As the field of communications networks continues to evolve, the challenging area of
wireless sensor networks is rapidly coming of age. Recent advances have made it possible …

Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms
and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical …

For a set S of points in ℝ3, an s-spanner is a graph on S such that any pair of points is
connected via some path in the spanner whose total length is at most s times the Euclidean …

A k-spanner of a graph G is a sparse subgraph H whose shortest path distances match
those of G up to a multiplicative error k. In this paper we study spanners that are resistant to …

We present two new results about vertex and edge fault-tolerant spanners in Euclidean
spaces. We describe the first construction of vertex and edge fault-tolerant spanners having …

Chan, Har-Peled, and Jones [SICOMP 2020] developed locality-sensitive orderings (LSO)
for Euclidean space. A $(\tau,\rho) $-LSO is a collection $\Sigma $ of orderings such that for …

We extend the classic notion of well-separated pair decomposition [10] to the (weighted) unit-
disk graph metric: the shortest path distance metric induced by the intersection graph of unit …

Given a set S of n points in the plane, we give an O (n log n)-time algorithm that constructs a
plane t-spanner for S, with t≈ 10, such that the degree of each point of S is bounded from …

Chan, Har-Peled, and Jones [2020] recently developed locality-sensitive ordering (LSO), a
new tool that allows one to reduce problems in the Euclidean space ℝ d to the 1 …

We introduce the concept of region-fault tolerant spanners for planar point sets and prove
the existence of region-fault tolerant spanners of small size. For a geometric graph G on a …