Searching efficiency of multiple walkers on the weighted networks

Dai, Lingfei; Dai, Meifeng; Huang, Yu; Yin, Li; Shen, Jizhong; Chi, Huijia; Su, Weiyi

doi:10.1016/j.physa.2019.123352

Cited by 4 publications

(2 citation statements)

References 27 publications

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“…Some such applications include cellular signal transduction 24 , exciton transport in molecular crystals, web search algorithms 16 , a class of image segmentation algorithms 25 , graph clustering 26 and recommender systems 27 which are widely used for personalization of user experience on websites. But the problem of multiple walkers on networks has not attracted sufficient attention yet and apart from ones which are a straightforward generalization of the single walker case, it is largely an unexplored area of research and known results are very few [28][29][30] .…”

Section: Introductionmentioning

confidence: 99%

Extreme events in stochastic transport on networks

Kumar

Kulkarni

Santhanam

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Extreme events are emergent phenomena in multi-particle transport processes on complex networks. In practice, such events could range from power blackouts to call drops in cellular networks to traffic congestion on roads. All the earlier studies of extreme events on complex networks have focused only on the nodal events. If random walks are used to model transport process on a network, it is known that degree of the nodes determines the extreme event properties. In contrast, in this work, it is shown that extreme events on the edges display a distinct set of properties from that of the nodes. It is analytically shown that the probability for the occurrence of extreme events on an edge is independent of the degree of the nodes linked by the edge and is dependent only on the total number of edges on the network and the number of walkers on it. Further, it is also demonstrated that non-trivial correlations can exist between the extreme events on the nodes and the edges. These results are in agreement with the numerical simulations on a synthetic and real-life network.

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Section: Introductionmentioning

confidence: 99%

Extreme events in stochastic transport on networks

Kumar

Kulkarni

Santhanam

2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Despite these potential applications, a complete theoretical framework for the analysis of simultaneous random walkers is still missing. Some of the recent advances consider the searching ef-ficiency of multiple walkers on networks, exploring the mean time required to find a given target by one or some of the walkers [45], universal laws governing the search time [39,45,46], analytical results for encounter times for many random walkers [47] and the expected time searchers take to capture moving targets specified in advance [48,49]. Figure 1 illustrates some of the possible situations that arise when we consider the activity of two agents visiting nodes following edges represented by lines.…”

Section: Introductionmentioning

confidence: 99%

Mean encounter times for multiple random walkers on networks

Riascos,

Sanders

2020

Preprint

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We introduce a general approach for the study of the collective dynamics of non-interacting random walkers on connected networks. We analyze the movement of R independent (Markovian) walkers, each defined by its own transition matrix. By using the eigenvalues and eigenvectors of the R independent transition matrices, we deduce analytical expressions for the collective stationary distribution and the average number of steps needed by the random walkers to start in a particular configuration and reach specific nodes the first time (mean firstpassage times), as well as global times that characterize the global activity. We apply these results to the study of mean first-encounter times for local and non-local random walk strategies on different types of networks, with both synchronous and asynchronous motion.

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Mean encounter times for multiple random walkers on networks

Riascos

Sanders

2021

Phys. Rev. E

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Searching efficiency of multiple walkers on the weighted networks

Cited by 4 publications

References 27 publications

Extreme events in stochastic transport on networks

Extreme events in stochastic transport on networks

Mean encounter times for multiple random walkers on networks

Mean encounter times for multiple random walkers on networks

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