LIPIcs.APPROX-RANDOM.2020.52.pdf
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Online Coloring of Short Intervals
Authors
Joanna Chybowska-Sokół 
,
Grzegorz Gutowski ,
Konstanty Junosza-Szaniawski ,
Patryk Mikos ,
Adam Polak
-
Part of:
Volume:
Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Randomization and Computation (RANDOM)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2020-08-11
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Author Details
- Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
- Institute of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
- Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
- Institute of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Cite As Get BibTex
Joanna Chybowska-Sokół, Grzegorz Gutowski, Konstanty Junosza-Szaniawski, Patryk Mikos, and Adam Polak. Online Coloring of Short Intervals. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 52:1-52:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.52
Abstract
We study the online graph coloring problem restricted to the intersection graphs of intervals with lengths in [1,σ]. For σ = 1 it is the class of unit interval graphs, and for σ = ∞ the class of all interval graphs. Our focus is on intermediary classes. We present a (1+σ)-competitive algorithm, which beats the state of the art for 1 < σ < 2, and proves that the problem we study can be strictly easier than online coloring of general interval graphs. On the lower bound side, we prove that no algorithm is better than 5/3-competitive for any σ > 1, nor better than 7/4-competitive for any σ > 2, and that no algorithm beats the 5/2 asymptotic competitive ratio for all, arbitrarily large, values of σ. That last result shows that the problem we study can be strictly harder than unit interval coloring. Our main technical contribution is a recursive composition of strategies, which seems essential to prove any lower bound higher than 2.
Subject Classification
ACM Subject Classification
- Theory of computation → Online algorithms
Keywords
- Online algorithms
- graph coloring
- interval graphs
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References
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