arXiv
Open Access
2020
Coloring and Maximum Weight Independent Set of Rectangles
Parinya Chalermsook
Bartosz Walczak
Abstrak
In 1960, Asplund and Grünbaum proved that every intersection graph of axis-parallel rectangles in the plane admits an $O(ω^2)$-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 $O(ω\logω)$-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 $O(\frac{\log n}{\log\log n})$.
Penulis (2)
P
Parinya Chalermsook
B
Bartosz Walczak
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2020
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- en
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- arXiv
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- Open Access ✓