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We consider the b-matching problem in a hypergraph on n vertices and edge cardinality bounded by ℓ. Oblivious greedy algorithms achieve approximations of $(\sqrt{n}+1)^{-1}$ and (ℓ + 1)− 1 independently of b (Krysta 2005). Randomized rounding achieves constant-factor approximations of 1 − ε for large b, namely b = Ω(ε− 2, ln n), (Srivastav and Stangier 1997). Hardness of approximation...
Let H=(V,E) be a hypergraph with vertex set V and edge set E, where n:=|V| and m:=|E|. Let l be the maximum size of an edge and Δ be the maximum vertex degree. A hitting set (or vertex cover) in H is a subset of V in which all edges are incident. The hitting set problem is to find a hitting set of minimum cardinality. It is known that an approximation ratio of l can be achieved easily. On the other...
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