Unstructured path problems and the making of semirings

  • T. Lengauer
  • D. Theune
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)


The solution of the algebraic path problem, for instance with the algorithm by Floyd and Warshall, is part of the classical repertoire on algorithms. This solution presupposes that path costs are computed in a closed semiring or a similar algebraic structure. The associativity and distributivity laws in such algebraic structures exclude many possible path costs. In the seventies, several authors have developed algebraic methods in order to overcome such restrictions.

Recently, applications have created the need for handling such unstructured path costs. Motivated by such applications, we investigate the efficiency of algorithms solving path problems with unstructured costs. The resulting procedure allows for developing efficient algorithms for solving the algebraic path problem with respect to a wide variety of cost measures, including finding shortest paths with discounting, and counting paths or computing the expected length of paths with desired properties.


Short Path Cost Structure Path Cost Neutral Element Edge Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • T. Lengauer
    • 1
  • D. Theune
    • 1
  1. 1.Cadlab and University of PaderbornPaderbornGermany

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