Optimal and Efficient Link Insertion for Hitting-Time Minimization

Aristides Gionis, Alessio Mazzetto, Ilie Sarpe

Keywords: graph algorithms, social network algorithms, polarization reduction, combinatorial optimization, scalable algorithms, greedy algorithms

TL;DR: We design an efficient and optimal algorithm to reduce the hitting-time among two groups in a graph.

Abstract:

We study the computational problem of strategically adding links to a graph to minimize the hitting-time between two group of nodes. Our problem has various applications in social network analysis, including bridging polarized groups with opposite views in a network. Formally, we are given a graph where the set of nodes is partitioned into two disjoint groups, R and B, and we assume a random-walk process modeling navigation over the graph. Our goal is to add a given number of edges to the graph to minimize the expected number of steps to encounter a node in B starting from nodes in R, via the random walk. While the problem is generally NP-hard, we show that when the random walk follows stationary transitions over the induced subgraph of R, the problem becomes optimally solvable in polynomial-time, and we present an extremely efficient optimal greedy strategy. Remarkably, our method applies to both directed and undirected graphs, and many widely-adopted random-walk models, for example, PageRank.

Our experimental evaluation demonstrates that our method outperforms state-of-the-art baselines for similar metrics. Remarkably, our method achieves up to four orders of magnitude of speedup compared to existing methods, scaling to networks with millions of edges,
which cannot be processed with current methods.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

Submission Number: 24447