de.mpg.escidoc.pubman.appbase.FacesBean
Deutsch
 
Hilfe Wegweiser Impressum Kontakt Einloggen
  DetailsucheBrowse

Datensatz

DATENSATZ AKTIONENEXPORT

Freigegeben

Zeitschriftenartikel

Upper bound on the number of vertices of polyhedra with 0, 1-constraint matrices

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44374

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

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44944

Lotker,  Zvi
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

Elbassioni, K., Lotker, Z., & Seidel, R. (2006). Upper bound on the number of vertices of polyhedra with 0, 1-constraint matrices. Information Processing Letters, 100, 69-71.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-246E-7
Zusammenfassung
In this note we give upper bounds for the number of vertices of the polyhedron $P(A,b) = \{x \in Rd: Ax < b\}$ when the $m \times d$ constraint matrix $A$ is subjected to certain restriction. For instance, if $A$ is a 0/1-matrix, then there can be at most $d!$ vertices and this bound is tight, or if the entries of $A$ are non-negative integers so that each row sums to at most $C$, then there can be at most $Cd$ vertices. These bounds are consequences of a more general theorem that the number of vertices of $P(A,b)$ is at most $d! ċ W/D$, where $W$ is the volume of the convex hull of the zero vector and the row vectors of $A$, and $D$ is the smallest absolute value of any non-zero $d \times d$ subdeterminant of $A$.