A matroid approach to finding edge connectivity and packing arborescences
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
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
A Distributed Algorithm for Minimum-Weight Spanning Trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Algorithmic aspects of topology control problems for ad hoc networks
Proceedings of the 3rd ACM international symposium on Mobile ad hoc networking & computing
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Energy-efficient broadcast and multicast trees in wireless networks
Mobile Networks and Applications
Energy-efficient broadcast and multicast trees in wireless networks
Mobile Networks and Applications
Minimum-energy broadcasting in static ad hoc wireless networks
Wireless Networks
Power Consumption in Packet Radio Networks (Extended Abstract)
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
An Efficient Orthogonal Grid Drawing Algorithm For Cubic Graphs
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
On the Symmetric Range Assignment Problem in Wireless Ad Hoc Networks
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Symmetric Connectivity with Minimum Power Consumption in Radio Networks
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks
Proceedings of the 9th annual international conference on Mobile computing and networking
Max-Life Power Schedule for connectivity and biconnectivity in wireless ad hoc networks
Mobile Networks and Applications
On approximate optimal dual power assignment for biconnectivity and edge-biconnectivity
Theoretical Computer Science
Symmetric range assignment with disjoint MST constraints
Proceedings of the fifth international workshop on Foundations of mobile computing
Approximating Minimum-Power k-Connectivity
ADHOC-NOW '08 Proceedings of the 7th international conference on Ad-hoc, Mobile and Wireless Networks
Approximating minimum-power edge-covers and 2,3-connectivity
Discrete Applied Mathematics
On minimum power connectivity problems
Journal of Discrete Algorithms
Approximating minimum power covers of intersecting families and directed edge-connectivity problems
Theoretical Computer Science
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
Power optimization in ad hoc wireless network topology control with biconnectivity requirements
Computers and Operations Research
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Depending on whether bidirectional links or unidirectional links are used for communications, the network topology under a given range assignment is either an undirected graph referred to as the bidirectional topology, or a directed graph referred to as the unidirectional topology. The Min-Power Bidirectional (resp., Unidirectional) k-Node Connectivity problem seeks a range assignment of minimum total power subject to the constraint that the produced bidirectional (resp. unidirectional) topology is k-vertex connected. Similarly, the Min-Power Bidirectional (resp., Unidirectional) k-Edge Connectivity problem seeks a range assignment of minimum total power subject to the constraint the produced bidirectional (resp., unidirectional) topology is k-edge connected.The Min-Power Bidirectional Biconnectivity problem and the Min-Power Bidirectional Edge-Biconnectivity problem have been studied by Lloyd et al. [23]. They show that range assignment based the approximation algorithm of Khuller and Raghavachari [18], which we refer to as Algorithm KR, has an approximation ratio of at most 2(2-2/n)(2 + 1/n) for Min-Power Bidirectional Biconnectivity, and range assignment based on the approximation algorithm of Khuller and Vishkin [19], which we refer to as Algorithm KV, has an approximation ratio of at most 8(1-1/n) for Min-Power Bidirectional Edge-Biconnectivity.In this paper, we first establish the NP-hardness of Min-Power Bidirectional (Edge-) Biconnectivity. Then we show that Algorithm KR has an approximation ratio of at most 4 for both Min-Power Bidirectional Biconnectivity and Min-Power Unidirectional Biconnectivity, and Algorithm KV has an approximation ratio of at most 2k for both Min-Power Bidirectional k-Edge Connectivity and Min-Power Unidirectional k-Edge Connectivity. We also propose a new simple constant-approximation algorithm for both Min-Power Bidirectional Biconnectivity and Min-Power Unidirectional Biconnectivity. This new algorithm applies only to Euclidean instances, but is best suited for distributed implementation.