Abstract
Given a set P of n points in the plane such that each point has a positive weight, we study the problem of finding an obnoxious line that intersects the convex hull of P and maximizes the minimum weighted Euclidean distance to all points of P. We also consider a variant of this problem whose input is a set of m polygons with totally n vertices in the plane such that each polygon has a positive weight and whose goal is to locate an obnoxious line with respect to the weighted polygons. We improve the previous results for both problems. Our algorithms are based on new geometric observations and interesting algorithmic techniques.
This research was supported in part by NSF under Grants CCF-0515203 and CCF-0916606.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bereg, S., Díaz-Báñez, J.M., Seara, C., Ventura, I.: On finding widest empty curved corridors. Computational Geometry: Theory and Applications 38(3), 154–169 (2007)
Chattopadhyay, S., Das, P.: The k-dense corridor problems. Pattern Recognition Letters 11(7), 463–469 (1990)
Chen, D.Z., Wang, H.: Locating an obnoxious line among planar objects (2009) (manuscript)
Cheng, S.: Widest empty L-shaped corridor. Information Processing Letters 58(6), 277–283 (1996)
Cole, R.: Slowing down sorting networks to obtain faster sorting algorithms. Journal of the ACM 34(1), 200–208 (1987)
Cormen, T., Leiserson, C., Rivest, R., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Díaz-Báñez, J.M., Ramos, P.A., Sabariego, P.: The maximin line problem with regional demand. European Journal of Operational Research 181(1), 20–29 (2007)
Drezner, Z., Wesolowsky, G.O.: Location of an obnoxious route. Journal of Operational Research Society 40(11), 1011–1018 (1989)
Houle, M., Maciel, A.: Finding the widest empty corridor through a set of points. In: Tousssaint, G.T. (ed.) Snapshots of Computational and Discrete Geometry. TR SOCS–88.11, Dept. of Computer Science, McGill University, Montreal, Canada (1988)
Houle, M.E., Toussaint, G.T.: Computing the width of a set. IEEE Trans. Pattern Anal. Mach. Intell. 10(5), 761–765 (1988)
Janardan, R., Preparata, F.P.: Widest-corridor problems. Nordic Journal of Computing 1(2), 231–245 (1994)
Lee, D.T., Wu, Y.F.: Geometric complexity of some location problems. Algorithmica 1(1-4), 193–211 (1986)
Nielsen, F., Yvinec, M.: Output-sensitive convex hull algorithms of planar convex objects. International Journal of Computational Geometry and Applications 8(1), 39–66 (1998)
Rappaport, D.: A convex hull algorithm for discs, and applications. Computational Geometry: Theory and Applications 1(3), 171–187 (1992)
Shin, C., Shin, S.Y., Chwa, K.: The widest k-dense corridor problems. Information Processing Letters 68(1), 25–31 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, D.Z., Wang, H. (2009). Locating an Obnoxious Line among Planar Objects. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_75
Download citation
DOI: https://doi.org/10.1007/978-3-642-10631-6_75
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
Online ISBN: 978-3-642-10631-6
eBook Packages: Computer ScienceComputer Science (R0)