A Fast Heuristic for Computing Geodesic Cores in Large Networks

TL;DR

This paper introduces a linear-time heuristic for approximating geodesic convex hulls in large networks, significantly speeding up computations compared to exact algorithms, and demonstrates its effectiveness on real-world networks.

Contribution

The paper presents a novel linear-time heuristic for approximating geodesic convex hulls, enabling scalable analysis of large networks in data mining and machine learning.

Findings

Heuristic runs in linear time relative to the number of edges.

Produces close approximations of convexity-based core-periphery decompositions.

Achieves results in hours for networks where exact algorithms take days.

Abstract

Motivated by the increasing interest in applications of graph geodesic convexity in machine learning and data mining, we present a heuristic for computing the geodesic convex hull of node sets in networks. It generates a set of almost maximal outerplanar spanning subgraphs for the input graph, computes the geodesic closure in each of these graphs, and regards a node as an element of the convex hull if it belongs to the closed sets for at least a user specified number of outerplanar graphs. Our heuristic algorithm runs in time linear in the number of edges of the input graph, i.e., it is faster with one order of magnitude than the standard algorithm computing the closure exactly. Its performance is evaluated empirically by approximating convexity based core-periphery decomposition of networks. Our experimental results with large real-world networks show that for most networks, the proposed heuristic was able to produce close approximations significantly faster than the standard algorithm computing the exact convex hulls. For example, while our algorithm calculated an approximate core-periphery decomposition in 5 hours or less for networks with more than 20 million edges, the standard algorithm did not terminate within 50 days.