Estimating Hitting Times Locally At Scale

TL;DR

This paper introduces scalable local algorithms for estimating hitting times in large graphs, enabling applications in network analysis and epidemiology without full graph access.

Contribution

It presents novel local algorithms for hitting time estimation that overcome scalability issues of previous global methods, including a new spectral cutoff adaptation for directed graphs.

Findings

Algorithms are efficient and scalable for large graphs.

The methods are validated on real and synthetic datasets.

Theoretical bounds and connections to distribution testing are established.

Abstract

Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network centrality analysis, ranking and recommendation systems, and epidemiology. In this work, we develop local algorithms for estimating hitting times between a pair of vertices $u,v$ without accessing the full graph, overcoming scalability issues of prior global methods. Our first algorithm uses the key insight that hitting time computations can be truncated at the meeting time of two independent random walks from $u$ and $v$. This leads to an efficient estimator analyzed via the Kronecker product graph and Markov Chain Chernoff bounds. We also present an algorithm extending the work of [Peng et al.; KDD 2021], that introduces a novel adaptation of the spectral cutoff technique to account for the asymmetry of hitting times. This adaptation captures the directionality of the underlying random walk and requires non-trivial modifications to ensure accuracy and efficiency. In addition to the algorithmic upper bounds, we also provide tight asymptotic lower bounds. We also reveal a connection between hitting time estimation and distribution testing, and validate our algorithms using experiments on both real and synthetic data.