Abstract
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.
(preliminary version)
This research has been supported by the Project EMC Simulation Systems by the German Ministery of Research and Technology (BMFT) No. 0118/13AS0099
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Lengauer, T., Theune, D. (1991). Unstructured path problems and the making of semirings. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028261
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DOI: https://doi.org/10.1007/BFb0028261
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