Abstract
We study the problem of finding all Pareto-optimal solutions for the multi-criteria single-source shortest-path problem with nonnegative edge lengths. The standard approaches are generalizations of label-setting (Dijkstra) and label-correcting algorithms, in which the distance labels are multi-dimensional and more than one distance label is maintained for each node. The crucial parameter for the run time and space consumption is the total number of Pareto optima. In general, this value can be exponentially large in the input size. However, in various practical applications one can observe that the input data has certain characteristics, which may lead to a much smaller number — small enough to make the problem efficiently tractable from a practical viewpoint.
In this paper, we identify certain key characteristics, which occur in various applications. These key characteristics are evaluated on a concrete application scenario (computing the set of best train connections in view of travel time, fare, and number of train changes) and on a simplified randomized model, in which these characteristics occur in a very purist form. In the applied scenario, it will turn out that the number of Pareto optima on each visited node is restricted by a small constant. To counter-check the conjecture that these characteristics are the cause of these uniformly positive results, we will also report negative results from another application, in which these characteristics do not occur.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
J. Brumbaugh-Smith and D. Shier. An empirical investigation of some bicriterion shortest path algorithms. European Journal of Operations Research, 43:216–224, 1989.
M. Ehrgott and X. Gandibleux. An annotated biliography of multiobjective combinatorial optimization. OR Spektrum, pages 425–460, 2000.
P. Hansen. Bicriteria path problems. In G. Fandel and T. Gal, editors, Multiple Criteria Decision Making Theory and Applications, volume 177 of Lecture Notes in Economics and Mathematical Systems, pages 109–127. Springer Verlag, Berlin, 1979.
O. Jahn, R. H. Möhring, and A. S. Schulz. Optimal routing of traffic flows with length restrictions. In K. Inderfurth et al., editor, Operations Research Proceedings 1999, pages 437–442. Springer, 2000.
K. Mehlhorn and G. Schäfer. A heuristic for Dijkstra’s algorithm with many targets and its use in weighted matching algorithms. In Proceedings of 9th Annual European Symposium on Algorithms (ESA’2001), to appear. 2001.
K. Mehlhorn and M. Ziegelmann. Resource constrained shortest paths. In Proceedings of 8th Annual European Symposium on Algorithms (ESA’ 2000), volume 1879 of Lecture Notes in Computer Science, pages 326–337. Springer, 2000.
K. Mehlhorn and M. Ziegelmann. CNOP — a package for constrained network optimization. In 3rd Workshop on Algorithm Engineering and Experiments (ALENEX’01). 2001.
J. Mote, I. Murthy, and D. L. Olson. A parametric approach to solving bicriterion shortest path problems. European Journal of Operations Research, 53:81–92, 1991.
F. Schulz, D. Wagner, and K. Weihe. Dijkstra’s algorithm on-line: An empirical case study from public railroad transport. In Proceedings of 3rd Workshop on Algorithm Engineering (WAE’99), volume 1668 of Lecture Notes in Computer Science, pages 110–123. Springer, 1999.
A. J. V. Skriver and K. A. Andersen. A label correcting approach for solving bicriterion shortest path problems. Computers and Operations Research, 27:507–524, 2000.
D. Theune. Robuste und effiziente Methoden zur Lösung von Wegproblemen. Teubner Verlag, Stuttgart, 1995.
A. Warburton. Approximation of pareto optima in multiple-objective shortest path problems. Operations Research, 35:70–79, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Müller-Hannemann, M., Weihe, K. (2001). Pareto Shortest Paths is Often Feasible in Practice. In: Brodal, G.S., Frigioni, D., Marchetti-Spaccamela, A. (eds) Algorithm Engineering. WAE 2001. Lecture Notes in Computer Science, vol 2141. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44688-5_15
Download citation
DOI: https://doi.org/10.1007/3-540-44688-5_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42500-7
Online ISBN: 978-3-540-44688-0
eBook Packages: Springer Book Archive