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# Monotonic Polygons and Paths in Weighted Point Sets

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

## Abstract

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.

## Keywords

Simple Polygon Weight Point Monotonic Path Empty Convex Convex Position
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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