How to Tame Rectangles: Solving Independent Set and Coloring of Rectangles via Shrinking

In the Maximum Weight Independent Set of Rectangles (MWISR) problem, we are given a collection of weighted axis-parallel rectangles in the plane. Our goal is to compute a maximum weight subset of pairwise non-overlapping rectangles. Due to its various applications, as well as connections to many other problems in computer science, MWISR has received a lot of attention from the computational geometry and the approximation algorithms community. However, despite being extensively studied, MWISR remains not very well understood in terms of polynomial time approximation algorithms, as there is a large gap between the upper and lower bounds, i.e., O(log n/ log log n) v.s. NP-hardness. Another important, poorly understood question is whether one can color rectangles with at most O(ω(R)) colors where ω(R) is the size of a maximum clique in the intersection graph of a set of input rectangles R. Asplund and Grünbaum obtained an upper bound of O(ω(R)2 ) about 50 years ago, and the result has...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Anna Adamaszek, Parinya Chalermsook, Andreas Wiese
• Keywords: Algorithms, APPROX 2015