Abstract
The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and experimental results for CSP. In the theoretical part we present the hull approach, a combinatorial algorithm for solving a linear programming relaxation and prove that it runs in polynomial time in the case of one resource. In the experimental part we compare the hull approach to previous methods for solving the LP relaxation and give an exact algorithm based on the hull approach. We also compare our exact algorithm to previous exact algorithms and approximation algorithms for the problem.
An extended version of this paper is available athttp://www.mpi-sb.mpg.de/~mark/rcsp.ps
Supported by a Graduate Fellowship of the German Research Foundation (DFG).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Y. Aneja, V. Aggarwal, and K. Nair. Shortest chain subject to side conditions. Networks, 13:295–302, 1983.
R. Anderson and S. Sobti. The table layout problem. In Proc. 15th SoCG, pages 115–123, 1999.
J. Beasley and N. Christofides. An Algorithm for the Resource Constrained Shortest Path Problem. Networks, 19:379–394, 1989.
W. Cook, W. Cunningham, W. Pulleyblank, and A. Shrijver. Combinatorial Optimization. John Wiley & Sons, Inc, 1998.
K. Clarkson, K. Mehlhorn, and R. Seidel. Four results on randomized incremental construction. Computational Geometry: Theory and Applications, 3(4): 185–212, 1993.
D. Eppstein. Finding the k shortest paths. SIAM Journal on Computing, 28(2):652–673, 1999.
P. Hansen. Bicriterion path problems. In G. Fandel and T. Gal, editors, Multiple Criteria Decision Making: Theory and Application, pages 109–127. Springer verlag, Berlin, 1980.
R. Hassin. Approximation Schemes for the Restricted Shortest Path Problem. Math. Oper. Res., 17(1):36–42, 1992.
M. Henig. The shortest path problem with two objective functions. European Journal of Operational Research, 25:281–291, 1985.
G. Handler and I. Zang. A Dual Algorithm for the Constrained Shortest Path Problem. Networks, 10:293–310, 1980.
V. Jiminez and A. Marzal. Computing the k shortest paths. A new algorithm and an experimental comparison. In Proc. 3rd Workshop on Algorithm Engineering (WAE99), LNCS 1668, pages 25–29, 1999.
H. Joksch. The Shortest Route Problem with Constraints. Journal of Mathematical Analysis and Application, 14:191–197, 1966.
K. Mehlhorn and S. Näher. The LEDA platform for combinatorial and geometric computing. Cambridge University Press, 1999.
K. Mehlhorn, S. Näher, M. Seel, and C. Uhrig. The LEDA User Manual. Max-Planck-Institut für Informatik. http://www.mpi-sb.mpg.de/LEDA.
M. Minoux and C. Ribero. A heuristic approach to hard constrained shortest path problems. Discrete Applied Mathematics, 10:125–137, 1985.
C. Phillips. The Network Inhibition Problem. In 25th ACM STOC, pages 776–785, 1993.
A. Warburton. Approximation of pareto-optima in multiple-objective shortest path problems. Operations Research, 35(1):70–79, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mehlhorn, K., Ziegelmann, M. (2000). Resource Constrained Shortest Paths. In: Paterson, M.S. (eds) Algorithms - ESA 2000. ESA 2000. Lecture Notes in Computer Science, vol 1879. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45253-2_30
Download citation
DOI: https://doi.org/10.1007/3-540-45253-2_30
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41004-1
Online ISBN: 978-3-540-45253-9
eBook Packages: Springer Book Archive