Resource Constrained Shortest Paths

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.

[1]  Refael Hassin,et al.  Approximation Schemes for the Restricted Shortest Path Problem , 1992, Math. Oper. Res..

[2]  Kurt Mehlhorn,et al.  Four Results on Randomized Incremental Constructions , 1992, Comput. Geom..

[3]  Kurt Mehlhorn,et al.  LEDA: a platform for combinatorial and geometric computing , 1997, CACM.

[4]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[5]  Kurt Mehlhorn,et al.  A platform for combinatorial and geometric computing , 1995 .

[6]  William J. Cook,et al.  Combinatorial Optimization: Cook/Combinatorial , 1997 .

[7]  H. Joksch.  The shortest route problem with constraints , 1966 .

[8]  Richard J. Anderson,et al.  The table layout problem , 1999, SCG '99.

[9]  Gabriel Y. Handler,et al.  A dual algorithm for the constrained shortest path problem , 1980, Networks.

[10]  Nicos Christofides,et al.  An algorithm for the resource constrained shortest path problem , 1989, Networks.

[11]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[12]  Kurt Mehlhorn,et al.  Four Results on Randomized Incremental Constructions , 1992, STACS.

[13]  M. I. Henig.  The shortest path problem with two objective functions , 1986 .

[14]  Kurt Mehlhorn,et al.  The LEDA Platform of Combinatorial and Geometric Computing , 1997, ICALP.

[15]  Andrés Marzal,et al.  Computing the K Shortest Paths: A New Algorithm and an Experimental Comparison , 1999, WAE.

[16]  David Eppstein,et al.  Finding the k Shortest Paths , 1999, SIAM J. Comput..

[17]  Y. P. Aneja,et al.  Shortest chain subject to side constraints , 1983, Networks.

[18]  Arthur Warburton,et al.  Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems , 1987, Oper. Res..

[19]  Kurt Mehlhorn,et al.  The leda user manual , 1996 .

[20]  Cynthia A. Phillips,et al.  The network inhibition problem , 1993, STOC.

[21]  Celso C. Ribeiro,et al.  A heuristic approach to hard constrained shortest path problems , 1985, Discret. Appl. Math..