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- Toshihide Ibaraki, Naoki Katoh
- MIT Press series in the foundations of computing
- 1988

- Mary Inaba, Naoki Katoh, Hiroshi Imai
- Symposium on Computational Geometry
- 1994

In this paper we consider the<italic>k</italic>-clustering problem for a set <italic>S</italic> of <italic>n</italic> points <inline-equation><f><inf>i</inf>=<fen lp="par"><b>x<inf>i</inf></b><rp post="par"> </fen></f> </inline-equation> in the<italic>d</italic>-dimensional space with variance-based errors as clustering criteria, motivated from the color… (More)

- Naoki Katoh, Toshihide Ibaraki, Hisashi Mine
- Networks
- 1982

- Toshihide Ibaraki, Naoki Katoh
- Inf. Process. Lett.
- 1983

- Alok Aggarwal, Hiroshi Imai, Naoki Katoh, Subhash Suri
- J. Algorithms
- 1991

We consider the problem of selecting a specified number of points, k, from a given set S, subject to some optimization criterion. Problems of this type often arise in statistical clustering and pattern recognition (see Andrews [3] and Hartigan [7]). From an algorithmic standpoint, these problems usually can be solved in time O(nk+c), where 12 is the number… (More)

- Danny Ziyi Chen, Ovidiu Daescu, Yang Dai, Naoki Katoh, Xiaodong Wu, Jinhui Xu
- SODA
- 2000

1 I n t r o d u c t i o n . The problem of optimizing the sum of linear fractional functions (SOLF) is defined as follows: max f(Zl,...,Xd)= ~ [ : 7 : ~ d ) (Xl ..... z~t)ES i=1 ~ a r t m e n t of Computer Science and Engineering, University of Notre Dame, Notre Dame, IN 46556, USA, {chen,odaescu,xwu,jxu}@cse.nd.edu. This research was supported in part by… (More)

- Tetsuo Asano, Naoki Katoh, Hisao Tamaki, Takeshi Tokuyama
- STOC
- 1997

Let P be a set of n points in the plane. A k-tour through P is a tour in the plane that starts and ends at the fixed origin and visits at most k points of P. Our goal is to cover all the points of P by k-tours so as to minimize the total length of the tours. We give a polynomial time approximation scheme (PTAS) for this problem whose running time is… (More)

- Kazuo Iwano, Naoki Katoh
- Inf. Process. Lett.
- 1993

Despite its simplicity and its linear time, a serial K-means algorithm's time complexity remains expensive when it is applied to a problem of large size of multidimensional vectors. In this paper we show an improvement by a factor of O(K/2), where K is the number of desired clusters, by applying theories of parallel computing to the algorithm. In addition… (More)

- Tetsuo Asano, Danny Ziyi Chen, Naoki Katoh, Takeshi Tokuyama
- SODA
- 1996

Separating an object in an image from its background is a central problem (called segmentation) in pattern recognition and computer vision. In this paper, we study the complexity of the segmentation problem, assuming that the object forms a connected region in an intensity image. We show that the optimization problemof separating a connected region in an… (More)