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
Rounds in communication complexity revisited
SIAM Journal on Computing
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Communication complexity
A SubLinear Time Distributed Algorithm for Minimum-Weight Spanning Trees
SIAM Journal on Computing
The small-world phenomenon: an algorithmic perspective
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Spatial gossip and resource location protocols
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Distributed MST for constant diameter graphs
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
Search and replication in unstructured peer-to-peer networks
ICS '02 Proceedings of the 16th international conference on Supercomputing
SIAM Journal on Computing
Peer-to-Peer Membership Management for Gossip-Based Protocols
IEEE Transactions on Computers
Random Leaders and Random Spanning Trees
Proceedings of the 3rd International Workshop on Distributed Algorithms
A self-stabilizing distributed algorithm for spanning tree construction in wireless ad hoc networks
Journal of Parallel and Distributed Computing - Special issue on wireless and mobile ad hoc networking and computing
Graph-theoretic analysis of structured peer-to-peer systems: routing distances and fault resilience
Proceedings of the 2003 conference on Applications, technologies, architectures, and protocols for computer communications
Mercury: supporting scalable multi-attribute range queries
Proceedings of the 2004 conference on Applications, technologies, architectures, and protocols for computer communications
Distributed approximation: a survey
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Random walk based node sampling in self-organizing networks
ACM SIGOPS Operating Systems Review
Generating random spanning trees
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Proceedings of the 28th ACM symposium on Principles of distributed computing
Graph Distances in the Data-Stream Model
SIAM Journal on Computing
Spanders: distributed spanning expanders
Proceedings of the 2010 ACM Symposium on Applied Computing
Efficient distributed random walks with applications
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Distributed verification and hardness of distributed approximation
Proceedings of the forty-third annual ACM symposium on Theory of computing
Quickly routing searches without having to move content
IPTPS'05 Proceedings of the 4th international conference on Peer-to-Peer Systems
Networks cannot compute their diameter in sublinear time
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Fast distributed computation in dynamic networks via random walks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Dense subgraphs on dynamic networks
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Journal of the ACM (JACM)
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We consider the problem of performing a random walk in a distributed network. Given bandwidth constraints, the goal of the problem is to minimize the number of rounds required to obtain a random walk sample. Das Sarma et al. [PODC'10] show that a random walk of length l on a network of diameter D can be performed in Õ(√{l D}+D) time. A major question left open is whether there exists a faster algorithm, especially whether the multiplication of √{l} and √{D} is necessary. In this paper, we show a tight unconditional lower bound on the time complexity of distributed random walk computation. Specifically, we show that for any n, D, and D ≤ l ≤ (n/(D3 log n))1/4, performing a random walk of length Θ(l) on an n-node network of diameter D requires Ω(√{lD}+D) time. This bound is unconditional, i.e., it holds for any (possibly randomized) algorithm. To the best of our knowledge, this is the first lower bound that the diameter plays a role of multiplicative factor. Our bound shows that the algorithm of Das Sarma et al. is time optimal. Our proof technique introduces a new connection between bounded-round communication complexity and distributed algorithm lower bounds with D as a trade-off parameter, strengthening the previous study by Das Sarma et al. [STOC'11]. In particular, we make use of the bounded-round communication complexity of the pointer chasing problem. Our technique can be of independent interest and may be useful in showing non-trivial lower bounds on the complexity of other fundamental distributed computing problems.