Article

Constraint solving via fractional edge covers

Authors:

Dániel MarxAuthors Info & Claims

SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm

Pages 289 - 298

Published: 22 January 2006 Publication History

Abstract

Many important combinatorial problems can be modelled as constraint satisfaction problems, hence identifying polynomial-time solvable classes of constraint satisfaction problems received a lot of attention. In this paper, we are interested in structural properties that can make the problem tractable. So far, the largest structural class that is known to be polynomial-time solvable is the class of bounded hypertree width instances introduced by Gottlob et al. [20]. Here we identify a new class of polynomial-time solvable instances: those having bounded fractional edge cover number.Combining hypertree width and fractional edge cover number, we then introduce the notion of fractional hypertree width. We prove that constraint satisfaction problems with bounded fractional hypertree width can be solved in polynomial time (provided that a the tree decomposition is given in the input). We also prove that certain parameterized constraint satisfaction, homomorphism, and embedding problems are fixed-parameter tractable on instances having bounded fractional hypertree width.

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Cited By

Deeds KSuciu DBalazinska M(2023)SafeBound: A Practical System for Generating Cardinality BoundsProceedings of the ACM on Management of Data10.1145/35889071:1(1-26)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.1145/3588907
Gottlob GLanzinger MPichler RRazgon I(2021)Complexity Analysis of Generalized and Fractional Hypertree DecompositionsJournal of the ACM10.1145/345737468:5(1-50)Online publication date: 13-Sep-2021
https://dl.acm.org/doi/10.1145/3457374
Olteanu D(2020)The relational data borg is learningProceedings of the VLDB Endowment10.14778/3415478.341557213:12(3502-3515)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.14778/3415478.3415572
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Index Terms

Constraint solving via fractional edge covers
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Combinatorial algorithms
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
    1. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
  2. Randomness, geometry and discrete structures

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cover image ACM Conferences

SODA '06: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm

January 2006

1261 pages

ISBN:0898716055

Sponsors

SIAM Activity Group on Discrete Mathematics
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 22 January 2006

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Overall Acceptance Rate 411 of 1,322 submissions, 31%

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Cited By

Deeds KSuciu DBalazinska M(2023)SafeBound: A Practical System for Generating Cardinality BoundsProceedings of the ACM on Management of Data10.1145/35889071:1(1-26)Online publication date: 30-May-2023
https://dl.acm.org/doi/10.1145/3588907
Gottlob GLanzinger MPichler RRazgon I(2021)Complexity Analysis of Generalized and Fractional Hypertree DecompositionsJournal of the ACM10.1145/345737468:5(1-50)Online publication date: 13-Sep-2021
https://dl.acm.org/doi/10.1145/3457374
Olteanu D(2020)The relational data borg is learningProceedings of the VLDB Endowment10.14778/3415478.341557213:12(3502-3515)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.14778/3415478.3415572
Yolov NCzumaj A(2018)Minor-matching hypertree widthProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3174304.3175282(219-233)Online publication date: 7-Jan-2018
https://dl.acm.org/doi/10.5555/3174304.3175282
Ngo HVan den Bussche JArenas M(2018)Worst-Case Optimal Join AlgorithmsProceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3196959.3196990(111-124)Online publication date: 27-May-2018
https://dl.acm.org/doi/10.1145/3196959.3196990
Fischl WGottlob GPichler RVan den Bussche JArenas M(2018)General and Fractional Hypertree DecompositionsProceedings of the 37th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3196959.3196962(17-32)Online publication date: 27-May-2018
https://dl.acm.org/doi/10.1145/3196959.3196962
Ngo HPorat ERé CRudra A(2018)Worst-case Optimal Join AlgorithmsJournal of the ACM10.1145/318014365:3(1-40)Online publication date: 13-Mar-2018
https://dl.acm.org/doi/10.1145/3180143
Abo Khamis MNgo HSuciu DSallinger EVan den Bussche JGeerts F(2017)What Do Shannon-type Inequalities, Submodular Width, and Disjunctive Datalog Have to Do with One Another?Proceedings of the 36th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3034786.3056105(429-444)Online publication date: 9-May-2017
https://dl.acm.org/doi/10.1145/3034786.3056105
Koutris PMilo TRoy SSuciu D(2017)Answering Conjunctive Queries with InequalitiesTheory of Computing Systems10.1007/s00224-016-9684-261:1(2-30)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1007/s00224-016-9684-2
Khamis MNgo HRé CRudra A(2016)Joins via Geometric ResolutionsACM Transactions on Database Systems10.1145/296710141:4(1-45)Online publication date: 8-Nov-2016
https://dl.acm.org/doi/10.1145/2967101
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