Abstract
We revisit the problem of online conflict-free coloring of intervals on a line, where each newly inserted interval must be assigned a color upon insertion such that the coloring remains conflict-free, i.e. for each point $p$ in the union of the current intervals, there must be an interval $I$ with a unique color among all intervals covering $p$. To best of our knowledge, the best-known algorithm uses $O(log^3 n )$ colors, where $n$ is the number of current intervals. We present a simple greedy algorithm that uses only $O(log n)$ colors. Therefore, we settle down the open problem raised in cite{ars14}.
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