Brief Announcement: Distributed Lightweight Spanner Construction for Unit Ball Graphs in Doubling Metrics

Abstract

Resolving an open question from 2006, we prove the existence of light-weight bounded-degree (1+ε)-spanners for unit ball graphs in the metrics of bounded doubling dimension, and we design a simple O(log*n)-round distributed algorithm in the LOCAL model for finding such spanners using only 2-hop neighborhood information. We further study the problem in the two dimensional Euclidean plane and we propose a construction with similar properties that has a low-intersection property as well. Lastly, we provide experimental results that confirm the performance of our algorithms.