Transitions in geometric minimum spanning trees
Discrete & Computational Geometry - Special issue on ACM symposium on computational geometry, North Conway
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
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
On the power assignment problem in radio networks
Mobile Networks and Applications - Discrete algorithms and methods for mobile computing and communications
Algorithmic aspects of topology control problems for ad hoc networks
Mobile Networks and Applications
Range assignment for biconnectivity and k-edge connectivity in wireless ad hoc networks
Mobile Networks and Applications
Approximating minimum-power degree and connectivity problems
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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If V is a set of n points in the unit square [0,1]2, and if R:V- Re+ is an assignment of positive real numbers (radii) to to those points, define a graph G(R) as follows: [v,w] is an undirected edge if and only if the Euclidean distance d(v,w) is less than or equal to min(R(v),R(w)). Given α≥ 1 and k∈ Z+, let Rk* be the range assignment that minimizes the function J(R) =sum limitsv #8712; VR(v)α, subject to the constraint that G(R) has at least k edge-disjoint spanning trees. For n random points in [0,1]2, the expected value of the optimum, E(J(Rk*)), is asymptotically Θ(n1-α/2). This is proved by analyzing a crude approximation algorithm that finds a range assignment Rka such that the ratio J(Rka)/J(Rk*) is bounded.