The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Approximation Algorithms for the Vertex Cover Problem in Graphs and Hypergraphs
SIAM Journal on Computing
Covering Problems with Hard Capacities
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
On the multi-radius cover problem
Information Processing Letters
Rounding to an integral program
Operations Research Letters
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Let G = (V,E) be a graph with a non-negative edge length lu,v for every (u,v) ∈ E. The vertices of G represent locations at which transmission stations are positioned, and each edge of G represents a continuum of demand points to which we should transmit. A station located at v is associated with a set Rv of allowed transmission radii, where the cost of transmitting to radius r ∈ Rv is given by cv(r). The multi-radius cover problem asks to determine for each station a transmission radius, such that for each edge (u,v) ∈ E the sum of the radii in u and v is at least lu,v, and such that the total cost is minimized. In this paper we present LP-rounding and primal-dual approximation algorithms for discrete and continuous variants of multi-radius cover. Our algorithms cope with the special structure of the problems we consider by utilizing greedy rounding techniques and a novel method for constructing primal and dual solutions.