# Fast Deterministic Algorithms for Highly-Dynamic Networks

## TL;DR

This paper introduces a deterministic distributed algorithm framework for highly-dynamic networks, achieving fast, $O(1)$ amortized time complexity with minimal message size, applicable to multiple fundamental graph problems.

## Contribution

The work presents a novel deterministic framework that handles arbitrary edge changes efficiently, improving upon prior algorithms in dynamic network settings.

## Key findings

- Achieves $O(1)$ amortized time complexity per round.
- Uses only $O( ext{log} n)$-bit messages.
- Applicable to multiple graph problems including maximal matching and coloring.

## Abstract

This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in its combination of (1) having an $O(1)$ amortized time complexity, (2) using only $O(\log{n})$-bit messages, (3) not posing any restrictions on the dynamic behavior of the environment, (4) being deterministic, (5) having strong guarantees for intermediate solutions, and (6) being applicable for a wide family of tasks. The tasks for which we deduce such an algorithm are maximal matching, $(degree+1)$-coloring, 2-approximation for minimum weight vertex cover, and maximal independent set (which is the most subtle case). For some of these tasks, node insertions can also be among the allowed topology changes, and for some of them also abrupt node deletions.