Distributed Construction of Purely Additive Spanners

TL;DR

This paper explores the distributed construction of purely additive spanners in the CONGEST model, presenting algorithms, a new communication complexity lower bound, and extending the analytical tools for distributed graph algorithms.

Contribution

It introduces algorithms for distributed construction of additive spanners, develops a novel lower bound technique using information theory, and extends the analytical toolkit for the CONGEST model.

Findings

Algorithms for constructing additive spanners in distributed settings.

A new lower bound on the number of rounds for computing pairwise spanners.

Extension of lower bound techniques using information theory.

Abstract

This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far apart locations, the algorithms use additional mechanisms compared to their sequential counterparts. We complement our algorithms with a lower bound on the number of rounds required for computing pairwise spanners. The standard reductions from set-disjointness and equality seem unsuitable for this task because no specific edge needs to be removed from the graph. Instead, to obtain our lower bound, we define a new communication complexity problem that reduces to computing a sparse spanner, and prove a lower bound on its communication complexity using information theory. This technique significantly extends the current toolbox used for obtaining lower bounds for the CONGEST model, and we believe it may find additional applications.