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Semirings and the shortest path problem

Veronika Horvat (2014) Semirings and the shortest path problem. EngD thesis.

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    The thesis presents the problem of finding the shortest path in a directed graph with the Bellman's algorithm. This algorithm a version of Bellman equation with the novelty that the we work with matrices and operations over tropical semiring. Given a weighted directed graph, its arc prices are written in a matrix A. The matrix has a quasi-inverse A^* over tropical semiring, which is used to compute the minimal solution of the system of equations expressed from the Bellman equation. The solution of the algorithm is a vector of prices that represents the prices of the shortest paths to all nodes in the graph.

    Item Type: Thesis (EngD thesis)
    Keywords: Tropical algebra, quasi inverse, Bellman's algorithm, directed graph
    Number of Pages: 31
    Language of Content: Slovenian
    Mentor / Comentors:
    Name and SurnameIDFunction
    doc. dr. Polona Oblak6760Mentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1536062403 )
    Institution: University of Ljubljana
    Department: Faculty of Computer and Information Science
    Item ID: 2667
    Date Deposited: 12 Sep 2014 14:25
    Last Modified: 25 Nov 2014 11:12
    URI: http://eprints.fri.uni-lj.si/id/eprint/2667

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