The Robot Crawler Model on Complete k-Partite and Erdos-Renyi Random Graphs

Web crawlers are used by internet search engines to gather information about the web graph. In this paper we investigate a simple process which models such software by walking around the vertices of a graph. Once initial random vertex weights have been assigned, the robot crawler traverses the graph deterministically following a greedy algorithm, always visiting the neighbour of least weight and then updating this weight to be the highest overall. We consider the maximum, minimum and average number of steps taken by the crawler to visit every vertex of firstly, sparse Erdos-Renyi random graphs and secondly, complete k-partite graphs. Our work is closely related to a paper of Bonato et al. who introduced the model.