Abstract
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 \(\mathcal{H}=(V,\mathcal{E})\) a subset \(M_{b}\subseteq \mathcal{E}\) 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 \(\mathcal{P}=\mathcal{NP}\). This result generalizes a result of Kann from b = 1 to the case that b ∈ ℕ with \( 0 < b\leq \frac{B}{3}\). Furthermore, we extend a result of Srivastav and Stangier, who gave an approximation algorithm for the unweighted b-matching problem.
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El Ouali, M., Jäger, G. (2012). The b-Matching Problem in Hypergraphs: Hardness and Approximability. In: Lin, G. (eds) Combinatorial Optimization and Applications. COCOA 2012. Lecture Notes in Computer Science, vol 7402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31770-5_18
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DOI: https://doi.org/10.1007/978-3-642-31770-5_18
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