- Let P be an x-monotone polygonal path in the plane. For a path Q that approximates P let WA (Q) be the area above P and below Q, and let WB (Q) be the area above Q and below P. Given P and an integer k, we show how to compute a path Q with at most k edges that minimizes WA (Q) + WB (Q). Given P and a cost C, we show how to find a path Q with the smallest possible number of edges such that WA (Q) + WB (Q) ≤ C. However, given P, an integer k, and a cost C, it is NP-hard to determine if a path Q with at most k edges exists such that max {WA (Q), WB (Q)} ≤ C. We describe an approximation algorithm for this setting. Finally, it is also NP-hard to decide whether a path Q exists such that | WA (Q) - WB (Q) | = 0. Nevertheless, in this error measure we provide an algorithm for computing an optimal approximation up to an additive error. ？ 2005 Elsevier B.V. All rights reserved.

- Publisher
- Elsevier BV

- Issue Date
- 2006-12

- Language
- ENG

- Citation
JOURNAL OF DISCRETE ALGORITHMS, v.4, no.4, pp.554 - 566

- ISSN
- 1570-8667

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

- Files in This Item
- pp942.pdf
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