On sparse spanners of weighted graphs
Discrete & Computational Geometry
Power consumption in packet radio networks
Theoretical Computer Science
Hardness Results for the Power Range Assignmet Problem in Packet Radio Networks
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
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
Geometric Spanner Networks
Introduction to Algorithms, Third Edition
Introduction to Algorithms, Third Edition
The MST of symmetric disk graphs (in arbitrary metric spaces) is light
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
The MST of Symmetric Disk Graphs (in Arbitrary Metric Spaces) is Light
SIAM Journal on Discrete Mathematics
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Symmetric disk graphs are often used to model wireless communication networks. Given a set S of n points in ℝd (representing n transceivers) and a transmission range assignment r: S →ℝ, the symmetric disk graph of S (denoted SDG(S)) is the undirected graph over S whose set of edges is E={(u,v) | r(u)≥|uv| and r(v)≥|uv|}, where |uv| denotes the Euclidean distance between points u and v. We prove that the weight of the MST of any connected symmetric disk graph over a set S of n points in the plane, is only O(logn) times the weight of the MST of the complete Euclidean graph over S. We then show that this bound is tight, even for points on a line. Next, we prove that if the number of different ranges assigned to the points of S is only k, kn, then the weight of the MST of SDG(S) is at most 2k times the weight of the MST of the complete Euclidean graph. Moreover, in this case, the MST of SDG(S) can be computed efficiently in time O(knlogn). We also present two applications of our main theorem, including an alternative and simpler proof of the Gap Theorem, and a result concerning range assignment in wireless networks. Finally, we show that in the non-symmetric model (where E={(u,v) | r(u)≥|uv|}), the weight of a minimum spanning subgraph might be as big as Ω(n) times the weight of the MST of the complete Euclidean graph.