Monotonic Polygons and Paths in Weighted Point Sets

  • Toshinori Sakai
  • Jorge Urrutia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)


Let P be a set of n points such that each of its elements has a unique weight in {1, …,n}. P is called a wp-set. A non-crossing polygonal line connecting some elements of P in increasing (or decreasing) order of their weights is called a monotonic path of P. A simple polygon with vertices in P is called monotonic if it is formed by a monotonic path and an edge connecting its endpoints. In this paper we study the problem of finding large monotonic polygons and paths in wp-sets. We establish some sharp bounds concerning these problems. We also study extremal problems on the number of monotonic paths and polygons of a wp-set.


Simple Polygon Weight Point Monotonic Path Empty Convex Convex Position 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Toshinori Sakai
    • 1
  • Jorge Urrutia
    • 2
  1. 1.Tokai UniversityShibuya-kuJapan
  2. 2.Universidad Nacional Autónoma de MéxicoMéxico D.F.México

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