theoretical Computer Science  
Many fundamental tasks in artiÿcial intelligence 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)).  ... 
doi:10.1016/s0304-3975(00)00013-x fatcat:opeg2rqoifhv7m75omvahabreu

Proof Complexity Meets Algebra

Albert Atserias, Joanna Ochremiak
2018 ACM Transactions on Computational Logic  
the proof complexity of the 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  ... 
doi:10.1145/3265985 fatcat:hhamzk75vfhrbj4vuf7eo5lzmm
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