Faster Fully-Dynamic Minimum Spanning Forest

TL;DR

This paper introduces a new data structure for the fully-dynamic minimum spanning forest problem that improves update times in simple graphs, achieving faster amortized performance than previous methods.

Contribution

It presents a novel data structure that reduces the amortized update time for fully-dynamic minimum spanning forests in simple graphs.

Findings

Supports edge updates in $O(rac{ ext{log}^4 n}{ ext{log} ext{log} n})$ amortized time

Improves upon the previous $O( ext{log}^4 n)$ bound by Holm et al.

Operates in the Word-RAM model with standard instructions.

Abstract

We give a new data structure for the fully-dynamic minimum spanning forest problem in simple graphs. Edge updates are supported in $O(\log^4n/\log\log n)$ amortized time per operation, improving the $O(\log^4n)$ amortized bound of Holm et al. (STOC'98, JACM'01). We assume the Word-RAM model with standard instructions.