2011/04/07 by Noga Alon, Chen Avin, Michal Koucký +3 · 5 citations
Computer Science · #Complexity and Algorithms in Graphs #Caching and Content Delivery #Optimization and Search Problems
paper · doi:10.1017/s0963548311000125
openalex publication_date 2011/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the cover time – the expected time required to visit every node in a graph at least once – and we show that for a large collection of interesting graphs, running many random walks in parallel yields a speed-up in the cover time that is linear in the number of parallel walks. We demonstrate that an exponential speed-up is sometimes possible, but that some natural graphs allow only a logarithmic speed-up. A problem related to ours (in which the walks start from some probabilistic distribution on vertices) was previously studied in the context of space efficient algorithms for undirected s – t connectivity and our results yield, in certain cases, an improvement upon some of the earlier bounds.