Abstract
Computing a (short) path between two vertices is one of the most fundamental primitives in graph algorithmics. In recent years, the study of paths in temporal graphs, that is, graphs where the vertex set is fixed but the edge set changes over time, gained more and more attention. A path is timerespecting, or temporal, if it uses edges with nondecreasing time stamps.
We investigate a basic constraint for temporal paths, where the time spent at each vertex must not exceed a given duration Δ, referred to as Δrestless temporal paths. This constraint arises naturally in the modeling of realworld processes like packet routing in communication networks and infection transmission routes of diseases where recovery confers lasting resistance.
While finding temporal paths without waiting time restrictions is known to be doable in polynomial time, we show that the "restless variant" of this problem becomes computationally hard even in very restrictive settings. For example, it is W[1]hard when parameterized by the feedback vertex number or the pathwidth of the underlying graph. The main question thus is whether the problem becomes tractable in some natural settings. We explore several natural parameterizations, presenting FPT algorithms for three kinds of parameters: (1) outputrelated parameters (here, the maximum length of the path), (2) classical parameters applied to the underlying graph (e.g., feedback edge number), and (3) a new parameter called timed feedback vertex number, which captures finergrained temporal features of the input temporal graph, and which may be of interest beyond this work.
BibTeX  Entry
@InProceedings{casteigts_et_al:LIPIcs:2020:13374,
author = {Arnaud Casteigts and AnneSophie Himmel and Hendrik Molter and Philipp Zschoche},
title = {{Finding Temporal Paths Under Waiting Time Constraints}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {30:130:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959771733},
ISSN = {18688969},
year = {2020},
volume = {181},
editor = {Yixin Cao and SiuWing Cheng and Minming Li},
publisher = {Schloss DagstuhlLeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13374},
URN = {urn:nbn:de:0030drops133745},
doi = {10.4230/LIPIcs.ISAAC.2020.30},
annote = {Keywords: Temporal graphs, disease spreading, waitingtime policies, restless temporal paths, timed feedback vertex set, NPhard problems, parameterized algorithms}
}
Keywords: 

Temporal graphs, disease spreading, waitingtime policies, restless temporal paths, timed feedback vertex set, NPhard problems, parameterized algorithms 
Collection: 

31st International Symposium on Algorithms and Computation (ISAAC 2020) 
Issue Date: 

2020 
Date of publication: 

04.12.2020 