Distributed Stochastic Graph Algorithms

TL;DR

This paper introduces fast distributed algorithms for stochastic graph optimization problems, demonstrating they outperform traditional methods and lower bounds in tasks like maximum matching and vertex cover.

Contribution

It presents novel distributed stochastic algorithms that significantly improve efficiency for key graph optimization problems under uncertainty.

Findings

Distributed stochastic algorithms are faster than non-stochastic counterparts.

They can surpass known lower bounds in distributed settings.

Achieved efficient approximation algorithms for maximum matching, vertex cover, and dominating set.

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.