Parallel Batch-Dynamic Coreness Decomposition with Worst-Case Guarantees

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 poly(log n) depth, using a worst-case work bound of b. poly(log n) where b denotes the batch size. This means the batch gets processed in Õ(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.