Distributed Stochastic Graph Algorithms

2026-05-20

AI Summary

This work addresses combinatorial optimization problems—specifically maximum matching, minimum vertex cover, and minimum dominating set—on random graphs where edges appear independently with known probabilities, under a distributed synchronous model in which each node observes only its incident random edges. The study proposes novel distributed randomized algorithms that significantly reduce the number of communication rounds while relying solely on local information. Notably, it establishes for the first time that distributed randomized algorithms can surpass the lower bounds inherent to existing deterministic approaches, achieving improved round complexity for approximation guarantees. These results provide both theoretical insights and algorithmic foundations for efficient distributed optimization in uncertain graph environments.

Abstract

We study stochastic graph optimization problems in a novel distributed setting. As in the standard centralized setting, a random subgraph $G^*$ of a known base graph $G$ is realized by including each edge $e$ independently with a known probability $p_e$, and we must solve an optimization problem on $G^*$ despite uncertainty about its edges. In the standard setting, to cope with this uncertainty, the algorithm can query any edge of $G$ to learn if the edge exists in $G^*$, and its complexity is the number of queried edges. The distributed setting incorporates uncertainty in a natural manner, by having each vertex know only about its own edges in $G^*$ (and only communicate over them), and the complexity is measured by the number of synchronous communication rounds. We establish that distributed stochastic algorithms can be drastically faster than their non-stochastic counterparts and overcome known lower bounds, by showing fast distributed approximation algorithms for maximum matching, minimum vertex cover, and minimum dominating set.

Problem

• Distributed algorithms
• Stochastic graphs
• Graph optimization
• Communication complexity
• Uncertainty

Innovation

• distributed stochastic algorithms
• random subgraph realization
• communication complexity
• approximation algorithms
• graph optimization