Deutsch
 
Benutzerhandbuch Datenschutzhinweis Impressum Kontakt
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Konferenzbeitrag

An Intersection Inequality for Discrete Distributions and Related Generation Problems

MPG-Autoren
/persons/resource/persons44374

Elbassioni,  Khaled M.
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

Externe Ressourcen
Es sind keine Externen Ressourcen verfügbar
Volltexte (frei zugänglich)
Es sind keine frei zugänglichen Volltexte verfügbar
Ergänzendes Material (frei zugänglich)
Es sind keine frei zugänglichen Ergänzenden Materialien verfügbar
Zitation

Boros, E., Elbassioni, K. M., Gurvich, V., Khachiyan, L., & Makino, K. (2003). An Intersection Inequality for Discrete Distributions and Related Generation Problems. In Automata, Languages and Programming (pp. 543-555). Berlin: Springer. doi:10.1007/3-540-45061-0_44.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0019-EBF5-4
Zusammenfassung
Given two finite sets of points \mathcal X},{\mathcal Y} in {\mathbb{R}}^n which can be separated by a nonnegative linear function, and such that the componentwise minimum of any two distinct points in {\mathcal X} is dominated by some point in {\mathcal Y}, we show that \vert{\mathcal X}\vert≤q n\vert{\mathcal Y}\vert. As a consequence of this result, we obtain quasi-polynomial time algorithms for generating all maximal integer feasible solutions for a given monotone system of separable inequalities, for generating all p-inefficient points of a given discrete probability distribution, and for generating all maximal empty hyper-rectangles for a given set of points in {\mathbb{R}^n. This provides a substantial improvement over previously known exponential algorithms for these generation problems related to Integer and Stochastic Programming, and Data Mining. Furthermore, we give an incremental polynomial time generation algorithm for monotone systems with fixed number of separable inequalities, which, for the very special case of one inequality, implies that for discrete probability distributions with independent coordinates, both p-efficient and p-inefficient points can be separately generated in incremental polynomial time.