An approximation algorithm for the partial vertex cover problem in hypergraphs

Mourad El Ouali (), Helena Fohlin () and Anand Srivastav ()
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Mourad El Ouali: University of Kiel
Helena Fohlin: Linköping University
Anand Srivastav: University of Kiel

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 24, 846-864

Abstract: Abstract Let $$\mathcal {H}=(V,\mathcal {E})$$ H = ( V , E ) be a hypergraph with set of vertices $$V, n:=|V|$$ V , n : = | V | and set of (hyper-)edges $$\mathcal {E}, m:=|\mathcal {E}|$$ E , m : = | E | . Let $$l$$ l be the maximum size of an edge, $$\varDelta $$ Δ be the maximum vertex degree and $$D$$ D be the maximum edge degree. The $$k$$ k -partial vertex cover problem in hypergraphs is the problem of finding a minimum cardinality subset of vertices in which at least $$k$$ k hyperedges are incident. For the case of $$k=m$$ k = m and constant $$l$$ l it known that an approximation ratio better than $$l$$ l cannot be achieved in polynomial time under the unique games conjecture (UGC) (Khot and Ragev J Comput Syst Sci, 74(3):335–349, 2008), but an $$l$$ l -approximation ratio can be proved for arbitrary $$k$$ k (Gandhi et al. J Algorithms, 53(1):55–84, 2004). The open problem in this context has been to give an $$\alpha l$$ α l -ratio approximation with $$\alpha

Keywords: Combinatorial optimization; Approximation algorithms; Hypergraphs; Vertex cover; Probabilistic methods (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-014-9793-2

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