Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data

Authors Niels Lindner , Pedro Maristany de las Casas , Philine Schiewe

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Author Details

Niels Lindner
  • Zuse Institut Berlin, Germany
Pedro Maristany de las Casas
  • Zuse Institut Berlin, Germany
Philine Schiewe
  • Department of Mathematics, Technische Universität Kaiserslautern, Germany


We thank Lufthansa Systems GmbH & Co. KG. and in particular Marco Blanco for the data required to build the instance representing the airway network over Germany.

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Niels Lindner, Pedro Maristany de las Casas, and Philine Schiewe. Optimal Forks: Preprocessing Single-Source Shortest Path Instances with Interval Data. In 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021). Open Access Series in Informatics (OASIcs), Volume 96, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


We investigate preprocessing for single-source shortest path queries in digraphs, where arc costs are only known to lie in an interval. More precisely, we want to decide for each arc whether it is part of some shortest path tree for some realization of costs. We show that this problem is solvable in polynomial time by giving a combinatorial algorithm, using optimal structures that we call forks. Our algorithm turns out to be very efficient in practice, and is sometimes even superior in quality to a heuristic developed for the one-to-one shortest path problem in the context of passenger routing in public transport.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Paths and connectivity problems
  • Theory of computation → Shortest paths
  • Mathematics of computing → Graph algorithms
  • Preprocessing Shortest Path Problems
  • Interval Data
  • Graph Algorithms


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