Reports de recerca
http://hdl.handle.net/2117/3431
2017-02-22T22:33:09ZGeneric algorithms for the generation of combinatorial objects
http://hdl.handle.net/2117/97031
Generic algorithms for the generation of combinatorial objects
Molinero Albareda, Xavier; Martínez Parra, Conrado
This report briefly describes our generic approach to the exhaustive generation of unlabelled and labelled combinatorial classes. Our algorithms receive a size n and a finite description of a combinatorial class A using combinatorial operators such as union, product, set or sequence, in order to list all objects of size n in A. The algorithms work in constant amortized time per generated object and thus they are suitable for rapid prototyping or for inclusion in general libraries.
2016-11-22T14:37:57ZMolinero Albareda, XavierMartínez Parra, ConradoThis report briefly describes our generic approach to the exhaustive generation of unlabelled and labelled combinatorial classes. Our algorithms receive a size n and a finite description of a combinatorial class A using combinatorial operators such as union, product, set or sequence, in order to list all objects of size n in A. The algorithms work in constant amortized time per generated object and thus they are suitable for rapid prototyping or for inclusion in general libraries.An Efficient generic algorithm for the generation of unlabelled cycles
http://hdl.handle.net/2117/97029
An Efficient generic algorithm for the generation of unlabelled cycles
Martínez Parra, Conrado; Molinero Albareda, Xavier
In this report we combine two recent generation algorithms to obtain a
new algorithm for the generation of unlabelled cycles. Sawada's
algorithm lists all k-ary unlabelled cycles with fixed
content, that is, the
number of occurences of each symbol is fixed and given a priori.
The other algorithm, by the authors, generates all
multisets of objects with given total size n from any admissible
unlabelled class A. By admissible
we mean that the class can be specificied using atomic classes,
disjoints unions, products, sequences, (multi)sets, etc.
The resulting algorithm, which is the main contribution of this paper,
generates all cycles of objects with given total size n from any
admissible class A. Given the
generic nature of the algorithm, it is suitable for inclusion in
combinatorial libraries and for rapid prototyping. The new algorithm
incurs constant amortized time per generated cycle, the constant only
depending in the class A to which the objects in the cycle belong.
2016-11-22T14:33:29ZMartínez Parra, ConradoMolinero Albareda, XavierIn this report we combine two recent generation algorithms to obtain a
new algorithm for the generation of unlabelled cycles. Sawada's
algorithm lists all k-ary unlabelled cycles with fixed
content, that is, the
number of occurences of each symbol is fixed and given a priori.
The other algorithm, by the authors, generates all
multisets of objects with given total size n from any admissible
unlabelled class A. By admissible
we mean that the class can be specificied using atomic classes,
disjoints unions, products, sequences, (multi)sets, etc.
The resulting algorithm, which is the main contribution of this paper,
generates all cycles of objects with given total size n from any
admissible class A. Given the
generic nature of the algorithm, it is suitable for inclusion in
combinatorial libraries and for rapid prototyping. The new algorithm
incurs constant amortized time per generated cycle, the constant only
depending in the class A to which the objects in the cycle belong.Some advances in the theory of voting systems based on experimental algorithms
http://hdl.handle.net/2117/87345
Some advances in the theory of voting systems based on experimental algorithms
Freixas Bosch, Josep; Molinero Albareda, Xavier
In voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.
2016-05-26T08:32:43ZFreixas Bosch, JosepMolinero Albareda, XavierIn voting systems, game theory, switching functions, threshold logic, hypergraphs or coherent structures there is an important problem that consists in determining the weightedness of a voting system by means of trades among voters in sets of coalitions. The fundamental theorem by Taylor and Zwicker cite{TaZw92} establishes the equivalence between weighted voting games and $k$-trade robust games for each positive integer $k$. Moreover, they also construct, in cite{TaZw95}, a succession of games $G_k$ based on magic squares which are $(k-1)$-trade robust but not $k$-trade robust, each one of these games $G_k$ has $k^2$ players. The goal of this paper is to provide improvements by means of different experiments to the problem described above. In particular, we will classify all complete games (a basic class of games) of less than eight players according to they are: a weighted voting game or a game which is $(k-1)$-trade robust but not $k$-trade robust for all values of $k$. As a consequence it will we showed the existence of games with less than $k^2$ players which are $(k-1)$-trade robust but not $k$-trade robust. We want to point out that the classifications obtained in this paper by means of experiments are new in the mentioned fields.Minimal representations for majority games
http://hdl.handle.net/2117/86215
Minimal representations for majority games
Freixas Bosch, Josep; Molinero Albareda, Xavier; Roura Ferret, Salvador
This paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.
2016-04-27T07:22:54ZFreixas Bosch, JosepMolinero Albareda, XavierRoura Ferret, SalvadorThis paper presents some new results about majority games. Isbell (1959) was the first to find a majority game without a minimum normalized representation; he needed 12 voters to construct such a game. Since then, it has been an open problem to find the minimum number of voters of a majority game without a minimum normalized representation. Our main new results are: 1. All majority games with less than 9 voters have a minimum representation. 2. For 9 voters there are 14 majority games without a minimum integer representation, but these games admit a minimal normalized integer representation. 3. For 10 voters exist majority games with neither a minimum integer representation nor a minimal normalized integer representation.Bisemivalues, binomial bisemivalues and multilinear extension for bicooperative games
http://hdl.handle.net/2117/78354
Bisemivalues, binomial bisemivalues and multilinear extension for bicooperative games
Domènech Blázquez, Margarita; Giménez Pradales, José Miguel; Puente del Campo, María Albina
We introduce bisemivalues for bicooperative games and we also provide an interesting characterization of this kind of values by means of weighting coefficients in a similar way than given for semivalues in the context of cooperative games. Moreover, the notion of induced bisemivalues on lower cardinalities also makes sense and an adaptation of Dragan’s recurrence formula is obtained. Besides its characterization, a computational procedure in terms of the multilinear extension of the game is given.
2015-10-27T14:22:43ZDomènech Blázquez, MargaritaGiménez Pradales, José MiguelPuente del Campo, María AlbinaWe introduce bisemivalues for bicooperative games and we also provide an interesting characterization of this kind of values by means of weighting coefficients in a similar way than given for semivalues in the context of cooperative games. Moreover, the notion of induced bisemivalues on lower cardinalities also makes sense and an adaptation of Dragan’s recurrence formula is obtained. Besides its characterization, a computational procedure in terms of the multilinear extension of the game is given.On the complexity of exchanging
http://hdl.handle.net/2117/27400
On the complexity of exchanging
Molinero Albareda, Xavier; Olsen, Martin; Serna Iglesias, María José
We analyze the computational complexity of the problem of deciding
whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.
2015-04-16T17:13:57ZMolinero Albareda, XavierOlsen, MartinSerna Iglesias, María JoséWe analyze the computational complexity of the problem of deciding
whether, for a given simple game, there exists the possibility of rearranging the participants in a set of j given losing coalitions into a set of j winning coalitions. We also look at the problem of turning winning coalitions into losing coalitions. We analyze the problem when the simple game is represented by a list of wining, losing, minimal winning or maximal loosing coalitions.Decisiveness of decisive symmetric games
http://hdl.handle.net/2117/12437
Decisiveness of decisive symmetric games
Carreras Escobar, Francisco; Freixas Bosch, Josep; Puente del Campo, María Albina
Binary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the "decisiveness index" of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricited to decisive symmetric gammes and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negaive, in p when p=1/2 takes the decisiveness to quickly approach , respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.
Reseach supported by Grant SGR 2009-01029 of the Catalonia Government (Generalitat de Catalunya) and Frants MTM 2006-06064 and MTM 2009-08037 of the Science and Innovation Spanish Ministry and the European Regional Development Fund.
2011-04-29T15:46:53ZCarreras Escobar, FranciscoFreixas Bosch, JosepPuente del Campo, María AlbinaBinary voting systems, usually represented by simple games, constitute a main DSS topic. A crucial feature of such a system is the easiness with which a proposal can be collectively accepted, which is measured by the "decisiveness index" of the corresponding game. We study here several functions related to the decisiveness of any simple game. The analysis, including the asymptotic behavior as the number n of players increases, is restricited to decisive symmetric gammes and their compositions, and it is assumed that all players have a common probability p to vote for the proposal. We show that, for n large enough, a small variation, either positive or negaive, in p when p=1/2 takes the decisiveness to quickly approach , respectively, 1 or 0. Moreover, we analyze the speed of the decisiveness convergence.Symmetric coalitional binomial semivalues
http://hdl.handle.net/2117/12436
Symmetric coalitional binomial semivalues
Carreras Escobar, Francisco; Puente del Campo, María Albina
We introduce here a family of mixed coalitional values. they extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotidient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.
Reseach supported by Grant SGR 2009-01029 of the Catalonia Government (Generalitat de Catalunya) and Frants MTM 2006-06064 and MTM 2009-08037 of the Science and Innovation Spanish Ministry and the European Regional Development Fund.
2011-04-29T15:19:06ZCarreras Escobar, FranciscoPuente del Campo, María AlbinaWe introduce here a family of mixed coalitional values. they extend the binomial semivalues to games endowed with a coalition structure, satisfy the property of symmetry in the quotidient game and the quotient game property, generalize the symmetric coalitional Banzhaf value introduced by Alonso and Fiestras and link and merge the shapley value and the binomial semivalues. A computational procedure in terms of the multilinear extension of the original game is also provided and an application to political science is sketched.Maximum tolerance and maximum greatest tolerance
http://hdl.handle.net/2117/9550
Maximum tolerance and maximum greatest tolerance
Freixas Bosch, Josep; Molinero Albareda, Xavier
An important consideration when applying neural networks is the sensitivity
to weights and threshold in strict separating systems representing a
linearly separable function. Two parameters have been introduced to measure
the relative errors in weights and threshold of strict separating systems:
the tolerance and the greatest tolerance. Given an arbitrary separating system
we study which is the equivalent separating system that provides maximum
tolerance or/and maximum greatest tolerance.
2010-10-07T14:19:24ZFreixas Bosch, JosepMolinero Albareda, XavierAn important consideration when applying neural networks is the sensitivity
to weights and threshold in strict separating systems representing a
linearly separable function. Two parameters have been introduced to measure
the relative errors in weights and threshold of strict separating systems:
the tolerance and the greatest tolerance. Given an arbitrary separating system
we study which is the equivalent separating system that provides maximum
tolerance or/and maximum greatest tolerance.The influence of the node criticality relation on some measures of component importance
http://hdl.handle.net/2117/9302
The influence of the node criticality relation on some measures of component importance
Freixas Bosch, Josep; Pons Vallès, Montserrat
Estudi de la relació entre diverses mesures d'importància probabilístiques i la relació crítica associada al sistema
2010-10-04T18:09:51ZFreixas Bosch, JosepPons Vallès, MontserratEstudi de la relació entre diverses mesures d'importància probabilístiques i la relació crítica associada al sistema