Abstract
We consider new versions of the two-center problem where the input consists of a set \(\mathcal{D}\) of disks in the plane. We first study the problem of finding two smallest congruent disks such that each disk in \(\mathcal{D}\) intersects one of these two disks. Then we study the problem of covering the set \(\mathcal{D}\) by two smallest congruent disks. We give exact and approximation algorithms for these versions.
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References
Agarwal, P., Procopiuc, C.: Exact and approximation algorithms for clustering. Algorithmica 33(2), 201–226 (2002)
Agarwal, P.K., Sharir, M., Toledo, S.: Applications of parametric searching in geometric optimization. J. Algorithms 17, 292–318 (1994)
Chan, T.M.: More planar two-center algorithms. Comput. Geom. Theory Appl. 13, 189–198 (1997)
Chan, T.M.: Deterministic algorithms for 2-d convex programming and 3-d online linear programming. J. Algorithms 27(1), 147–166 (1998)
Clarkson, K.L.: Las Vegas algorithms for linear and integer programming when the dimension is small. J. ACM 42, 488–499 (1995)
de Berg, M., Cheong, O., van Kreveld, M., Overmars, M.: Computational Geometry Algorithms and Applications, 3rd edn. Springer, Heidelberg (2008)
Drezner, Z.: The planar two-center and two-median problems. Transportation Science 18, 351–361 (1984)
Eppstein, D.: Faster construction of planar two-centers. In: Proc. of SODA 1997, pp. 131–138 (1997)
Fischer, K., Gartner, B.: The smallest enclosing ball of balls: combinatorial structure and algorithms. In: Proc. of SoCG 2003, pp. 292–301 (2003)
Gonzalez, T.: Clustering to minimize the maximum intercluster distance. Theor. Comput. Sci. 38, 293–306 (1985)
Löffler, M., van Kreveld, M.: Largest bounding box, smallest diameter, and related problems on imprecise points. Comput. Geom. Theory Appl. 43, 419–433 (2010)
Megiddo, N.: On the ball spanned by balls. Discr. Comput. Geom. 4, 605–610 (1989)
Sharir, M., Welzl, E.: A Combinatorial Bound for Linear Programming and Related Problems. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 567–579. Springer, Heidelberg (1992)
Shin, C.-S., Kim, J.-H., Kim, S.K., Chwa, K.-Y.: Two-center Problems for a Convex Polygon. In: Bilardi, G., Pietracaprina, A., Italiano, G.F., Pucci, G. (eds.) ESA 1998. LNCS, vol. 1461, pp. 199–210. Springer, Heidelberg (1998)
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Ahn, HK., Kim, SS., Knauer, C., Schlipf, L., Shin, CS., Vigneron, A. (2011). Covering and Piercing Disks with Two Centers. In: Asano, T., Nakano, Si., Okamoto, Y., Watanabe, O. (eds) Algorithms and Computation. ISAAC 2011. Lecture Notes in Computer Science, vol 7074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25591-5_7
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DOI: https://doi.org/10.1007/978-3-642-25591-5_7
Publisher Name: Springer, Berlin, Heidelberg
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