Discrete Mathematics - Topics on domination
Construction of multidimensional spanner graphs, with applications to minimum spanning trees
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Low degree spanning trees of small weight
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Unidirectional links prove costly in wireless ad hoc networks
DIALM '99 Proceedings of the 3rd international workshop on Discrete algorithms and methods for mobile computing and communications
Power consumption in packet radio networks
Theoretical Computer Science
A minimum spanning tree algorithm with inverse-Ackermann type complexity
Journal of the ACM (JACM)
Polynomial-time approximation schemes for geometric graphs
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Representing graphs by disks and balls (a survey of recognition-complexity results)
Discrete Mathematics
An optimal minimum spanning tree algorithm
Journal of the ACM (JACM)
Efficient minimum spanning tree construction without Delaunay triangulation
Information Processing Letters
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
An o(n) Work EREW Parallel Algorithm for Updating MST
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
End-to-end packet-scheduling in wireless ad-hoc networks
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Applications of k-Local MST for Topology Control and Broadcasting in Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
On distance constrained labeling of disk graphs
Theoretical Computer Science
Connected Dominating Sets in Wireless Networks with Different Transmission Ranges
IEEE Transactions on Mobile Computing
A tight bound for online colouring of disk graphs
Theoretical Computer Science
On Construction of Virtual Backbone in Wireless Ad Hoc Networks with Unidirectional Links
IEEE Transactions on Mobile Computing
Algorithms for ad hoc and sensor networks
Computer Communications
Estimating the Weight of Metric Minimum Spanning Trees in Sublinear Time
SIAM Journal on Computing
Approximate MST for UDG locally
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Localized spanner construction for ad hoc networks with variable transmission range
ACM Transactions on Sensor Networks (TOSN)
Distributed spanner construction in doubling metric spaces
OPODIS'06 Proceedings of the 10th international conference on Principles of Distributed Systems
Approximation algorithms for unit disk graphs
WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science
The MST of symmetric disk graphs is light
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
Hi-index | 0.00 |
Consider an n-point metric space M = (V, δ), and a transmission range assignment r : V → R+ that maps each point v ∈ V to the disk of radius r(v) around it. The symmetric disk graph (henceforth, SDG) that corresponds to M and r is the undirected graph over V whose edge set includes an edge (u, v) if both r(u) and r(v) are no smaller than δ(u, v). SDGs are often used to model wireless communication networks. Abu-Affash, Aschner, Carmi and Katz (SWAT 2010, [1]) showed that for any n-point 2-dimensional Euclidean space M, the weight of the MST of every connected SDG for M is O(log n) ċ w(MST(M)), and that this bound is tight. However, the upper bound proof of [1] relies heavily on basic geometric properties of constant-dimensional Euclidean spaces, and does not extend to Euclidean spaces of super-constant dimension. A natural question that arises is whether this surprising upper bound of [1] can be generalized for wider families of metric spaces, such as high-dimensional Euclidean spaces. In this paper we generalize the upper bound of Abu-Affash et al. [1] for Euclidean spaces of any dimension. Furthermore, our upper bound extends to arbitrary metric spaces and, in particular, it applies to any of the normed spaces lp. Specifically, we demonstrate that for any n-point metric space M, the weight of the MST of every connected SDG for M is O(log n) ċ w(MST(M)).