Combinatorica
Trading space for time in undirected s-t connectivity
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The electrical resistance of a graph captures its commute and cover times
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A technique for lower bounding the cover time
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
A tight upper bound on the cover time for random walks on graphs
Random Structures & Algorithms
SIAM Journal on Discrete Mathematics
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
An optimal randomised logarithmic time connectivity algorithm for the EREW PRAM
Journal of Computer and System Sciences
A spectrum of time-space trade-offs for undirected s-tconnectivity
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
A tight lower bound on the cover time for random walks on graphs
Random Structures & Algorithms
Fast Connected Components Algorithms for the EREW PRAM
SIAM Journal on Computing
An O(log(n)4/3) space algorithm for (s, t) connectivity in undirected graphs
Journal of the ACM (JACM)
WSNA '02 Proceedings of the 1st ACM international workshop on Wireless sensor networks and applications
Rumor routing algorthim for sensor networks
WSNA '02 Proceedings of the 1st ACM international workshop on Wireless sensor networks and applications
The cover time of sparse random graphs.
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete 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
Efficient and robust query processing in dynamic environments using random walk techniques
Proceedings of the 3rd international symposium on Information processing in sensor networks
RaWMS -: random walk based lightweight membership service for wireless ad hoc network
Proceedings of the 7th ACM international symposium on Mobile ad hoc networking and computing
Random walks, universal traversal sequences, and the complexity of maze problems
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Undirected connectivity in O(log/sup 1.5/n) space
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
On the cover time of random geometric graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
A Device Search Strategy Based on Connections History for Patient Monitoring
IWANN '09 Proceedings of the 10th International Work-Conference on Artificial Neural Networks: Part II: Distributed Computing, Artificial Intelligence, Bioinformatics, Soft Computing, and Ambient Assisted Living
Multiple Random Walks and Interacting Particle Systems
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Tight Bounds for the Cover Time of Multiple Random Walks
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Proceedings of the 28th ACM symposium on Principles of distributed computing
Power-aware recovery for geographic routing
WCNC'09 Proceedings of the 2009 IEEE conference on Wireless Communications & Networking Conference
A study of information dissemination under multiple random walkers and replication mechanisms
MobiOpp '10 Proceedings of the Second International Workshop on Mobile Opportunistic Networking
Stochastic models for tabbed browsing
Proceedings of the 19th international conference on World wide web
Spanders: distributed spanning expanders
Proceedings of the 2010 ACM Symposium on Applied Computing
Partial information spreading with application to distributed maximum coverage
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Expansion and the cover time of parallel random walks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Energy efficient and low latency biased walk techniques for search in wireless sensor networks
Journal of Parallel and Distributed Computing
Second order centrality: Distributed assessment of nodes criticity in complex networks
Computer Communications
Multiple Random Walks in Random Regular Graphs
SIAM Journal on Discrete Mathematics
Tight bounds for the cover time of multiple random walks
Theoretical Computer Science
Tight bounds on information dissemination in sparse mobile networks
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Random walks, interacting particles, dynamic networks: randomness can be helpful
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Analysis of latency of stateless opportunistic forwarding in intermittently connected networks
IEEE/ACM Transactions on Networking (TON)
Fast information spreading in graphs with large weak conductance
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Information dissemination dynamics in delay tolerant network: a bipartite network approach
Proceedings of the third ACM international workshop on Mobile Opportunistic Networks
Fast distributed computation in dynamic networks via random walks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Spanders: Distributed spanning expanders
Science of Computer Programming
The multi-agent rotor-router on the ring: a deterministic alternative to parallel random walks
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Coalescing-branching random walks on graphs
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Random spanning trees and the prediction ofweighted graphs
The Journal of Machine Learning Research
| Hi-index | 0.00 |
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 probablistic 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.