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Computing

, Volume 26, Issue 4, pp 361–366 | Cite as

A note on linear expected time algorithms for finding convex hulls

  • L. Devroye
  • G. T. Toussaint
Short Communications

Abstract

Considern independent identically distributed random vectors fromR d with common densityf, and letE (C) be the average complexity of an algorithm that finds the convex hull of these points. Most well-known algorithms satisfyE (C)=0(n) for certain classes of densities. In this note, we show thatE (C)=0(n) for algorithms that use a “throw-away” pre-processing step whenf is bounded away from 0 and ∞ on any nondegenerate rectangle ofR2.

Key words and phrases

Convex hull average complexity geometrical complexity algorithms 

Über Algorithmen mit mittlerem linearen Zeitbedarf zur Bestimmung der konvexen Hülle

Zusammenfassung

Wir betrachtenn als unabhängig identisch verteilte Zufallsvektoren imR d mit der gemeinsamen Verteilungsdichtef. Die mittlere Konvexität eines Algorithmus zur Bestimmung der konvexen Hülle dieser Punkte seiE (C). Die meisten bekannten Algorithmen genügen für gewisse Klassen von Dichten der BedingungE (C)=0(n). In dieser Mitteilung zeigen wirE (C)=0(n) für Algorithmen, die im Vorlauf einen „Wegwerf-Schritt” benützen, wennf auf jedem nicht ausgearteten Rechteck desR2 beschränkt ist und positiven Abstand von 0 besitzt.

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • L. Devroye
    • 1
  • G. T. Toussaint
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada

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