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On Universal Shortest Paths

In: Operations Research Proceedings 2010

Author

Listed:
  • Lara Turner

    (Technical University of Kaiserslautern)

  • Horst W. Hamacher

    (Technical University of Kaiserslautern)

Abstract

The universal combinatorial optimization problem (Univ-COP) generalizes classical and new objective functions for combinatorial problems given by a ground set, a set of feasible solutions and costs assigned to the elements in the ground set. The corresponding universal objective function is of the sum type and associates additional multiplicative weights with the ordered cost coefficients of a feasible solution such that sum, bottleneck or balanced objectives can, for instance, be modeled. For the special case of shortest paths, we give two alternative definitions for the corresponding universal shortest path problem denoted Univ-SPP, one based on a sequence of cardinality constrained subproblems, the other using an auxiliary construction to establish uniform length for all paths from s to t. We show that the second version can be solved as classical sum shortest path problem on graphs with specific assumptions on edge costs and path lengths. In general, however, the problem is NP-hard. Integer programming formulations are proposed.

Suggested Citation

  • Lara Turner & Horst W. Hamacher, 2011. "On Universal Shortest Paths," Operations Research Proceedings, in: Bo Hu & Karl Morasch & Stefan Pickl & Markus Siegle (ed.), Operations Research Proceedings 2010, pages 313-318, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-20009-0_50
    DOI: 10.1007/978-3-642-20009-0_50
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