A model of self-avoiding random walks for searching complex networks

  • Authors:
  • Víctor M. López Millán;Vicent Cholvi;Luis López;Antonio Fernández Anta

  • Affiliations:
  • Departamento de Sistemas Informáticos y de Telecomunicación, Universidad CEU San Pablo, Madrid, Spain;Departamento de Lenguajes y Sistemas Informáticos, Universitat Jaume I, Castellón, Spain;Departamento de Sistemas Telemáticos y Computación, Universidad Rey Juan Carlos, Madrid, Spain;Institute IMDEA Networks, Madrid, Spain

  • Venue:
  • Networks
  • Year:
  • 2012

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Abstract

Random walks have been proven useful in several applications in networks. Some variants of the basic random walk have been devised pursuing a suitable trade-off between better performance and limited cost. A self-avoiding random walk (SAW) is one that tries not to revisit nodes, therefore covering the network faster than a random walk. Suggested as a network search mechanism, the performance of the SAW has been analyzed using essentially empirical studies. A strict analytical approach is hard since, unlike the random walk, the SAW is not a Markovian stochastic process. We propose an analytical model to estimate the average search length of a SAW when used to locate a resource in a network. The model considers single or multiple instances of the resource sought and the possible availability of one-hop replication in the network (nodes know about resources held by their neighbors). The model characterizes networks by their size and degree distribution, without assuming a particular topology. It is, therefore, a mean-field model, whose applicability to real networks is validated by simulation. Experiments with sets of randomly built regular networks, Erdős–Rényi networks, and scale-free networks of several sizes and degree averages, with and without one-hop replication, show that model predictions are very close to simulation results, and allow us to draw conclusions about the applicability of SAWs to network search. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012 © 2012 Wiley Periodicals, Inc.