Local Algorithms for Graphs

TL;DR

This paper explores local algorithms applied to sparse random graphs, focusing on their decision-making based on local neighborhood information and their potential as efficient approximation methods like Belief Propagation.

Contribution

It provides an analysis of local algorithms' effectiveness and behavior on sparse random graphs, highlighting their reliance on local information and probabilistic assumptions.

Findings

Local algorithms perform well on sparse graphs.

Belief Propagation is an example of a local approximation method.

Local information suffices for effective decision-making in certain graph problems.

Abstract

We are going to analyze local algorithms over sparse random graphs. These algorithms are based on local information where local regards to a decision made by the exploration of a small neighbourhood of a certain vertex plus a believe of the structure of the whole graph and maybe added some randomness. This kind of algorithms can be a natural response to the given problem or an efficient approximation such as the Belief Propagation Algorithm.