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 constructive enumeration of fullerenes
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges
DIALM '01 Proceedings of the 5th international workshop on Discrete algorithms and methods for mobile computing and communications
Fast Greedy Algorithms for Constructing Sparse Geometric Spanners
SIAM Journal on Computing
A unified energy-efficient topology for unicast and broadcast
Proceedings of the 11th annual international conference on Mobile computing and networking
Local approximation schemes for topology control
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Local Construction and Coloring of Spanners of Location Aware Unit Disk Graphs
Graph-Theoretic Concepts in Computer Science
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In this paper we present local distributed algorithms for constructing spanners in wireless sensor networks modeled as unit ball graphs (shortly UBGs ) and quasi-unit ball graphs (shortly quasi-UBGs ), in the 3-dimensional Euclidean space. Our first contribution is a local distributed algorithm that, given a UBG U and a parameter *** *** /3, constructs a sparse spanner of U with stretch factor 1/(1 *** 2sin(*** /2)), improving the previous upper bound of 1/(1 *** *** ) by Althöfer et al. which is applicable only when $\alpha . The second contribution of this paper is in presenting the first local distributed algorithm for the construction of bounded-degree lightweight spanners of UBGs and quasi-UBGs. The simulation results we obtained show that, empirically, the weight of the spanners, the stretch factor and locality of the algorithms, are much better than the theoretical upper bounds proved in this paper.