TY - GEN

T1 - Computing and Listing st-Paths in Public Transportation Networks

AU - Böhmová, Katerina

AU - Mihalák, Matús

AU - Pröger, Tobias

AU - Sacomoto, Gustavo

AU - Sagot, Marie-France

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

U2 - 10.1007/978-3-319-34171-2_8

DO - 10.1007/978-3-319-34171-2_8

M3 - Conference article in proceeding

SN - 978-3-319-34170-5

T3 - Lecture Notes in Computer Science

SP - 102

EP - 116

BT - Computer Science – Theory and Applications CSR 2016

PB - Springer, Cham

ER -