The cover time of random geometric graphs

The cover time of random geometric graphs

We study the cover time of random geometric graphs. Let I(d) = [0, 1] denote the unit torus in d dimensions. Let D(x, r) denote the ball (disc) of radius r. Let Υd be the volume of the unit ball D(0, 1) in d dimensions. A random geometric graph G = G(d, r, n) in d dimensions is defined as follows: Sample n points V independently and uniformly at random from I(d). For each point x draw a ball D(...

On the Cover Time of Random Geometric Graphs

The cover time of graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of ad-hoc and sensor networks, an interesting class of random graphs, namely random geometric graphs, has gained new relevance and its properties have been the subject of much study. A random geometric graph G(n, r) is obtained by placing n points uniformly at...

The Cover Time of Random Regular Graphs

The cover time of regular random graphs

Let r ≥ 3 be integer, and let Gr denote the set of r-regular graphs with vertex set V = {1, 2, . . . , n}. Let G be chosen randomly from Gr. We prove that whp the cover time of a random walk on G is asymptotic to r−1 r−2 n log n.

On the cover time and mixing time of random geometric graphs

The cover time and mixing time of graphs has much relevance to algorithmic applications and has been extensively investigated. Recently, with the advent of ad-hoc and sensor networks, an interesting class of random graphs, namely random geometric graphs, has gained new relevance and its properties have been the subject of much study. A random geometric graph G(n, r) is obtained by placing n poi...