Testing Robustness of Temporal Transportation Networks via Interval Separators

TL;DR

This paper introduces a new NP-hard problem for identifying critical time intervals in transportation networks to block paths within deadlines, and evaluates an ILP approach on real data.

Contribution

It formalizes the d-MinIntSep problem, proves its computational hardness, and proposes an ILP solution evaluated on transportation datasets.

Findings

The ILP approach's runtime depends on temporal dimension, deadline, and network density.

d-MinIntSep is NP-hard and hard to approximate.

Experimental results demonstrate the impact of temporal factors on solution computation.

Abstract

This paper addresses the problem of identifying time interval separators in temporal networks. We introduce d-MinIntSep, a new variant of the temporal separator problem, which models failures as time intervals assigned to vertices and aims to block all temporal paths between a source and a target that can be completed within a given deadline d. We prove that the d-MinIntSep problem is NP-hard and hard to approximate within a logarithmic function of the size of the vertex set, assuming P is not equal to NP, and we propose an Integer Linear Programming (ILP) formulation to compute minimum interval separators. This latter method is evaluated on synthetic and real-world temporal networks derived from transportation datasets. The experimental results show that the running time is strongly influenced by the temporal dimension, the imposed deadline, and the density of temporal paths.