Optimization Letters

, Volume 12, Issue 3, pp 475–483 | Cite as

Multi-criteria approximation schemes for the resource constrained shortest path problem

Original Paper
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Abstract

In the resource constrained shortest path problem we are given a directed graph along with a source node and a destination node, and each arc has a cost and a vector of weights specifying its requirements from a set of resources with finite budget limits. A minimum cost source-destination path is sought such that the total consumption of the arcs from each resource does not exceed its budget limit. In the case of constant number of weight functions we give a fully polynomial time multi-criteria approximation scheme for the problem which returns a source-destination path of cost at most the optimum, however, the path may slightly violate the budget limits. On the negative side, we show that there does not exist a polynomial time multi-criteria approximation scheme for the problem if the number of weight functions is not a constant. The latter result applies to a broad class of problems as well, including the multi-dimensional knapsack, the multi-budgeted spanning tree, the multi-budgeted matroid basis and the multi-budgeted bipartite perfect matching problems.

Keywords

Multi-criteria approximation algorithms Resource constrained shortest path Multi-budgeted combinatorial optimization 

Notes

Acknowledgements

The authors are grateful to an anonymous referee for constructive comments that helped to improve the presentation of the paper. This work has been supported by the OTKA Grant K112881, and by the Grant GINOP-2.3.2-15-2016-00002 of the Ministry of National Economy of Hungary.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Institute for Computer Science and ControlHungarian Academy of SciencesBudapestHungary

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