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.
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Sakai, T., Urrutia, J. (2011). Monotonic Polygons and Paths in Weighted Point Sets. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_17
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DOI: https://doi.org/10.1007/978-3-642-24983-9_17
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