Network exploration using true self-avoiding walks

Abstract

We study the mean first passage time (MFPT) of true self-avoiding walks (TSAWs) on various networks as a measure of searching efficiency. From the numerical analysis, we find that the MFPT of TSAWs, τ^{TSAW}, approaches the theoretical minimum τ^{th}/N=1/2 on synthetic networks whose degree-degree correlations are positive. On the other hand, for biased random walks (BRWs) we find that the MFPT, τ^{BRW}, depends on the parameter α, which controls the degree-dependent bias. More importantly, we find that the minimum MFPT of BRWs, τ_{min}^{BRW}, always satisfies the inequality τ_{min}^{BRW}>τ^{TSAW} on any synthetic network. The inequality is also satisfied on various real networks. From these results, we show that the TSAW is one of the most efficient models, whose efficiency approaches the theoretical limit in network explorations.

Knowledge acquisition: A Complex networks approach

“…The TSAW dynamics; nonetheless, is more analytically tractable than SAW because the former does not depend on a path restart mechanism [13]. Recently, Kim et al [12] showed that the TSAW dynamics is an efficient way to explore complex networks with agents having only the knowledge of the local structure of the network.…”

“…The memory aspect is encompassed into the proposed dynamics by an specific type of random walk, the true self-avoiding walk (TSAW), which was found to be one of the most efficient models to explore networks [12]. In the TSAW dynamics, the agent tends to avoid passing through already visited nodes.…”

A comparative analysis of knowledge acquisition performance in complex networks

“…random walked biased by the inverse of the degree (RWID) [10], and true self-avoiding walk (TSAW) [3,24]. These walks have been widely employed to study the dynamics of learning curves in the last few years [5,6,28].…”

“…Network science has been employed to represent a great variety of complex systems [2,7,17,18,20,27]. In recent studies, complex networks have displayed the potential to represent the space of transitions between states for many types of systems [14,24,25]. In this context, the driving processes generating sequences are represented by stochastic walks of a variety of heuristics.…”

Análise estrutural de redes complexas modulares por meio de caminhadas auto-excludentes

“…88,90,91 Além deste, recentemente, Kim estudou analiticamente o tempo médio de primeira passagem em vários tipos de redes, mostrando ser um recurso exploratório bem eficiente. 166 Aplicações práticas desta dinâmica são encontradas nos trabalhos de Travençolo, 167,168 que aplicou este modelo aleatório para detecção de bordas em redes complexas e, baseado nas definições de acessibilidades proposta por Rosvall, 169 estudou as características desta definição utilizando SAW aplicado a ruas de cidades. Mais recentemente, Bertozzi 170 estudou a evolução hierárquica de organizações criminosas e aplicou a caminha auto-excludente como estratégia para capturar os participantes e consequentemente acabar com tais organizações.…”