Improved Worst-Case Deterministic Parallel Dynamic Minimum Spanning Forest

TL;DR

This paper presents a new deterministic parallel algorithm for maintaining a minimum spanning forest in dynamic graphs, achieving improved worst-case update time and work efficiency in the EREW PRAM model.

Contribution

It introduces a deterministic algorithm that improves worst-case update time and work for dynamic MSF in the EREW PRAM model compared to previous methods.

Findings

Achieves $O(rac{1}{ } ext{processors and } O( ext{ update time}

Reduces total work to $O( ext{ for dynamic MSF maintenance}

Provides worst-case guarantees in the EREW PRAM model.

Abstract

This paper gives a new deterministic algorithm for the dynamic Minimum Spanning Forest (MSF) problem in the EREW PRAM model, where the goal is to maintain a MSF of a weighted graph with $n$ vertices and $m$ edges while supporting edge insertions and deletions. We show that one can solve the dynamic MSF problem using $O(\sqrt n)$ processors and $O(\log n)$ worst-case update time, for a total of $O(\sqrt n \log n)$ work. This improves on the work of Ferragina [IPPS 1995] which costs $O(\log n)$ worst-case update time and $O(n^{2/3} \log{\frac{m}{n}})$ work.