Sublinear-Time Maintenance of Breadth-First Spanning Trees in Partially Dynamic Networks

TL;DR

This paper introduces deterministic algorithms for maintaining approximate BFS trees in dynamic networks with sublinear amortized update time, improving efficiency over classical exact methods.

Contribution

It presents the first sublinear-time, deterministic, approximate algorithms for BFS maintenance in partially dynamic networks, and extends these techniques to approximate shortest paths in sequential models.

Findings

Achieved sublinear amortized update time for BFS in dynamic networks.

Developed deterministic $(1+ta)$-approximate algorithms.

Extended techniques to approximate shortest paths in RAM model.

Abstract

We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic $(1+\epsilon)$-approximation algorithms whose amortized time (over some number of link changes) is sublinear in $D$, the maximum diameter of the network. Our technique also leads to a deterministic $(1+\epsilon)$-approximate incremental algorithm for single-source shortest paths (SSSP) in the sequential (usual RAM) model. Prior to our work, the state of the art was the classic exact algorithm of Even and Shiloach [JACM 1981] that is optimal under some assumptions [Roditty and Zwick ESA 2004, Henzinger et al. STOC 2015]. Our result is the first to show that, in the incremental setting, this bound can be beaten in certain cases if some approximation is allowed.