Variants of Shortest Path Problems

Authors

  • Lara Turner

Keywords:

shortest path problem, universal objective function, resource constrained shortest path problem, strongly polynomial-time algorithm

Abstract

The shortest path problem in which the (s, t) -paths P of a given digraph G = (V, E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k -sum and k -max objectives, (k 1, k 2) -max, (k 1, k 2) -balanced and several types of trimmed-mean objectives. We give a survey on existing algorithms and propose a general model for those problems not yet treated in literature. The latter is based on the solution of resource constrained shortest path problems with equality constraints which can be solved in pseudo-polynomial time if the given graph is acyclic and the number of resources is fixed. In our setting, however, these problems can be solved in strongly polynomial time. Combining this with known results on k -sum and k -max optimization for general combinatorial problems, we obtain strongly polynomial algorithms for a variety of path problems on acyclic and general digraphs.

Author Biography

Lara Turner

Ph.D. student at Department of Mathematics, University of Kaiserslautern, Germany

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Published

2012-01-03

How to Cite

Turner, L. (2012). Variants of Shortest Path Problems. Algorithmic Operations Research, 6(2), Pages 91 – 104. Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/18312

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