標題: Are there more almost separable partitions than separable partitions?
作者: Chang, Fei-Huang
Chen, Hong-Bin
Hwang, Frank K.
應用數學系
Department of Applied Mathematics
關鍵字: Partition;Separable partition;Optimal partition;Almost separable partition
公開日期: 1-四月-2014
摘要: A partition of a set of n points in d-dimensional space into p parts is called an (almost) separable partition if the convex hulls formed by the parts are (almost) pairwise disjoint. These two partition classes are the most encountered ones in clustering and other partition problems for high-dimensional points and their usefulness depends critically on the issue whether their numbers are small. The problem of bounding separable partitions has been well studied in the literature (Alon and Onn in Discrete Appl. Math. 91:39-51, 1999; Barnes et al. in Math. Program. 54:69-86, 1992; Harding in Proc. Edinb. Math. Soc. 15:285-289, 1967; Hwang et al. in SIAM J. Optim. 10:70-81, 1999; Hwang and Rothblum in J. Comb. Optim. 21:423-433, 2011a). In this paper, we prove that for da parts per thousand currency sign2 or pa parts per thousand currency sign2, the maximum number of almost separable partitions is equal to the maximum number of separable partitions.
URI: http://dx.doi.org/10.1007/s10878-012-9536-1
http://hdl.handle.net/11536/23748
ISSN: 1382-6905
DOI: 10.1007/s10878-012-9536-1
期刊: JOURNAL OF COMBINATORIAL OPTIMIZATION
Volume: 27
Issue: 3
起始頁: 567
結束頁: 573
顯示於類別:期刊論文


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  1. 000332006100012.pdf