LATIN 2008: Theoretical Informatics
Volume 4957 of the series Lecture Notes in Computer Science pp 423-435
Approximating Minimum-Power Degree and Connectivity Problems
- Guy KortsarzAffiliated withRutgers University, Camden
- , Vahab S. MirrokniAffiliated withMicrosoft Research
- , Zeev NutovAffiliated withThe Open University of Israel, Raanana
- , Elena TsankoAffiliated withIBM, Haifa
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(log4
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,
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 \(3\frac{2}{3}\)-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.
- Title
- Approximating Minimum-Power Degree and Connectivity Problems
- Book Title
- LATIN 2008: Theoretical Informatics
- Book Subtitle
- 8th Latin American Symposium, Búzios, Brazil, April 7-11, 2008. Proceedings
- Pages
- pp 423-435
- Copyright
- 2008
- DOI
- 10.1007/978-3-540-78773-0_37
- Print ISBN
- 978-3-540-78772-3
- Online ISBN
- 978-3-540-78773-0
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- 4957
- Series ISSN
- 0302-9743
- Publisher
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Topics
- Industry Sectors
- eBook Packages
- Editors
- Authors
-
- Guy Kortsarz (1)
- Vahab S. Mirrokni (2)
- Zeev Nutov (3)
- Elena Tsanko (4)
- Author Affiliations
-
- 1. Rutgers University, Camden,
- 2. Microsoft Research,
- 3. The Open University of Israel, Raanana,
- 4. IBM, Haifa,
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