Document Type
Article
Journal/Book Title/Conference
Computational Geometry
Publisher
Elsevier BV
Publication Date
2-16-2017
First Page
1
Last Page
36
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Abstract
Given n intervals on a line ℓ, we consider the problem of moving these intervals on ℓ such that no two intervals overlap and the maximum moving distance of the intervals is minimized. The difficulty for solving the problem lies in determining the order of the intervals in an optimal solution. By interesting observations, we show that it is sufficient to consider at most n "candidate" lists of ordered intervals. Further, although explicitly maintaining these lists takes Ω(n2) time and space, by more observations and a pruning technique, we present an algorithm that can compute an optimal solution in O(n log n) time and O(n) space. We also prove an Ω(n log n) time lower bound for solving the problem, which implies the optimality of our algorithm.
Recommended Citation
Li, Shimin, and Haitao Wang. "Separating Overlapped Intervals on a Line." arXiv preprint arXiv:1609.07766 (2016).
