Abstract
In a public transport network a passengerâ€™s preferred route from a point x to another point y is usually the shortest path from x to y. However, it is simply impossible to provide all the shortest paths of a network via public transport. Hence, it is a natural question how a lighter subnetwork should be designed in order to satisfy both the operator as well as the passengers.
We provide a detailed analysis of the interplay of the following three quality measures of lighter public transport networks:
 building cost: the sum of the costs of all edges remaining in the lighter network,
 routing costs: the sum of all shortest paths costs weighted by the demands,
 fairness: compared to the original network, for each two points the shortest path in the new network should cost at most a given multiple of the shortest path in the original network. We study the problem by generalizing the concepts of optimum communication spanning trees (Hu, 1974) and optimum requirement graphs (Wu, Chao, and Tang, 2002) to generalized optimum requirement graphs (GORGs), which are graphs achieving the social optimum amongst all subgraphs satisfying a given upper bound on the building cost. We prove that the corresponding decision problem is NPcomplete, even on orbwebs, a variant of grids which serves as an important model of cities with a center. For the case that the given network is a parametric city (cf. Fielbaum et. al., 2017) with a heavy vertex we provide a polynomialtime algorithm solving the GORGproblem. Concerning the fairnessaspect, we prove that light spanners are a strong concept for public transport optimization.
We underpin our theoretical considerations with integer programmingbased experiments that allow us to compare the fairnessapproach with the routing costapproach as well as passenger assignment approaches from the literature.
BibTeX  Entry
@InProceedings{heinrich_et_al:OASIcs.ATMOS.2023.2,
author = {Heinrich, Irene and Herrala, Olli and Schiewe, Philine and Terho, Topias},
title = {{Using Light Spanning Graphs for Passenger Assignment in Public Transport}},
booktitle = {23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)},
pages = {2:12:16},
series = {Open Access Series in Informatics (OASIcs)},
ISBN = {9783959773027},
ISSN = {21906807},
year = {2023},
volume = {115},
editor = {Frigioni, Daniele and Schiewe, Philine},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2023/18763},
URN = {urn:nbn:de:0030drops187637},
doi = {10.4230/OASIcs.ATMOS.2023.2},
annote = {Keywords: passenger assignment, line planning, public transport, discrete optimization, complexity, algorithm design}
}
Keywords: 

passenger assignment, line planning, public transport, discrete optimization, complexity, algorithm design 
Collection: 

23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023) 
Issue Date: 

2023 
Date of publication: 

31.08.2023 