Estimating Residual Connectivity for Random Graphs

TL;DR

This paper introduces sequential importance resampling and splitting algorithms to efficiently estimate the probability of connectivity in random graphs, addressing the computational challenge of this problem.

Contribution

The paper presents novel algorithms that improve the estimation of connectivity probabilities in random graphs through importance sampling techniques.

Findings

Algorithms effectively estimate connectivity probabilities

Numerical results demonstrate algorithm efficiency

Improved accuracy over traditional Monte Carlo methods

Abstract

Computation of the probability that a random graph is connected is a challenging problem, so it is natural to turn to approximations such as Monte Carlo methods. We describe sequential importance resampling and splitting algorithms for the estimation of these probabilities. The importance sampling steps of these algorithms involve identifying vertices that must be present in order for the random graph to be connected, and conditioning on the corresponding events. We provide numerical results demonstrating the effectiveness of the proposed algorithm.