Locality in distributed graph algorithms
SIAM Journal on Computing
On sparse spanners of weighted graphs
Discrete & Computational Geometry
Optimally sparse spanners in 3-dimensional Euclidean space
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
A fast algorithm for constructing sparse Euclidean spanners
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
A new way to weigh Malnourished Euclidean graphs
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Routing with guaranteed delivery in ad hoc wireless networks
Wireless Networks
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Local approximation schemes for topology control
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
Mobile Networks and Applications
Sensor networks: distributed algorithms reloaded – or revolutions?
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Localized Delaunay triangulation with application in ad hoc wireless networks
IEEE Transactions on Parallel and Distributed Systems
Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Stochastic minimum spanning trees in euclidean spaces
Proceedings of the twenty-seventh annual symposium on Computational geometry
Analysing local algorithms in location-aware quasi-unit-disk graphs
Discrete Applied Mathematics
Bounding interference in wireless ad hoc networks with nodes in random position
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
ACM Computing Surveys (CSUR)
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We consider the problem of computing bounded-degree lightweight plane spanners of unit disk graphs in the local distributed model of computation. We are motivated by the hypothesis that such subgraphs can provide the underlying network topology for efficient unicasting and multicasting in wireless distributed systems. We present the firstlocal distributed algorithm that computes a bounded-degree plane lightweight spanner of a given unit disk graph. The upper bounds on the degree, the stretch factor, and the weight of the spanner, are very small. For example, our results imply a local distributed algorithm that computes a plane spanner of a given unit disk graph U, whose degree is at most 14, stretch factor at most 8.81, and weight at most 8.81 times the weight of a Euclidean Minimum Spanning Tree of V(U).We show a wider application of our techniques by giving an O(nlogn) time centralized algorithm that constructs bounded-degree plane lightweight spanners of unit disk graphs (which include Euclidean graphs), with the bestupper bounds on the spanner degree, stretch factor, and weight.