Computing and Listing st-Paths in Public Transportation Networks

Katerina Böhmová, Matús Mihalák, Tobias Pröger*, Gustavo Sacomoto, Marie-France Sagot

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


Given a set of directed paths (called lines) l, a public transportation network is a directed graph g_l=(v_l,a_l)g_l=(v_l,a_l) which contains exactly the vertices and arcs of every line l\in ll\in l. An st-route is a pair (\pi ,\gamma )(\pi ,\gamma ) where \gamma =\langle l_1,\ldots ,l_h \rangle \gamma =\langle l_1,\ldots ,l_h \rangle is a line sequence and \pi \pi is an st-path in g_lg_l which is the concatenation of subpaths of the lines l_1,\ldots ,l_hl_1,\ldots ,l_h, in this order. Given a threshold \beta \beta , we present an algorithm for listing all st-paths \pi \pi for which a route (\pi ,\gamma )(\pi ,\gamma ) with |\gamma | \le \beta |\gamma | \le \beta exists, and we show that the running time of this algorithm is polynomial with respect to the input and the output size. We also present an algorithm for listing all line sequences \gamma \gamma with |\gamma |\le \beta |\gamma |\le \beta for which a route (\pi ,\gamma )(\pi ,\gamma ) exists, and show how to speed it up using preprocessing. Moreover, we show that for the problem of finding an st-route (\pi ,\gamma )(\pi ,\gamma ) that minimizes the number of different lines in \gamma \gamma , even computing an o(\log |v|)o(\log |v|)-approximation is np-hard.
Original languageEnglish
Title of host publicationComputer Science – Theory and Applications CSR 2016
PublisherSpringer, Cham
Number of pages15
ISBN (Electronic)978-3-319-34171-2
ISBN (Print)978-3-319-34170-5
Publication statusPublished - 2016

Publication series

SeriesLecture Notes in Computer Science

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