Let C be the unit circle in R-2. We can view C as a plane graph whose vertices are all the points on C, and the distance between any two points on C is the length of the smaller arc between them. We consider a graph augmentation problem on C, where we want to place k >= I shortcuts on C such that the diameter of the resulting graph is minimized. We analyze for each k with 1 <= k <= 7 what the optimal set of shortcuts is. Interestingly, the minimum diameter one can obtain is not a strictly decreasing function of k. For example, with seven shortcuts one cannot obtain a smaller diameter than with six shortcuts. Finally, we prove that the optimal diameter is 2 + Theta(1/k(2/3)) for any k. (C) 2019 Elsevier B.V. All rights reserved.

- Publisher
- ELSEVIER SCIENCE BV

- Issue Date
- 2019-02

- Language
- English

- Article Type
- Article

- Citation
COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, v.79, pp.37 - 54

- ISSN
- 0925-7721

- Appears in Collection
- CS-Journal Papers(저널논문)

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