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http://hdl.handle.net/2445/176011
Title: | Arbres de cost mı́nim i jocs cooperatius |
Author: | Camacho Martı́n, Laura |
Director/Tutor: | Jarque i Ribera, Xavier Martínez de Albéniz, F. Javier |
Keywords: | Arbres (Teoria de grafs) Treballs de fi de grau Jocs cooperatius (Matemàtica) Xarxes elèctriques Trees (Graph theory) Bachelor's theses Cooperative games (Mathematics) Electric networks |
Issue Date: | Jun-2020 |
Abstract: | [en] In this project we study minimun cost spanning tree problems and how to associate them with a cooperative game of transferable utility. Some real economic situations such as the construction of an electricity network for the supply of energy to an entire village from a common power station can be modelled by these problems. This case was studied by Dutta and Kar (2004). On the one hand, we define two algorithms capable of obtaining a minimum cost spanning tree of a connected graph, namely Prim’s (1957) and Kruskal’s (1956). On the other hand, we explain a series of cost allocation rules, which are interpreted under the prism of cooperative games. A series of properties are detailed to see which of these properties determine them. We also study the irreducible form introduced by Bird (1976) associated with a minimum cost spanning tree problem. We see how to associate one to each problem and analyze the equivalence between rules in this irreducible form. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Xavier Jarque i Ribera i F. Javier Martínez de Albéniz |
URI: | http://hdl.handle.net/2445/176011 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
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File | Description | Size | Format | |
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176011.pdf | Memòria | 460.7 kB | Adobe PDF | View/Open |
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