Temporal Connectivity: Coping with Foreseen and Unforeseen Delays

TL;DR

This paper studies the problem of planning robust train connections in temporal networks considering delays, providing algorithms for different delay scenarios and analyzing their computational complexity.

Contribution

It introduces polynomial algorithms for delay-robust connectivity in temporal networks and analyzes the complexity of the problem under various delay information scenarios.

Findings

Polynomial algorithms for known delays before departure.

PSPACE-completeness for path itineraries with unknown delays.

Delay announcement timing significantly impacts computational complexity.

Abstract

Consider planning a trip in a train network. In contrast to, say, a road network, the edges are temporal, i.e., they are only available at certain times. Another important difficulty is that trains, unfortunately, sometimes get delayed. This is especially bad if it causes one to miss subsequent trains. The best way to prepare against this is to have a connection that is robust to some number of (small) delays. An important factor in determining the robustness of a connection is how far in advance delays are announced. We give polynomial-time algorithms for the two extreme cases: delays known before departure and delays occurring without prior warning (the latter leading to a two-player game scenario). Interestingly, in the latter case, we show that the problem becomes PSPACE-complete if the itinerary is demanded to be a path.