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 …

Map matching is a common preprocessing step for analysing vehicle trajectories. In the
theory community, the most popular approach for map matching is to compute a path on the …

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 show how to construct a (1+ ε)(1+ ε)-spanner over a set PP of n points in R^ d R d that is
resilient to a catastrophic failure of nodes. Specifically, for prescribed parameters ϑ, ε ∈ (0 …

The notion of distance is fundamental to many aspects of computational geometry. A classic
approach to characterize the distance properties of planar (and high-dimensional) point sets …

Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth)
are fundamental, widely a pplicable and extensively studied combinatorial objects. We …

A fault-tolerant structure for a network is required for continued functioning following the
failure of some of the network's edges or vertices. This article considers breadth-first search …

We present a new optimal construction of semi-separated pair decomposition (SSPD) for a
set of n points in IR d. In the new construction each point participates in a few pairs, and it …

Strong ties play a crucial role in transmitting sensitive information in social networks,
especially in the criminal justice domain. However, large social networks containing many …

In this paper, we present an approximate distance oracle for fault-tolerant Euclidean
spanners. An $ f $-fault-tolerant Euclidean $ t $-spanner for a point set $ V\subset\mathbb …