Parallel Batch Dynamic Vertex Coloring in $O(\log \Delta)$ Amortized Update Time

TL;DR

This paper introduces a parallel batch-dynamic algorithm for maintaining proper vertex coloring with an expected amortized update time of O(log Δ), leveraging a new sequential algorithm and achieving efficient parallel span.

Contribution

It presents the first parallel batch-dynamic algorithm for proper vertex coloring with provably efficient update times based on a new sequential approach.

Findings

Expected amortized update time is O(log Δ).

Parallel span is polylogarithmic in batch size and number of vertices.

Algorithm is randomized with high probability guarantees.

Abstract

We present the first parallel batch-dynamic algorithm for maintaining a proper $(\Delta + 1)$-vertex coloring. Our approach builds on a new sequential dynamic algorithm inspired by the work of Bhattacharya et al. (SODA'18). The resulting randomized algorithm achieves $O(\log \Delta)$ expected amortized update time and, for any batch of $b$ updates, has parallel span $O(\operatorname{polylog} b + \operatorname{polylog} n)$ with high probability.