Combinatorica
Constructing disjoint paths on expander graphs
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Expanding graphs contain all small trees
Combinatorica
Conductance and the rapid mixing property for Markov chains: the approximation of permanent resolved
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Lower bounds on the length of universal traversal sequences
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Lower bounds on the length of universal traversal sequences
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
Random walks on weighted graphs, and applications to on-line algorithms
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Time-space trade-offs for undirected st-connectivity on a JAG
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Random walks on weighted graphs and applications to on-line algorithms
Journal of the ACM (JACM)
An analysis of diffusive load-balancing
SPAA '94 Proceedings of the sixth annual ACM symposium on Parallel algorithms and architectures
Memory versus randomization in on-line algorithms
IBM Journal of Research and Development
Efficient stopping rules for Markov chains
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Design of on-line algorithms using hitting times
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
More on random walks, electrical networks, and the harmonic k-server algorithm
Information Processing Letters
On mixing times for stratified walks on the d-cube
Random Structures & Algorithms
Universal traversal sequences with backtracking
Journal of Computer and System Sciences - Complexity 2001
Robotic Exploration, Brownian Motion and Electrical Resistance
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Optimizing a Computational Method for Length Lower Bounds for Reflecting Sequences
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Efficient and robust query processing in dynamic environments using random walk techniques
Proceedings of the 3rd international symposium on Information processing in sensor networks
Fast discovery of connection subgraphs
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
How randomized search heuristics find maximum cliques in planar graphs
Proceedings of the 8th annual conference on Genetic and evolutionary computation
The power of choice in random walks: an empirical study
Proceedings of the 9th ACM international symposium on Modeling analysis and simulation of wireless and mobile systems
Note: Resistance distance and the normalized Laplacian spectrum
Discrete Applied Mathematics
On the cover time and mixing time of random geometric graphs
Theoretical Computer Science
IEEE Transactions on Knowledge and Data Engineering
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
The power of choice in random walks: An empirical study
Computer Networks: The International Journal of Computer and Telecommunications Networking
Efficient routing in intermittently connected mobile networks: the single-copy case
IEEE/ACM Transactions on Networking (TON)
Graph sparsification by effective resistances
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Many random walks are faster than one
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Robust and Efficient Covering of Unknown Continuous Domains with Simple, Ant-Like A(ge)nts
International Journal of Robotics Research
Bypass rates: reducing query abandonment using negative inferences
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 14th ACM SIGKDD international conference on Knowledge discovery and data mining
The cover time of random geometric graphs
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Memory Efficient Anonymous Graph Exploration
Graph-Theoretic Concepts in Computer Science
Graph nodes clustering with the sigmoid commute-time kernel: A comparative study
Data & Knowledge Engineering
How Well Do Random Walks Parallelize?
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Least-Resistance Path in Reasoning about Unstructured Overlay Networks
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
Using Heterogeneity to Enhance Random Walk-based Queries
Journal of Signal Processing Systems
Affinity measures based on the graph Laplacian
TextGraphs-3 Proceedings of the 3rd Textgraphs Workshop on Graph-Based Algorithms for Natural Language Processing
Commute times and the effective resistances of random trees
Probability in the Engineering and Informational Sciences
Do neighbor-avoiding walkers walk as if in a small-world network?
INFOCOM'09 Proceedings of the 28th IEEE international conference on Computer Communications Workshops
Electricity based external similarity of categorical attributes
PAKDD'03 Proceedings of the 7th Pacific-Asia conference on Advances in knowledge discovery and data mining
Note: Random walks and the effective resistance sum rules
Discrete Applied Mathematics
Radio cover time in hyper-graphs
Proceedings of the 6th International Workshop on Foundations of Mobile Computing
A class of graph-geodetic distances generalizing the shortest-path and the resistance distances
Discrete Applied Mathematics
A Spanning Tree Method for Bounding Hitting Times of Random Walks on Graphs
SIAM Journal on Discrete Mathematics
Robust network planning in nonuniform traffic scenarios
Computer Communications
On the cover time of random geometric graphs
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On time analysis of random walk based token circulation algorithms
ISSADS'05 Proceedings of the 5th international conference on Advanced Distributed Systems
Commute times of random walks on trees
Discrete Applied Mathematics
Spectral sparsification of graphs: theory and algorithms
Communications of the ACM
A recursion formula for resistance distances and its applications
Discrete Applied Mathematics
Radio cover time in hyper-graphs
Ad Hoc Networks
Hi-index | 0.02 |
View an n-vertex, m-edge undirected graph as an electrical network with unit resistors as edges. We extend known relations between random walks and electrical networks by showing that resistance in this network is intimately connected with the lengths of random walks on the graph. For example, the commute time between two vertices s and t (the expected length of a random walk from s to t and back) is precisely characterized by the effective resistance Rst between s and t: commute time = 2mRst. Additionally, the cover time (the expected length of a random walk visiting all vertices) is characterized by the maximum resistance R in the graph to within a factor of log n: mR ≤ cover time ≤ O (mR log n). For many graphs, the bounds on cover time obtained in this manner are better than those obtained from previous techniques such as the eigenvalues of the adjacency matrix. In particular, using this approach, we improve known bounds on cover times for various classes of graphs, including high-degree graphs, expanders, and multi-dimensional meshes. Moreover, resistance seems to provide an intuitively appealing and tractable approach to these problems.