Pseudodeterministic Algorithms for Minimum Cut Problems

TL;DR

This paper introduces efficient pseudodeterministic algorithms for global and s-t minimum cut problems, outperforming existing deterministic algorithms and applicable across multiple computational models.

Contribution

It presents the first pseudodeterministic algorithms for minimum cut problems with improved running times and broad applicability across various computational models.

Findings

Asymptotically faster than previous deterministic algorithms for global minimum cut.

Successfully implemented in multiple models including streaming and PRAM.

No efficient deterministic algorithms are known for these models.

Abstract

In this paper, we present efficient pseudodeterministic algorithms for both the global minimum cut and minimum s-t cut problems. The running time of our algorithm for the global minimum cut problem is asymptotically better than the fastest sequential deterministic global minimum cut algorithm (Henzinger, Li, Rao, Wang; SODA 2024). Furthermore, we implement our algorithm in sequential, streaming, PRAM, and cut-query models, where no efficient deterministic global minimum cut algorithms are known.