A decentralized algorithm for spectral analysis
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Unsupervised Learning of Image Manifolds by Semidefinite Programming
International Journal of Computer Vision
Random walks in peer-to-peer networks: algorithms and evaluation
Performance Evaluation - P2P computing systems
A duality view of spectral methods for dimensionality reduction
ICML '06 Proceedings of the 23rd international conference on Machine learning
A scheme for robust distributed sensor fusion based on average consensus
IPSN '05 Proceedings of the 4th international symposium on Information processing in sensor networks
IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Mathematical aspects of mixing times in Markov chains
Foundations and Trends® in Theoretical Computer Science
Distributed average consensus with least-mean-square deviation
Journal of Parallel and Distributed Computing
Randomized Protocols for Duplicate Elimination in Peer-to-Peer Storage Systems
IEEE Transactions on Parallel and Distributed Systems
A decentralized algorithm for spectral analysis
Journal of Computer and System Sciences
Communication constraints in the average consensus problem
Automatica (Journal of IFAC)
RaWMS - Random Walk Based Lightweight Membership Service for Wireless Ad Hoc Networks
ACM Transactions on Computer Systems (TOCS)
Random sampling from a search engine's index
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Foundations and Trends® in Networking
International Journal of Robotics Research
Randomized shortest-path problems: Two related models
Neural Computation
Uniform Sampling for Directed P2P Networks
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
A packet-centric approach to distributed rateless coding in wireless sensor networks
SECON'09 Proceedings of the 6th Annual IEEE communications society conference on Sensor, Mesh and Ad Hoc Communications and Networks
Raptor packets: a packet-centric approach to distributed raptor code design
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
A distributed dynamical scheme for fastest mixing Markov chains
ACC'09 Proceedings of the 2009 conference on American Control Conference
Distributed information filtering using consensus filters
ACC'09 Proceedings of the 2009 conference on American Control Conference
Analysis of wireless optical communications feasibility in presence of clouds using Markov chains
IEEE Journal on Selected Areas in Communications - Special issue on optical wireless communications
Contaminated areas monitoring via distributed rateless coding with constrained data gathering
Proceedings of the 6th International Wireless Communications and Mobile Computing Conference
Distributed averaging via lifted Markov chains
IEEE Transactions on Information Theory
Rateless packet approach for data gathering wireless sensor networks
IEEE Journal on Selected Areas in Communications - Special issue on simple wireless sensor networking solutions
Weight optimization for consensus algorithms with correlated switching topology
IEEE Transactions on Signal Processing
Design is as Easy as Optimization
SIAM Journal on Discrete Mathematics
A Randomized Incremental Subgradient Method for Distributed Optimization in Networked Systems
SIAM Journal on Optimization
Scalable Uniform Graph Sampling by Local Computation
SIAM Journal on Scientific Computing
Proceedings of the 20th international conference on World wide web
Interaction-driven opinion dynamics in online social networks
Proceedings of the First Workshop on Social Media Analytics
Decentralized average consensus in wireless sensor networks with fading communication signals
Proceedings of the 5th International Conference on Ubiquitous Information Management and Communication
Walking on a graph with a magnifying glass: stratified sampling via weighted random walks
Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Walking on a graph with a magnifying glass: stratified sampling via weighted random walks
ACM SIGMETRICS Performance Evaluation Review - Performance evaluation review
Universal mixing of quantum walk on graphs
Quantum Information & Computation
Optimal gateway selection in multi-domain wireless networks: a potential game perspective
MobiCom '11 Proceedings of the 17th annual international conference on Mobile computing and networking
Hearing the clusters of a graph: A distributed algorithm
Automatica (Journal of IFAC)
Design is as easy as optimization
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Decentralized Average Consensus in Wireless Sensor Networks with Unreliable Communication Channels
International Journal of Handheld Computing Research
Stochastic surveillance strategies for spatial quickest detection
International Journal of Robotics Research
Stochastic activity authoring with direct user control
Proceedings of the 18th meeting of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games
Graph diameter, eigenvalues, and minimum-time consensus
Automatica (Journal of IFAC)
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We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate of the Markov chain, is determined by the second largest eigenvalue modulus (SLEM) of the transition probability matrix. In this paper we address the problem of assigning probabilities to the edges of the graph in such a way as to minimize the SLEM, i.e., the problem of finding the fastest mixing Markov chain on the graph. We show that this problem can be formulated as a convex optimization problem, which can in turn be expressed as a semidefinite program (SDP). This allows us to easily compute the (globally) fastest mixing Markov chain for any graph with a modest number of edges (say, $1000$) using standard numerical methods for SDPs. Larger problems can be solved by exploiting various types of symmetry and structure in the problem, and far larger problems (say, 100,000 edges) can be solved using a subgradient method we describe. We compare the fastest mixing Markov chain to those obtained using two commonly used heuristics: the maximum-degree method, and the Metropolis--Hastings algorithm. For many of the examples considered, the fastest mixing Markov chain is substantially faster than those obtained using these heuristic methods. We derive the Lagrange dual of the fastest mixing Markov chain problem, which gives a sophisticated method for obtaining (arbitrarily good) bounds on the optimal mixing rate, as well as the optimality conditions. Finally, we describe various extensions of the method, including a solution of the problem of finding the fastest mixing reversible Markov chain, on a fixed graph, with a given equilibrium distribution.