Coloring and maximum weight independent set of rectangles

Parinya Chalermsook*, Bartosz Walczak

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

11 Citations (Scopus)


In 1960, Asplund and Grünbaum proved that every intersection graph of axis-parallel rectangles in the plane admits an O(ω2)-coloring, where ω is the maximum size of a clique. We present the first asymptotic improvement over this six-decade-old bound, proving that every such graph is O(ω log ω)-colorable and presenting a polynomial-time algorithm that finds such a coloring. This improvement leads to a polynomial-time O(log log n)-approximation algorithm for the maximum weight independent set problem in axis-parallel rectangles, which improves on the previous approximation ratio of O(logloglognn).

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2021
EditorsDaniel Marx
Number of pages9
ISBN (Electronic)9781611976465
Publication statusPublished - 2021
MoE publication typeA4 Article in a conference publication
EventACM-SIAM Symposium on Discrete Algorithms - Virtual, Online, Alexandria, United States
Duration: 10 Jan 202113 Jan 2021
Conference number: 32


ConferenceACM-SIAM Symposium on Discrete Algorithms
Abbreviated titleSODA
Country/TerritoryUnited States
Internet address


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