TY - JOUR

T1 - Approximating minimum-power edge-covers and 2, 3-connectivity

AU - Kortsarz, Guy

AU - Nutov, Zeev

PY - 2009/4/28

Y1 - 2009/4/28

N2 - Given a graph with edge costs, 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. The Minimum-Power Edge-Cover (MPEC) problem is: given a graph G = (V, E) with edge costs {c (e) : e ∈ E} and a subset S ⊆ V of nodes, find a minimum-power subgraph H of G containing an edge incident to every node in S. We give a 3/2-approximation algorithm for MPEC, improving over the 2-approximation by [M.T. Hajiaghayi, G. Kortsarz, V.S. Mirrokni, Z. Nutov, Power optimization for connectivity problems, Mathematical Programming 110 (1) (2007) 195-208]. For the Min-Powerk-Connected Subgraph (MP k CS) problem we obtain the following results. For k = 2 and k = 3, we improve the previously best known ratios of 4 [G. Calinescu, P.J. Wan, Range assignment for biconnectivity and k-edge connectivity in wireless ad hoc networks, Mobile Networks and Applications 11 (2) (2006) 121-128] and 7 [M.T. Hajiaghayi, G. Kortsarz, V.S. Mirrokni, Z. Nutov, Power optimization for connectivity problems, Mathematical Programming 110 (1) (2007) 195-208] to 3 frac(2, 3) and 5 frac(2, 3), respectively. Finally, we give a 4 rmax-approximation algorithm for the Minimum-Power Steiner Network (MPSN) problem: find a minimum-power subgraph that contains r (u, v) pairwise edge-disjoint paths for every pair u, v of nodes.

AB - Given a graph with edge costs, 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. The Minimum-Power Edge-Cover (MPEC) problem is: given a graph G = (V, E) with edge costs {c (e) : e ∈ E} and a subset S ⊆ V of nodes, find a minimum-power subgraph H of G containing an edge incident to every node in S. We give a 3/2-approximation algorithm for MPEC, improving over the 2-approximation by [M.T. Hajiaghayi, G. Kortsarz, V.S. Mirrokni, Z. Nutov, Power optimization for connectivity problems, Mathematical Programming 110 (1) (2007) 195-208]. For the Min-Powerk-Connected Subgraph (MP k CS) problem we obtain the following results. For k = 2 and k = 3, we improve the previously best known ratios of 4 [G. Calinescu, P.J. Wan, Range assignment for biconnectivity and k-edge connectivity in wireless ad hoc networks, Mobile Networks and Applications 11 (2) (2006) 121-128] and 7 [M.T. Hajiaghayi, G. Kortsarz, V.S. Mirrokni, Z. Nutov, Power optimization for connectivity problems, Mathematical Programming 110 (1) (2007) 195-208] to 3 frac(2, 3) and 5 frac(2, 3), respectively. Finally, we give a 4 rmax-approximation algorithm for the Minimum-Power Steiner Network (MPSN) problem: find a minimum-power subgraph that contains r (u, v) pairwise edge-disjoint paths for every pair u, v of nodes.

KW - Approximation algorithms

KW - Edge-cover

KW - Minimum power

KW - Node-connectivity

KW - Wireless networks

UR - http://www.scopus.com/inward/record.url?scp=64549086307&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2008.12.001

DO - 10.1016/j.dam.2008.12.001

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:64549086307

SN - 0166-218X

VL - 157

SP - 1840

EP - 1847

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 8

ER -