Node Sampling using Random Centrifugal Walks

TL;DR

This paper introduces Random Centrifugal Walks (RCW), a new class of random walks for distributed network sampling, enabling efficient, exact probability-based node selection with minimal preprocessing and bounded walk length.

Contribution

The paper presents novel RCW algorithms for network sampling, including a preprocessing-based method for weighted sampling and a no-preprocessing approach for specific network types, improving efficiency and accuracy.

Findings

Preprocessing with MDST enables weighted sampling with bounded walk length.

RCW algorithms do not require warm-up or stabilization phases.

Sampling always completes within the network diameter, ensuring efficiency.

Abstract

Sampling a network with a given probability distribution has been identified as a useful operation. In this paper we propose distributed algorithms for sampling networks, so that nodes are selected by a special node, called the \emph{source}, with a given probability distribution. All these algorithms are based on a new class of random walks, that we call Random Centrifugal Walks (RCW). A RCW is a random walk that starts at the source and always moves away from it. Firstly, an algorithm to sample any connected network using RCW is proposed. The algorithm assumes that each node has a weight, so that the sampling process must select a node with a probability proportional to its weight. This algorithm requires a preprocessing phase before the sampling of nodes. In particular, a minimum diameter spanning tree (MDST) is created in the network, and then nodes' weights are efficiently aggregated using the tree. The good news are that the preprocessing is done only once, regardless of the number of sources and the number of samples taken from the network. After that, every sample is done with a RCW whose length is bounded by the network diameter. Secondly, RCW algorithms that do not require preprocessing are proposed for grids and networks with regular concentric connectivity, for the case when the probability of selecting a node is a function of its distance to the source. The key features of the RCW algorithms (unlike previous Markovian approaches) are that (1) they do not need to warm-up (stabilize), (2) the sampling always finishes in a number of hops bounded by the network diameter, and (3) it selects a node with the exact probability distribution.