Testing Robustness of Temporal Transportation Networks via Interval Separators

2026-04-28

AI Summary

This study addresses the problem of disconnecting all time-respecting paths from a source to a target within a given deadline \(d\) in temporal networks. It introduces, for the first time, a time-interval vertex failure model and formulates the minimum time-interval separator problem (\(d\)-MinIntSep). The problem is proven to be NP-hard and inapproximable within any logarithmic factor. The authors develop an exact solution approach based on an integer linear programming (ILP) formulation and evaluate its efficacy on both synthetic and real-world transportation temporal networks. Experimental results demonstrate that algorithmic runtime is significantly influenced by the temporal dimension, the deadline \(d\), and path density, thereby confirming the practical feasibility of the proposed method while also highlighting the inherent computational hardness of the problem.

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.

Problem

• temporal networks
• interval separators
• temporal paths
• NP-hard
• transportation networks

Innovation

• temporal networks
• interval separators
• d-MinIntSep
• NP-hardness
• Integer Linear Programming