Towards Scalable and Practical Batch-Dynamic Connectivity

TL;DR

This paper introduces a new parallel algorithm for dynamic graph connectivity that is work-efficient, supports batch updates, and is both space- and time-efficient, outperforming existing algorithms in empirical tests.

Contribution

It presents the first parallel, work-efficient algorithm for batch-dynamic connectivity with linear space and polylogarithmic update time, along with an empirical implementation.

Findings

Uses up to 19.7x less space than previous algorithms.

Runs up to 6.2x faster than the level-set algorithm.

Supports batch updates with polylogarithmic depth.

Abstract

We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of updates, runs in polylogarithmic depth, and uses only linear total space. The existing algorithms for the problem either use super-linear space, do not come with strong theoretical bounds, or are not parallel. On the empirical side, we provide the first implementation of the cluster forest algorithm, the first linear-space and poly-logarithmic update time algorithm for dynamic connectivity. Experimentally, we find that our algorithm uses up to 19.7x less space and is up to 6.2x faster than the level-set algorithm of HDT, arguably the most widely-implemented dynamic connectivity algorithm with strong theoretical guarantees.