Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Connectivity and network flows
Handbook of combinatorics (vol. 1)
Approximation algorithms for finding highly connected subgraphs
Approximation algorithms for NP-hard problems
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
A representation for crossing set families with applications to submodular flow problems
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Approximating k-node Connected Subgraphs via Critical Graphs
SIAM Journal on Computing
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Power optimization for connectivity problems
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Approximating Minimum-Power k-Connectivity
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
On construction of minimum energy k-fault resistant topologies
Ad Hoc Networks
Approximating minimum-power edge-covers and 2,3-connectivity
Discrete Applied Mathematics
On minimum power connectivity problems
Journal of Discrete Algorithms
On minimum power connectivity problems
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Approximating minimum power covers of intersecting families and directed edge-connectivity problems
Theoretical Computer Science
Approximating Steiner networks with node weights
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Approximating minimum-power degree and connectivity problems
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Survivable network design problems in wireless networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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Given a (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 the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider fundamental directed connectivity network design problems under the power minimization criteria: the k-outconnected and the k-connected spanning subgraph problems. For k = 1 these problems are at least as hard as the Set-Cover problem and thus have an Ω(ln |V|) approximation threshold, while for arbitrary k a polylogarithmic approximation algorithm is unlikely. We give an O(ln |V|)-approximation algorithm for any constant k. In fact, our results are based on a much more general O(ln |V|)-approximation algorithm for the problem of finding a min-power edge-cover of an intersecting set-family; a set-family ${\cal F}$ on a groundset V is intersecting if $X \cap Y,X \cup Y \in {\cal F}$ for any intersecting $X,Y \in {\cal F}$, and an edge set I covers ${\cal F}$ if for every $X \in {\cal F}$ there is an edge in I entering X.