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a ptas for the k-consensus structures problem under squared euclidean distance下的和平k-consensus结构问题的平方欧氏距离
Algorithms 2008, 1, 43-51; DOI: 10.3390/a1020043
OPEN ACCESS
algorithms
ISSN 1099-4300
Article /journal/algorithms
A PTAS For The -Consensus Structures Problem Under
Squared Euclidean Distance
Shuai Cheng Li , Yen Kaow Ng and Louxin Zhang
David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada N2L 3G1.
Department of Computer Science and Communication Engineering, Kyushu University, Fukuoka
819-0395, Japan.
Department of Mathematics, National University of Singapore, Singapore 117543.
E-mails: scli@cs.uwaterloo.ca; kalngyk@tcslab.csce.kyushu-u.ac.jp; matzlx@.sg
Author to whom correspondence should be addressed.
Received: 5 September 2008; in revised form: 1 October 2008; Accepted: 9 October 2008; Published:
9 October 2008
Abstract: In this paper we consider a basic clustering problem that has uses in bioinformat-
ics. A structural fragment is a sequence of points in a 3D space, where is a fixed natural
number. Two structural fragments and are equivalent if and only if
under some rotation and translation . We consider the distance between two structural
fragments to be the sum of the squared Euclidean distance between all corresponding points
of the structural fragments. Given a set of structural fragments, we consider the problem
of finding (or fewer) structural fragments , so as to minimize the sum of the
distances between each of to its nearest structural fragment in . In this
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