Abstract (EN)

We study an online model for the maximumView the MathML source-vertex-coverage problem, in which, given a graph G=(V,E) and an integer View the MathML source, we seek a subset A⊆V such that View the MathML source and the number of edges covered by A is maximized. In our model, at each step i, a new vertex vi is released, and we have to decide whether we will keep it or discard it. At any time of the process, only View the MathML source vertices can be kept in memory; if at some point the current solution already contains View the MathML source vertices, any inclusion of a new vertex in the solution must entail the definite deletion of another vertex of the current solution (a vertex not kept when released is definitely deleted). We propose algorithms for several natural classes of graphs (mainly regular and bipartite), improving on an easy View the MathML source-competitive ratio. We next settle a set version of the problem, called the maximumView the MathML source-(set)-coverage problem. For this problem, we present an algorithm that improves upon former results for the same model for small and moderate values of View the MathML source.