Reducing Search Lengths with Locally Precomputed Partial Random Walks

TL;DR

This paper introduces a search method in complex networks that uses precomputed partial random walks and Bloom filters to significantly reduce search lengths, with an analytic model and simulations validating the approach.

Contribution

It proposes a novel search mechanism combining precomputed partial walks and Bloom filters, along with an analytic model to optimize search efficiency.

Findings

The model accurately predicts expected search lengths.

Precomputing multiple partial walks improves search efficiency.

Optimal Bloom filter size balances false positives and search length.

Abstract

Random walks can be used to search a complex networks for a desired resource. To reduce the number of hops necessary to find the resource, we propose a search mechanism based on building random walks connecting together partial walks that have been precomputed at each network node in an initial stage. The resources found in each partial walk are registered in its associated Bloom filter. Searches can then jump over partial nodes in which the resource is not located, significantly reducing search length. However, additional unnecessary hops come from false positives at the Bloom filters. The analytic model provided predicts the expected search length of this mechanism, the optimal size of the partial walks and the corresponding optimal (shortest) expected search length. Simulation experiments are used to validate these predictions and to assess the impact of the number of partial walks precomputed in each node.