Parallel Batch-Dynamic Coreness Decomposition with Worst-Case Guarantees

TL;DR

This paper introduces the first parallel batch-dynamic algorithm for coreness decomposition that guarantees worst-case update times, efficiently processing batches of edge updates in polylogarithmic depth and work bounds.

Contribution

It presents a novel parallel algorithm for batch-dynamic coreness decomposition with worst-case guarantees, improving upon prior amortized-only methods.

Findings

Processes batch updates in polylogarithmic depth

Achieves optimal up to logarithmic factors work bounds

Provides worst-case guarantees unlike previous amortized algorithms

Abstract

We present the first parallel batch-dynamic algorithm for approximating coreness decomposition with worst-case update times. Given any batch of edge insertions and deletions, our algorithm processes all these updates in $ \text{poly}(\log n)$ depth, using a worst-case work bound of $b\cdot \text{poly}(\log n)$ where $b$ denotes the batch size. This means the batch gets processed in $\tilde{O}(b/p)$ time, given $p$ processors, which is optimal up to logarithmic factors. Previously, an algorithm with similar guarantees was known by the celebrated work of Liu, Shi, Yu, Dhulipala, and Shun [SPAA'22], but with the caveat of the work bound, and thus the runtime, being only amortized.