## 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.

Original language | English |
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Pages (from-to) | 24-35 |

Number of pages | 12 |

Journal | Lecture Notes in Computer Science |

Volume | 3608 |

DOIs | |

State | Published - 2005 |

Externally published | Yes |

Event | 9th International Workshop on Algorithms and Data Structures, WADS 2005 - Waterloo, Canada Duration: 15 Aug 2005 → 17 Aug 2005 |

## ASJC Scopus subject areas

- Theoretical Computer Science
- General Computer Science