The Painter's Problem: covering a grid with colored connected polygons

Research output: Contribution to journalArticleAcademic

74 Downloads (Pure)

Abstract

Motivated by a new way of visualizing hypergraphs, we study the following problem. Consider a rectangular grid and a set of colors χ. Each cell s in the grid is assigned a subset of colors χs⊆χ and should be partitioned such that for each color c∈χs at least one piece in the cell is identified with c. Cells assigned the empty color set remain white. We focus on the case where χ={red,blue}. Is it possible to partition each cell in the grid such that the unions of the resulting red and blue pieces form two connected polygons? We analyze the combinatorial properties and derive a necessary and sufficient condition for such a painting. We show that if a painting exists, there exists a painting with bounded complexity per cell. This painting has at most five colored pieces per cell if the grid contains white cells, and at most two colored pieces per cell if it does not.
Original languageEnglish
Article number1709.00001
Number of pages20
JournalarXiv
Issue number1709.00001
Publication statusPublished - 30 Sep 2017

Fingerprint

Dive into the research topics of 'The Painter's Problem: covering a grid with colored connected polygons'. Together they form a unique fingerprint.

Cite this