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Meeting times of random walks on graphs

1999
*
Information Processing Letters
*

W e prove an upper bound

doi:10.1016/s0020-0190(99)00017-4
fatcat:5i4c4gyf25ghrfg4ed3uux2iwe
*on*the*meeting**time**of*an arbitrary number*of**random**walks*in any connected undirected*graph*in terms*of*the*meeting**times**of*fewer*random**walks*. ... W Concluding remarks and open problems Theorem 6 bounds the*meeting**time**of*several*random**walks**on*an undirected connected*graph*by a function*of*the*meeting**times**of*fewer*random**walks*. ... The expected*time*until several*random**walks**on*a*graph*collapse into*one*characterizes the performance*of*this protocol. In the literature, however,*one**random**walk**on*a*graph*is usually analyzed. ...##
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Exact computation for meeting times and infection times of random walks on graphs

2015
*
Pacific Journal of Mathematics for Industry
*

We consider independent multiple

doi:10.1186/s40736-015-0016-2
fatcat:6yyovejhebdufkr23v25qqvw2e
*random**walks**on**graphs*and study comparison results*of**meeting**times*and infection*times*between many conditions*of*the*random**walks*by obtaining the exact density functions ... The author was supported by JST, ERATO, Kawarabayashi Large*Graph*Project. ... It is mentioned in [1] that*meeting**times**of*two*random**walks**on*some*graphs*can be regarded as a first hitting*time**of*a single*random**walk*. We give a generalization*of*this fact. ...##
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MEETING TIMES OF RANDOM WALKS ON GRAPHS
[article]

2008

Both bounds express the

doi:10.11575/prism/31330
fatcat:b2s6nhrpbjclnojfemdeprc26y
*meeting**time**of*several*random**walks*in terms*of*the*meeting**times**of*fewer*random**walks*. ... These techniques are used to prove two upper bounds*on*the*meeting**time**of*an arbitrary number*of**random**walks*in any connected undirected*graph*. ... Concluding remarks and open problems Theorem 6 bounds the*meeting**time**of*several*random**walks**on*an undirected connected*graph*by a function*of*the*meeting**times**of*fewer*random**walks*. ...##
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An efficient similarity search framework for SimRank over large dynamic graphs

2015
*
Proceedings of the VLDB Endowment
*

In the preprocessing stage, TSF samples a set

doi:10.14778/2757807.2757809
fatcat:kxltrqvpgramfbznz7b3ahcodm
*of**one*-way*graphs*to index raw*random**walks*in a novel manner within O(N Rg)*time*and space, where N is the number*of*vertices and Rg is the number*of**one*-way ... In this paper, we propose a novel two-stage*random*-*walk*sampling framework (TSF) for SimRank-based similarity search (e.g., top-k search). ... In the tsM ap, each*meeting*vertex is associated with its all possible*meeting**times*, like vertex 1 can be met at*times*1 or 2 based*on*the two sampled*random**walks*. ...##
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Multiple Random Walks and Interacting Particle Systems
[chapter]

2009
*
Lecture Notes in Computer Science
*

For k independent

doi:10.1007/978-3-642-02930-1_33
fatcat:axxnxxnv2fdcbfz2bb5ehupw2i
*walks**on*a*random*regular*graph*G, the cover*time*CG(k) is asymptotic to CG/k, where CG is the cover*time**of*a single*walk*. ... We study properties*of*multiple*random**walks**on*a*graph*under various assumptions*of*interaction between the particles. To give precise results, we make our analysis for*random*regular*graphs*. ... To make our analysis, we reduce the multiple*random**walks*to a single*random**walk**on*a suitably defined product*graph*, to which we apply the technique*of*[6] . ...##
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Graph Degree Heterogeneity Facilitates Random Walker Meetings
[article]

2020
*
arXiv
*
pre-print

The first

arXiv:2005.11161v3
fatcat:nnfqyidte5gvvkiac4ulyemuwy
*meeting**time*is*one**of*the important metrics for multiple*random**walks*. ... The first*meeting**time**of*multiple*random**walks*has been analyzed previously, but many*of*these analyses have focused*on*regular*graphs*. ... The first*meeting**time*is*one**of*the important metrics for multiple*random**walks*. ...##
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Coalescing random walks and voting on connected graphs
[article]

2016
*
arXiv
*
pre-print

In a coalescing

arXiv:1204.4106v3
fatcat:rwq5xit4xne33kee76d6qstdbe
*random**walk*, a set*of*particles make independent*random**walks**on*a*graph*. ... Whenever*one*or more particles*meet*at a vertex, they unite to form a single particle, which then continues the*random**walk*through the*graph*. ... Previous work*on*coalescing*random**walks*We summarize some known results for coalescing*random**walks*. There are two distinct models for the transition*times**of**random**walks**on*finite*graphs*. ...##
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On coalescence time in graphs--When is coalescing as fast as meeting?
[article]

2018
*
arXiv
*
pre-print

Coalescing

arXiv:1611.02460v4
fatcat:5av5epd5mbf7layr6i46g44t6y
*random**walks*is a fundamental stochastic process, where a set*of*particles perform independent discrete-*time**random**walks**on*an undirected*graph*. ... As a general result, we establish that for*graphs*whose*meeting**time*is only marginally larger than the mixing*time*(a factor*of*log^2 n), the coalescence*time**of*n*random**walks*equals the*meeting**time*... the hitting*time*(Theorem 1.4) . ...##
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Coalescing Random Walks and Voting on Connected Graphs

2013
*
SIAM Journal on Discrete Mathematics
*

In a coalescing

doi:10.1137/120900368
fatcat:rfptirzvvbgnpklh5zji2rwpna
*random**walk*, a set*of*particles make independent discrete-*time**random**walks**on*a*graph*. ... Whenever*one*or more particles*meet*at a vertex, they unite to form a single particle, which then continues a*random**walk*through the*graph*. ... We summarize some known results for coalescing*random**walks*. There are two distinct models for the transition*times**of**random**walks**on*finite*graphs*. ...##
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Random Walks on Random Graphs
[chapter]

2009
*
Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering
*

Among them are the following: Mixing

doi:10.1007/978-3-642-02427-6_18
fatcat:jsowgcrxznf6jgw4kvwggwkv4e
*time**of*the*random**walk*, cover*time**of*a*random**graph*, properties*of*multiple particle*walks*,*random**walks**on**graph*processes, constructing*random*networks using*random*...*Random**Graphs*Various topics arise in the context*of**random**walks**on**random**graphs*. ...##
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An experimental evaluation of simrank-based similarity search algorithms

2017
*
Proceedings of the VLDB Endowment
*

Our study reveals that none

doi:10.14778/3055540.3055552
fatcat:qb6alvxakfcd5dtyxqzrvpc6sm
*of*these algorithms dominates the others: algorithms based*on*iterative method often have higher accuracy while algorithms based*on**random**walk*can be more scalable. ... Given a*graph*, SimRank is*one**of*the most popular measures*of*the similarity between two vertices. ... An FPG organizes in a compact way*one**random**walk*with length T for each vertex together with the distance where each two*random**walks**meet*for the first*time*. ...##
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On the Convergence Time of Asynchronous Distributed Quantized Averaging Algorithms

2011
*
IEEE Transactions on Automatic Control
*

By appealing to

doi:10.1109/tac.2010.2093276
fatcat:ig6ybtimd5g6xcatdbfvoc7jri
*random**walks**on**graphs*, we derive polynomial bounds*on*the expected convergence*time**of*the algorithms presented, as a function*of*the number*of*agents in the network. ... The focus*of*this technical note is*on*the study*of*the convergence*time**of*the proposed quantized averaging algorithms. ... The*Meeting**Time**of*Two Natural*Random**Walks**on*a Fixed*Graph*G We first study a variation*of*the problem in [8] , namely, the*meeting**time**of*two natural*random**walks**on*a fixed*graph*G. ...##
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An Upper Bound on the Convergence Time for Quantized Consensus of Arbitrary Static Graphs

2015
*
IEEE Transactions on Automatic Control
*

We use the theory

doi:10.1109/tac.2014.2342071
fatcat:daapmymcw5ht5nt7ryf3ixtixm
*of*electric networks,*random**walks*, and couplings*of*Markov chains to derive an O(N^3 N) upper bound for the expected convergence*time**on*an arbitrary*graph**of*size N, improving*on*the ... Our result is not dependent*on**graph*topology. Example*of*complete*graphs*is given to show how to extend the analysis to*graphs**of*given topology. ... We use the degree*of*nodes*on*the shortest path*on*the*graph*to improve the bound*on*the hitting*time**of*the biased*random**walk*. • The analysis for arbitrary*graphs*is extended to a tighter bound for certain ...##
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The infection time of graphs

2006
*
Discrete Applied Mathematics
*

We easily get that an upper bound

doi:10.1016/j.dam.2006.04.026
fatcat:d6cmaplzlbhxzozct5sx3ihjau
*on*the expected value*of*T k is the worst case (over all initial positions) expected*meeting**time*m **of*two*random**walks*multiplied by (log k). ... The infection*time*T k*of*infecting all the white particles with red color is then a*random*variable that depends*on*k, the initial position*of*the particles, the number*of*nodes and edges*of*the*graph*... The machinery stated above can be used also for the*meeting**times*: Definition 8. Let M i,j be the first*time*that two independent copies*of*a*random**walk**on*G*meet*given that they start from i, j . ...##
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Robotic Surveillance Based on the Meeting Time of Random Walks
[article]

2019
*
arXiv
*
pre-print

First, by analyzing multiple

arXiv:1912.02693v1
fatcat:fssldkrtwjfdzeh4prjiy64wpi
*random**walks**on*a common*graph*as a single*random**walk**on*the Kronecker product*graph*, we provide the first closed-form expression for the expected*meeting**time*in terms*of*... This paper analyzes the*meeting**time*between a pair*of*pursuer and evader performing*random**walks**on*digraphs. ... The*meeting**time**of*two Markov chains Consider the pursuer and evader performing*random**walks**on*a strongly connected*graph*G = (V, E) with the node set V = {1, . . . , n} and E ⊂ V × V . ...
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