## Abstract

Power optimization is a central issue in wireless network design. Given a (possibly directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of a graph is the sum of the powers of its nodes. Motivated by applications in wireless networks, we consider several fundamental undirected network design problems under the power minimization criteria. Given a graph with edge costs and degree requirements {r(v):v ∈ V}, the Minimum-Power Edge-Multi-Cover ( ) problem is to find a minimum-power subgraph of so that the degree of every node v is at least r(v). We give an O(logn)-approximation algorithms for , improving the previous ratio O(log^{4} n) of [11]. This is used to derive an O(logn + α)-approximation algorithm for the undirected Minimum-Power k -Connected Subgraph ( ) problem, where is the best known ratio for the min-cost variant of the problem (currently, = O(In k) for n ≥ 2k^{2} and otherwise). Surprisingly, it shows that the min-power and the min-cost versions of the k -Connected Subgraph problem are equivalent with respect to approximation, unless the min-cost variant admits an o(logn)-approximation, which seems to be out of reach at the moment. We also improve the best known approximation ratios for small requirements. Specifically, we give a 3/2-approximation algorithm for with r(v) ∈ {0,1}, improving over the 2-approximation by [11], and a -approximation for the minimum-power 2-Connected and 2-Edge-Connected Subgraph problems, improving the 4-approximation by [4]. Finally, we give a 4 r _{max} -approximation algorithm for the undirected Minimum-Power Steiner Network ( ) problem: find a minimum-power subgraph that contains r(u,v) pairwise edge-disjoint paths for every pair u,v of nodes.

Original language | English |
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Title of host publication | LATIN 2008 |

Subtitle of host publication | Theoretical Informatics - 8th Latin American Symposium, Proceedings |

Publisher | Springer Verlag |

Pages | 423-435 |

Number of pages | 13 |

ISBN (Print) | 3540787720, 9783540787723 |

DOIs | |

State | Published - 2008 |

Event | 8th Latin American Theoretical INformatics Symposium, LATIN 2008 - Buzios, Brazil Duration: 7 Apr 2008 → 11 Apr 2008 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4957 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 8th Latin American Theoretical INformatics Symposium, LATIN 2008 |
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Country/Territory | Brazil |

City | Buzios |

Period | 7/04/08 → 11/04/08 |