TY - JOUR

T1 - Power optimization for connectivity problems

AU - Hajiaghayi, Mohammad T.

AU - Kortsarz, Guy

AU - Mirrokni, Vahab S.

AU - Nutov, Zeev

PY - 2005

Y1 - 2005

N2 - Given a graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of the nodes of this graph. Motivated by applications in wireless multi-hop networks, we consider four fundamental problems under the power minimization criteria: the Min-Power b-Edge-Cover problem (MPb-EC) where the goal is to find a min-power subgraph so that the degree of every node v is at least some given integer b(v), the Min-Power k-node Connected Spanning Subgraph problem (MP k-CSS), Min-Power k-edge Connected Spanning Subgraph problem (MP k-ECSS), and finally the Min-Power k-Edge-Disjoint Paths problem in directed graphs (MP k-EDP). We give an O(log4 n)-approximation algorithm for MPb-EC. This gives an O(log4 n)-approximation algorithm for MP k-CSS for most values of k, improving the best previously known O(k)-approximation guarantee. In contrast, we obtain an O(√n) approximation algorithm for MP k-ECSS, and for its variant in directed graphs (i.e., MP k-EDP), we establish the following inapproximability threshold: MP k-EDP cannot be approximated within O(2 log 1-ε n) for any fixed ε > 0, unless NP-hard problems can be solved in quasi-polynomial time.

AB - Given a graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of the nodes of this graph. Motivated by applications in wireless multi-hop networks, we consider four fundamental problems under the power minimization criteria: the Min-Power b-Edge-Cover problem (MPb-EC) where the goal is to find a min-power subgraph so that the degree of every node v is at least some given integer b(v), the Min-Power k-node Connected Spanning Subgraph problem (MP k-CSS), Min-Power k-edge Connected Spanning Subgraph problem (MP k-ECSS), and finally the Min-Power k-Edge-Disjoint Paths problem in directed graphs (MP k-EDP). We give an O(log4 n)-approximation algorithm for MPb-EC. This gives an O(log4 n)-approximation algorithm for MP k-CSS for most values of k, improving the best previously known O(k)-approximation guarantee. In contrast, we obtain an O(√n) approximation algorithm for MP k-ECSS, and for its variant in directed graphs (i.e., MP k-EDP), we establish the following inapproximability threshold: MP k-EDP cannot be approximated within O(2 log 1-ε n) for any fixed ε > 0, unless NP-hard problems can be solved in quasi-polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=24944538657&partnerID=8YFLogxK

U2 - 10.1007/11496915_26

DO - 10.1007/11496915_26

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AN - SCOPUS:24944538657

SN - 0302-9743

VL - 3509

SP - 349

EP - 361

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

T2 - 11th International IPCO Conference on Integer Programming and Combinatorial Optimization

Y2 - 8 June 2005 through 10 June 2005

ER -