Abstract
We consider the optimization problem of finding k nonintersecting rectangles and tableaux in n ×n pixel plane where each pixel has a real valued weight. We discuss existence of efficient algorithms if a corner point of each rectangle/tableau is specified.
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References
Asano, T., Chen, D.Z., Katoh, N., Tokuyama, T.: Efficient Algorithms for Optimization-Based Image Segmentation. Int. J. Comput. Geometry Appl. 11(2), 145–166 (2001)
Bae, S.E., Takaoka, T.: Improved Algorithms for the K-Maximum Subarray Problem. The Computer Journal 49(3), 358–374 (2006)
Bae, S.E., Takaoka, T.: A Sub-Cubic Time Algorithm for the K-Maximum Subarray Problem. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 751–762. Springer, Heidelberg (2007)
Bae, S.E., Takaoka, T.: Algorithms for K-Disjoint Maximum Subarrays. Int. J. Found. Comput. Sci. 18(2), 319–339 (2007)
Bentley, J.: Algorithm Design Techniques. ACM Commu. 27(9), 865–871 (1984); Also found in Bentley, J.: Programming Pearls, 2nd edn. ACM Press, New York (2000)
Chen, D.Z., Chun, J., Katoh, N., Tokuyama, T.: Efficient algorithms for approximating a multi-dimensional voxel terrain by a unimodal terrain. In: Chwa, K.-Y., Munro, J.I.J. (eds.) COCOON 2004. LNCS, vol. 3106, pp. 238–248. Springer, Heidelberg (2004)
Chen, D.Z., Hu, X.S., Luan, S., Wu, X., Yu, C.X.: Optimal Terrain Construction Problems and Applications in Intensity-Modulated Radiation Therapy. Algorithmica 42(3-4), 265–288 (2005)
Chun, J., Kasai, R., Korman, M., Tokuyama, T.: Algorithms for Computing the Maximum Weight Region Decomposable into Elementary Shapes. In: Dong, Y., Du, D.-Z., Ibarra, O. (eds.) ISAAC 2009. LNCS, vol. 5878, pp. 1166–1174. Springer, Heidelberg (2009)
Chun, J., Korman, M., Nöllenburg, M., Tokuyama, T.: Consistent Digital Rays. In: Proc. 24th ACM SoCG, pp.355–364 (2008)
Formann, M., Wanger, F.: A Packing Probelm with Applications to Lettering of Maps. In: Proc. 7th ACM SoCG, pp. 281–290 (1991)
Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Data Mining with optimized two-dimensional association rules. ACM Trans. Database Syst. 26(2), 179–213 (2001)
Iturriaga, C.: Map Labeling Problems, Ph. D Thesis, Waterloo University (1999)
Koike, A., Nakano, S.-I., Nishizeki, T., Tokuyama, T., Watanabe, S.: Labeling Points with Rectangles of Various Shapes. Int. J. Comput. Geometry Appl. 12(6), 511–528 (2002)
Korman, M.: Theory and Applications of Geometric Optimization Problems in Rectilinear Metric Spaces, Ph. D Thesis, Tohoku University (2009)
Soltan, V., Gorpinevich, A.: Minimum Dissection of a Rectilinear Polygon with Arbitrary Holes into Rectangles. Disc. Comput. Geom. 9, 57–79 (1993)
Tamaki, H., Tokuyama, T.: Algorithms for the Maximum Subarray Problem Based on Matrix Multiplication. In: Proc. 9th SODA, pp. 446–452 (1998)
Yoda, K., Fukuda, T., Morimoto, Y., Morishita, S., Tokuyama, T.: Computing Optimized Rectilinear Regions for Association Rules. In: Proc. KDD 1997, pp. 96–103 (1997)
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Anzai, S., Chun, J., Kasai, R., Korman, M., Tokuyama, T. (2010). Effect of Corner Information in Simultaneous Placement of K Rectangles and Tableaux. In: Thai, M.T., Sahni, S. (eds) Computing and Combinatorics. COCOON 2010. Lecture Notes in Computer Science, vol 6196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14031-0_27
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DOI: https://doi.org/10.1007/978-3-642-14031-0_27
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