Fully Dynamic Shortest Paths in Sparse Digraphs

TL;DR

This paper introduces a new deterministic data structure for fully dynamic shortest path problems in sparse, weighted directed graphs, achieving improved worst-case update and query times.

Contribution

It presents the first non-trivial update/query tradeoff for the fully dynamic shortest paths problem in sparse weighted directed graphs.

Findings

Deterministic data structure with $ ilde{O}(mn^{4/5})$ update time.

Processes $s,t$-distance queries in $ ilde{O}(n^{4/5})$ time.

First such tradeoff in the sparse weighted directed graph regime.

Abstract

We study the exact fully dynamic shortest paths problem. For real-weighted directed graphs, we show a deterministic fully dynamic data structure with $\tilde{O}(mn^{4/5})$ worst-case update time processing arbitrary $s,t$-distance queries in $\tilde{O}(n^{4/5})$ time. This constitutes the first non-trivial update/query tradeoff for this problem in the regime of sparse weighted directed graphs.