Online maximum k-coverage

Authors:
G. Ausiello;N. Boria;A. Giannakos;G. Lucarelli;V. Th. Paschos
Affiliations:
Dipartimento di Informatica e Sistemistica, Universití degli Studi di Roma "La Sapienza", Italy;Paris Sciences et Lettres Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France;Paris Sciences et Lettres Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France;Paris Sciences et Lettres Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France;Paris Sciences et Lettres Research University, Université Paris-Dauphine, LAMSADE, CNRS UMR 7243, France and Institut Universitaire de France, France
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

We study an online model for the maximum k-vertex-coverage problem, in which, given a graph G=(V,E) and an integer k, we seek a subset A@?V such that |A|=k and the number of edges covered by A is maximized. In our model, at each step i, a new vertex v"i is released, and we have to decide whether we will keep it or discard it. At any time of the process, only k vertices can be kept in memory; if at some point the current solution already contains k 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 12-competitive ratio. We next settle a set version of the problem, called the maximum k-(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 k.