Delay-Robust Routes in Temporal Graphs

TL;DR

This paper studies the problem of designing delay-robust routes in temporal transportation networks, addressing the challenges posed by unreliable connections and delays, and analyzes its computational complexity.

Contribution

It introduces the problem of delay-robust routing in temporal graphs and provides complexity results including NP-completeness and tractability under certain parameters.

Findings

Proves NP-completeness of delay-robust routing.

Identifies parameters for which the problem is tractable.

Provides hardness and tractability results for natural parameterizations.

Abstract

Most transportation networks are inherently temporal: Connections (e.g. flights, train runs) are only available at certain, scheduled times. When transporting passengers or commodities, this fact must be considered for the the planning of itineraries. This has already led to several well-studied algorithmic problems on temporal graphs. The difficulty of the described task is increased by the fact that connections are often unreliable -- in particular, many modes of transportation suffer from occasional delays. If these delays cause subsequent connections to be missed, the consequences can be severe. Thus, it is a vital problem to design itineraries that are robust to (small) delays. We initiate the study of this problem from a parameterized complexity perspective by proving its NP-completeness as well as several hardness and tractability results for natural parameterizations.