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The b-Matching Problem in Hypergraphs: Hardness and Approximability
Computer Science Institute, Christian-Albrechts-University of Kiel, Germany.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)In: COCOA 2012: Combinatorial Optimization and Applications / [ed] Guohui Lin, Berlin-Heidelberg: Springer Berlin-Heidelberg , 2012, p. 200-211Conference paper, Published paper (Refereed)
##### Abstract [en]

In this paper we analyze the maximum cardinality b-matching problem in l-uniform hypergraphs with respect to the complexity class Max-Snp, where b-matching is defined as follows: for given b ∈ ℕ and a hypergraph H=(V,E)" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">H=(V,E)H=(V,E) a subset Mb&#x2286;E" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">Mb⊆EMb⊆E with maximum cardinality is sought so that no vertex is contained in more than b hyperedges of M b . We show that if the maximum degree of the vertices is bounded by a constant B ∈ ℕ , this problem has no approximation scheme, unless P=NP" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">P=NPP=NP. This result generalizes a result of Kann from b = 1 to the case that b ∈ ℕ with 0&lt;b&#x2264;B3" role="presentation" style="box-sizing: border-box; display: inline-table; line-height: normal; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">0<b≤B30<b≤B3. Furthermore, we extend a result of Srivastav and Stangier, who gave an approximation algorithm for the unweighted b-matching problem.

##### Place, publisher, year, edition, pages
Berlin-Heidelberg: Springer Berlin-Heidelberg , 2012. p. 200-211
##### Series
Lecture Notes in Computer Science ; 7402
##### Keywords [en]
Hypergraphs, matching, L-reduction, Boolean satisfiability, randomized rounding, MAX-SNP-hardness
##### National Category
Discrete Mathematics
##### Identifiers
Libris ID: 13537064ISBN: 978-3-642-31770-5 (print)OAI: oai:DiVA.org:umu-84483DiVA, id: diva2:684499
##### Conference
6th International Conference, COCOA 2012, Banff, AB, Canada, August 5-9, 2012
Available from: 2014-01-08 Created: 2014-01-08 Last updated: 2019-04-24Bibliographically approved

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Jäger, Gerold

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Jäger, Gerold
##### By organisation
Department of Mathematics and Mathematical Statistics
##### On the subject
Discrete Mathematics

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Cite
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