Improved Worst-Case Deterministic Parallel Dynamic Minimum Spanning Forest

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 $O(n^{2\mathrm{/}3}\log \frac{m}{n})$ work.