On a cover time problem on a dynamic graph with steps at random times

A Graph Patrol Problem with Random Attack Times

This paper presents a patrol problem, where a patroller traverses a graph through edges to detect potential attacks at nodes. To design a patrol policy, the patroller needs to take into account not only the graph structure, but also the different attack time distributions, as well as different costs incurred due to successful attacks, at different nodes. We consider both random attackers and st...

Explicit Bound on Cover Time and Cover Time of Random Walk on Complete Bipartite Graph

A Random Walk with Exponential Travel Times

Consider the random walk among N places with N(N - 1)/2 transports. We attach an exponential random variable Xij to each transport between places Pi and Pj and take these random variables mutually independent. If transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

The cover time of a biased random walk on a random cubic graph

Our aim in this paper is to analyse a variation on a simple random walk that may tend to speed up the cover time of a connected graph. This variation is just one of several possible approaches which include (i) non-bactracking walks, see Alon, Benjamini, Lubetzky and Sodin [3], (ii) walks that prefer unused edges, see Berenbrink, Cooper and Friedetzky [4] or (iii) walks that a biassed toward lo...

Cover time of a random graph with given degree sequence

In this paper we establish the cover time of a random graph G(d) chosen uniformly at random from the set of graphs with vertex set [n] and degree sequence d. We show that under certain restrictions on d, the cover time of G(d) is whp asymptotic to d−1 d−2 θ dn log n. Here θ is the average degree and d is the effective minimum degree.