Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
Improved approximation algorithms for uniform connectivity problems
Journal of Algorithms
Steiner tree problem with minimum number of Steiner points and bounded edge-length
Information Processing Letters
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
Information Processing Letters
Approximations for Steiner Trees with Minimum Number of Steiner Points
Journal of Global Optimization
Some structural and geometric properties of two-connected steiner networks
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
Relay sensor placement in wireless sensor networks
Wireless Networks
Wireless network design via 3-decompositions
Information Processing Letters
On the construction of 2-connected virtual backbone in wireless networks
IEEE Transactions on Wireless Communications
Deploying sensor networks with guaranteed fault tolerance
IEEE/ACM Transactions on Networking (TON)
Approximating survivable networks with minimum number of Steiner points
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
On the structure and complexity of the 2-connected Steiner network problem in the plane
Operations Research Letters
Two-connected Steiner networks: structural properties
Operations Research Letters
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Motivated by applications to wireless sensor networks, we study the following problem. We are given a set S of wireless sensor nodes, given as a multiset of points in a normed space. We must place a minimum-size (multi)set Q of wireless relay nodes in the normed space such that the unit-disk graph induced by Q ∪S is two-connected. The unit-disk graph of a set of points has an edge between two points if their distance is at most 1. Kashyap, Khuller, and Shayman (Infocom 2006) present algorithms for the two variants of the problem: two-edge-connectivity and biconnectivity. For both they prove an approximation ratio of at most 2 d MST , where d MST is the maximum degree of a minimum-degree Minimum Spanning Tree in the normed space. In the Euclidean two and three dimensional spaces, d MST =5, and d MST =13 respectively. We give a tight analysis of the same algorithms, obtaining approximation ratios of d MST for biconnectivity and 2 d MST −1 for two-edge-connectivity respectively.