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Obligation rules for minimum cost spanning tree situations and their monotonicity properties

Tijs, Stef; Branzei, Rodica; Moretti, Stefano; Norde, Henk (2006), Obligation rules for minimum cost spanning tree situations and their monotonicity properties, European Journal of Operational Research, 175, 1, p. 121-134. http://dx.doi.org/10.1016/j.ejor.2005.04.036

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Type
Article accepté pour publication ou publié
Date
2006
Journal name
European Journal of Operational Research
Volume
175
Number
1
Publisher
Elsevier
Pages
121-134
Publication identifier
Metadata
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Author(s)
Tijs, Stef
Branzei, Rodica
Moretti, Stefano cc
Norde, Henk
Abstract (EN)
We consider the class of Obligation rules for minimum cost spanning tree situations. The main result of this paper is that such rules are cost monotonic and induce also population monotonic allocation schemes. Another characteristic of Obligation rules is that they assign to a minimum cost spanning tree situation a vector of cost contributions which can be obtained as product of a double stochastic matrix with the cost vector of edges in the optimal tree provided by the Kruskal algorithm. It turns out that the Potters value (P-value) is an element of this class.
Subjects / Keywords
Cost allocation; Minimum cost spanning tree situations; Cost monotonicity; Population monotonic allocation schemes