Characterization of rankings generated by pseudo-Boolean functions
In this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pse...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Basque Center for Applied Mathematics (BCAM) |
| Repositorio: | BIRD. BCAM's Institutional Repository Data |
| OAI Identifier: | oai:bird.bcamath.org:20.500.11824/1786 |
| Acceso en línea: | http://hdl.handle.net/20.500.11824/1786 https://doi.org/10.1016/j.swevo.2024.101540 |
| Access Level: | acceso abierto |
| Palabra clave: | Binary-based combinatorial optimization problemsPseudo-Boolean functionsRankingsDyck wordsTheoretical analysis |
| Sumario: | In this paper we pursue the study of pseudo-Boolean functions as ranking generators. The objective of the work is to find new insights between the relation of the degree of a pseudo-Boolean function and the rankings that can be generated by these insights. Based on a characterization theorem for pseudo-Boolean functions of degree , several observations are made. First, we verify that pseudo-Boolean functions of degree , where is the search space dimension, cannot generate all the possible rankings of the solutions. Secondly, the sufficient condition for a ranking to be generated by a pseudo-Boolean function of dimension is presented, and also the necessary condition is conjectured. Finally, we observe that the same argument is not sufficient to prove which ranking can be generated by pseudo-Boolean functions of degree . |
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