Abstract
An instance of the maximum coverage problem is given by a set of weighted ground elements and a cost weighted family of subsets of the ground element set. The goal is to select a subfamily of total cost of at most that of a given budget maximizing the weight of the covered elements. We formulate the problem on graphs: In this situation the set of ground elements is speci.ed by the nodes of a graph, while the family of covering sets is restricted to connected subgraphs. We show that on general graphs the problem is polynomial time solvable if restricted to sets of size at most 2, but becomes NP-hard if sets of size 3 are permitted. On trees, we prove polynomial time solvability if each node appears in a fixed number of sets. In contrast, if vertices are allowed to appear an unbounded number of times, the problem is NP-hard even on stars. We finally give a polynomial time algorithm for the special case where a star is covered by paths.
Research supported by the German Science Foundation (DFG, grant GR 883/10)
Research supported by NSF Grant CCR-97-34936
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Krumke, S.O., Marathe, M.V., Poensgen, D., Ravi, S., Wirth, HC. (2002). Budgeted Maximum Graph Coverage. In: Goos, G., Hartmanis, J., van Leeuwen, J., Kučera, L. (eds) Graph-Theoretic Concepts in Computer Science. WG 2002. Lecture Notes in Computer Science, vol 2573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36379-3_28
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DOI: https://doi.org/10.1007/3-540-36379-3_28
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