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arXiv · 1412.8005

Dynamic Algorithms for Interval Scheduling on a Single Machine

Alex Gavryushkin·Bakhadyr Khoussainov·Mikhail Kokho·Jiamou Liu
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Abstract

We investigate dynamic algorithms for the interval scheduling problem. Our algorithm runs in amortised time $O(\log n)$ for query operation and $O(d\log^2 n)$ for insertion and removal operations, where $n$ and $d$ are the maximal numbers of intervals and pairwise overlapping intervals respectively. We also show that for a monotonic set, that is when no interval properly contains another interval, the amortised complexity is $O(\log n)$ for both query and update operations. We compare the two algorithms for the monotonic interval sets using experiments.

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Alex Gavryushkin, Bakhadyr Khoussainov, Mikhail Kokho, Jiamou Liu. 2014-12-27. Dynamic Algorithms for Interval Scheduling on a Single Machine. https://doi.org/10.1016/j.tcs.2014.09.046

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