论文信息 - On Separable Clusterings

On Separable Clusterings

Abstract For a finite set of points S in the Euclidean plane we introduce the so called C-s -clustering problem which can be stated in the following way: Partition S into C subsets S i such that S i is separable from S / S i by a line and | S i | = k i , where k i are given numbers. For a function f which maps C subsets S i of S into R we present an algorithm which finds a, with respect to f , optimal C-s -clustering ( C a constant) in O(n 3 2 log 2 n + n 3 2 U f (n) + P f (n)) steps (where P f ( n ) (resp. U f ( n )) are the time to calculate (resp. to update) f , if the arguments are slightly changed). If n - C is regarded as a constant we give an algorithm which decides in O ( n log n ) time whether a C-s -clustering exists.

Hartmut Noltemeier | Hugo Heusinger | H. Noltemeier | Hugo Heusinger

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