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In cooperative games, a key question is to find a division of payoffs to coalition members in a fair manner. Nucleolus is one of such solution concepts that provides a stable solution for the grand coalition. We study the computation of the nucleolus of a number of cooperative games, including fractional matching games and fractional edge cover games on general weighted graphs, as well as verte...

Motivated by the need for succinct representations of all “small” transversals (or hitting sets) of a hypergraph of fixed rank, we study the complexity of computing such a representation. Next, the existence of a minimal hitting set of at least a given size arises as a subproblem. We give one algorithm for hypergraphs of any fixed rank, and we largely improve an earlier algorithm (by H. Fernau,...

Article history: Received 21 October 2013 Received in revised form 30 September 2014 Accepted 21 October 2014 Available online 28 October 2014 Communicated by G. Ausiello

Given a tree and a set of paths in the tree, the problem of finding a minimum number of paths from the given path set to cover all the vertices in the tree is investigated in the paper. To distinguish from the classical path cover problem, such an optimization problem is referred to as vertex covering by paths. The problem and its edge variant, edge covering by paths, find applications in machi...

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We consider various hitting and piercing problems for the family of axis-parallel rectangles induced by a point set. Selection Lemmas on induced objects are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection Lemma type results typically bound the maximum number...