Better Bounds for Coalescing-Branching Random Walks

Mitzenmacher, Michael; Rajaraman, Rajmohan; Roche, Scott

doi:10.1145/3209688

Cited by 3 publications

(3 citation statements)

References 30 publications

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“…Other superficially related processes include coalescing random walks [6,30], and coalescing branching walks [7,36]. See also [13] for a survey on multiple random walks.…”

Section: Related Workmentioning

confidence: 99%

How to Spread a Rumor: Call Your Neighbors or Take a Walk?

Giakkoupis,

Mallmann-Trenn,

Saribekyan

2020

Preprint

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We study the problem of randomized information dissemination in networks. We compare the now standard push-pull protocol, with agent-based alternatives where information is disseminated by a collection of agents performing independent random walks. In the visit-exchange protocol, both nodes and agents store information, and each time an agent visits a node, the two exchange all the information they have. In the meet-exchange protocol, only the agents store information, and exchange their information with each agent they meet.We consider the broadcast time of a single piece of information in an n-node graph for the above three protocols, assuming a linear number of agents that start from the stationary distribution. We observe that there are graphs on which the agent-based protocols are significantly faster than push-pull, and graphs where the converse is true. We attribute the good performance of agent-based algorithms to their inherently fair bandwidth utilization, and conclude that, in certain settings, agent-based information dissemination, separately or in combination with push-pull, can significantly improve the broadcast time.The graphs considered above are highly non-regular. Our main technical result is that on any regular graph of at least logarithmic degree, push-pull and visit-exchange have the same asymptotic broadcast time. The proof uses a novel coupling argument which relates the random choices of vertices in push-pull with the random walks in visit-exchange. Further, we show that the broadcast time of meet-exchange is asymptotically at least as large as the other two's on all regular graphs, and strictly larger on some regular graphs.As far as we know, this is the first systematic and thorough comparison of the running times of these very natural information dissemination protocols.

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“…Other superficially related processes include coalescing random walks [6,30], and coalescing branching walks [7,36]. See also [13] for a survey on multiple random walks.…”

Section: Related Workmentioning

confidence: 99%

How to Spread a Rumor: Call Your Neighbors or Take a Walk?

Giakkoupis,

Mallmann-Trenn,

Saribekyan

2020

Preprint

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“…Remark 2. The random voting-DAG H(v 0 ) can be viewed as the trajectory of a Coalescing and Branching random walk or, for short, COBRA walk (see [3], [6], [9] for recent research). A COBRA walk is a discrete process on a graph G where vertices are occupied by particles.…”

Section: Model and Proof Strategymentioning

confidence: 99%

Best-of-Three Voting on Dense Graphs

Kang

Rivera

2019

The 31st ACM Symposium on Parallelism in Algorithms and Architectures

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Given a graph G of n vertices, where each vertex is initially attached an opinion of either red or blue. We investigate a random process known as the Bestof-three voting. In this process, at each time step, every vertex chooses three neighbours at random and adopts the majority colour. We study this process for a class of graphs with minimum degree d = n α , where α = Ω (log log n) −1 . We prove that if initially each vertex is red with probability greater than 1/2 + δ, and blue otherwise, where δ ≥ (log d) −C for some C > 0, then with high probability this dynamic reaches a final state where all vertices are red within O (log log n) + O log δ −1 steps .

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“…Other superficially related processes include coalescing random walks [5,26], and coalescing branching walks [6,30]. See also [12] for a survey on multiple random walks.…”

Section: Related Workmentioning

confidence: 99%

How to Spread a Rumor

Giakkoupis

Mallmann-Trenn

Saribekyan

2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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We study the problem of randomized information dissemination in networks. We compare the now standard push-pull protocol, with agent-based alternatives where information is disseminated by a collection of agents performing independent random walks. In the visit-exchange protocol, both nodes and agents store information, and each time an agent visits a node, the two exchange all the information they have. In the meet-exchange protocol, only the agents store information, and exchange their information with each agent they meet. We consider the broadcast time of a single piece of information in an n-node graph for the above three protocols, assuming a linear number of agents that start from the stationary distribution. We observe that there are graphs on which the agent-based protocols are significantly faster than push-pull, and graphs where the converse is true. We attribute the good performance of agent-based algorithms to their inherently fair bandwidth utilization, and conclude that, in certain settings, agent-based information dissemination, separately or in combination with push-pull, can significantly improve the broadcast time. The graphs considered above are highly non-regular. Our main technical result is that on any regular graph of at least logarithmic degree, push-pull and visit-exchange have the same asymptotic broadcast time. The proof uses a novel coupling argument which relates the random choices of vertices in push-pull with the random walks in visit-exchange. Further, we show that the broadcast time of meet-exchange is asymptotically at least as large as the other two's on all regular graphs, and strictly larger on some regular graphs. As far as we know, this is the first systematic and thorough comparison of the running times of these very natural information dissemination protocols. CCS CONCEPTS • Computing methodologies → Distributed algorithms; • Mathematics of computing → Stochastic processes.

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Better Bounds for Coalescing-Branching Random Walks

Cited by 3 publications

References 30 publications

How to Spread a Rumor: Call Your Neighbors or Take a Walk?

How to Spread a Rumor: Call Your Neighbors or Take a Walk?

Best-of-Three Voting on Dense Graphs

How to Spread a Rumor

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