Better Bounds for Coalescing-Branching Random Walks

Abstract

Coalescing-branching random walks, or cobra walks for short, are a natural variant of random walks on graphs that can model the spread of disease through contacts or the spread of information in networks. In a k-cobra walk, at each time step a subset of the vertices are active; each active vertex chooses k random neighbors (sampled independently and uniformly with replacement) that become active at the next step, and these are the only active vertices at the next step. A natural quantity to study for cobra walks is the cover time, which corresponds to the expected time when all nodes have become infected or received the disseminated information.