Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Randomized algorithms
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
Random Walk for Self-Stabilizing Group Communication in Ad-Hoc Networks
SRDS '02 Proceedings of the 21st IEEE Symposium on Reliable Distributed Systems
On the Cover Time for Random Walks on Random Graphs
Combinatorics, Probability and Computing
The cover time of two classes of random graphs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Impact of local topological information on random walks on finite graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Maximum hitting time for random walks on graphs
Random Structures & Algorithms
Derandomizing Random Walks in Undirected Graphs Using Locally Fair Exploration Strategies
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Note: The hitting and cover times of Metropolis walks
Theoretical Computer Science
How to design a linear cover time random walk on a finite graph
SAGA'09 Proceedings of the 5th international conference on Stochastic algorithms: foundations and applications
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
How slow, or fast, are standard random walks?: analysis of hitting and cover times on trees
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
How slow, or fast, are standard random walks?: analysis of hitting and cover times on trees
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Hi-index | 5.23 |
Standard random walks on finite graphs select the vertex visited next to the adjacent vertices at random with the same probability. Despite not using any global topological information, they guarantee O(n^3) hitting and cover times for any graph, where n is the order of the graph. Motivated by network protocol applications, this paper investigates the impact of local topological information on designing ''better'' random walks. We first show that (a) for any transition probability matrix, the hitting (and hence the cover) time of a path graph is @W(n^2). We next investigate for any graph G=(V,E) a transition probability matrix P=(p(u,v))"u","v"@?"V defined by p(u,v)={deg^-^1^/^2(v)@?w@?N(u)deg^-^1^/^2(w)if v@?N(u),0otherwise ,where N(u) and deg(u) are respectively the set of adjacent vertices of u and the u's degree. Random walks obeying this transition probability matrix are shown to guarantee the following: For any graph, (b) the hitting time is O(n^2), and (c) the cover time is O(n^2logn). Facts (a) and (b) show that the degree information on the adjacent vertices is powerful enough for random walks to achieve the optimum hitting time.