Abstract
Let G = (V,E) be a graph with a non-negative edge length l u,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 R v of allowed transmission radii, where the cost of transmitting to radius r ∈ R v is given by c v (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 l u,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.
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© 2005 Springer-Verlag Berlin Heidelberg
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Hassin, R., Segev, D. (2005). The Multi-radius Cover Problem. In: Dehne, F., López-Ortiz, A., Sack, JR. (eds) Algorithms and Data Structures. WADS 2005. Lecture Notes in Computer Science, vol 3608. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11534273_4
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DOI: https://doi.org/10.1007/11534273_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28101-6
Online ISBN: 978-3-540-31711-1
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