# The e-approximation of the Label Correcting Modification of the Dijkstra's Algorithm

### František Kolovský, Jan Ježek, Ivana Kolingerová

#### Abstract

This paper is focused on searching the shortest paths for all departure times (profile search). This problem is called a time-dependent shortest path problem (TDSP) and is important for optimization in transportation. Particularly this paper deals with the ε-approximation of TDSP. The proposed algorithm is based on a label correcting modification of Dijkstra’s algorithm (LCA). The main idea of the algorithm is to simplify the arrival function after every relaxation step so that the maximum relative error is maintained. When the maximum relative error is 0.001, the proposed solution saves more than 95% of breakpoints and 80% time compared to the exact version of LCA. A more efficient precomputation step for another time-dependent routing algorithms can be built using the developed algorithm.

Download#### Paper Citation

#### in Harvard Style

Kolovský F., Ježek J. and Kolingerová I. (2019). **The e-approximation of the Label Correcting Modification of the Dijkstra's Algorithm**.In *Proceedings of the 5th International Conference on Geographical Information Systems Theory, Applications and Management - Volume 1: GISTAM,* ISBN 978-989-758-371-1, pages 26-32. DOI: 10.5220/0007658200260032

#### in Bibtex Style

@conference{gistam19,

author={František Kolovský and Jan Ježek and Ivana Kolingerová},

title={The e-approximation of the Label Correcting Modification of the Dijkstra's Algorithm},

booktitle={Proceedings of the 5th International Conference on Geographical Information Systems Theory, Applications and Management - Volume 1: GISTAM,},

year={2019},

pages={26-32},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007658200260032},

isbn={978-989-758-371-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 5th International Conference on Geographical Information Systems Theory, Applications and Management - Volume 1: GISTAM,

TI - The e-approximation of the Label Correcting Modification of the Dijkstra's Algorithm

SN - 978-989-758-371-1

AU - Kolovský F.

AU - Ježek J.

AU - Kolingerová I.

PY - 2019

SP - 26

EP - 32

DO - 10.5220/0007658200260032