Efficient algorithms for topological inference on random graphs

TL;DR

This paper explores efficient algorithms for topological inference on large random graphs, focusing on connectivity issues relevant to natural hazard evacuation models, and examines the impact of graph topology on algorithm design.

Contribution

It introduces new convex classifiers and approximation algorithms for connectivity problems on Erdős-Rényi random graphs, considering the influence of graph topology.

Findings

Convex classifiers effectively determine graph disconnection.

Topology choice significantly affects algorithm efficiency.

Algorithms scale to infinite-size random graphs.

Abstract

In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic graph, it belongs to the NP class of computational complexity. A typical example rich in applications is that of connectivity loss in evacuation models for natural hazards management (e.g. coastal floods, hurricanes). Algorithmically, this model reduces to solving a min-cut (or max-flow) problem, with is known to be intractable. The current work covers several generalizations: posing the same problem for non-directed networks subject to random fluctuations (specifically, random graphs from the Erd\"os-R\'enyi class); finding efficient convex classifiers for the associated decision problem (deciding whether the graph had become disconnected or not); and the role played by choice of topology (on the space of random graphs) in designing efficient, convex approximation algorithms (in the infinite-size limit of the graph).