Semirings and the shortest path problem

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

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Abstract

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:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
doc. dr. Polona Oblak	6760	Mentor

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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