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
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
Range assignment for biconnectivity and k-edge connectivity in wireless ad hoc networks
Mobile Networks and Applications
Energy-Efficient Wireless Network Design
Theory of Computing Systems
Power optimization for connectivity problems
Mathematical Programming: Series A and B
On minimum power connectivity problems
Journal of Discrete Algorithms
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
Approximating minimum power covers of intersecting families and directed connectivity problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Approximating Steiner Networks with Node-Weights
SIAM Journal on Computing
Survivable network activation problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximating minimum-cost connectivity problems via uncrossable bifamilies
ACM Transactions on Algorithms (TALG)
Survivable network activation problems
Theoretical Computer Science
| Hi-index | 5.23 |
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. Let G=(V,E) be a graph with edge costs {c(e):e@?E} and let k be an integer. We consider problems that seek to find a min-power spanning subgraph G of G that satisfies a prescribed edge-connectivity property. In the Min-Powerk-Edge-Outconnected Subgraph problem we are given a root r@?V, and require that G contains k pairwise edge-disjoint rv-paths for all v@?V-r. In the Min-Powerk-Edge-Connected Subgraph problem G is required to be k-edge-connected. For k=1, these problems are at least as hard as the Set-Cover problem and thus have an @W(ln|V|) approximation threshold. For k=@W(n^@e), they are unlikely to admit a polylogarithmic approximation ratio [15]. We give approximation algorithms with ratio O(kln|V|). Our algorithms are based on a more general O(ln|V|)-approximation algorithm for the problem of finding a min-power directed edge-cover of an intersecting set-family; a set-family F is intersecting if X@?Y,X@?Y@?F for any intersecting X,Y@?F, and an edge set I covers F if for every X@?F there is an edge in I entering X.