Faster Pseudo-Deterministic Minimum Cut

2026-02-16

AI Summary

This work proposes the first efficient pseudo-deterministic algorithm for the global minimum cut problem that avoids black-box reductions, achieving high-probability output of a unique canonical solution while significantly improving efficiency. The key innovation lies in a graph-theoretic mechanism for canonical solution selection that naturally breaks ties. The algorithm attains an $O(m \log^2 n)$ time complexity on weighted graphs, matching the best-known randomized algorithms. It also achieves the first efficient maintenance of a canonical minimum cut in fully dynamic unweighted graphs, supporting $\text{polylog}(n)$ update time and $\tilde{O}(n)$ query time. Furthermore, in both streaming and cut-query models, its performance matches that of the best randomized algorithms.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Pseudo-deterministic algorithms are randomized algorithms that, with high constant probability, output a fixed canonical solution. The study of pseudo-deterministic algorithms for the global minimum cut problem was recently initiated by Agarwala and Varma [ITCS'26], who gave a black-box reduction incurring an $O(\log n \log \log n)$ overhead. We introduce a natural graph-theoretic tie-breaking mechanism that uniquely selects a canonical minimum cut. Using this mechanism, we obtain: (i) A pseudo-deterministic minimum cut algorithm for weighted graphs running in $O(m\log^2 n)$ time, eliminating the $O(\log n \log \log n)$ overhead of prior work and matching existing randomized algorithms. (ii) The first pseudo-deterministic algorithm for maintaining a canonical minimum cut in a fully-dynamic unweighted graph, with $\mathrm{polylog}(n)$ update time and $\tilde{O}(n)$ query time. (iii) Improved pseudo-deterministic algorithms for unweighted graphs in the dynamic streaming and cut-query models of computation, matching the best randomized algorithms.

Problem

• pseudo-deterministic
• minimum cut
• global minimum cut
• randomized algorithms
• canonical solution

Innovation

• pseudo-deterministic algorithms
• minimum cut
• tie-breaking mechanism
• dynamic graph algorithms
• graph streaming