Upper bound for the approximation ratio of a class of hypercube segmentation algorithms

Authors:
Jouni K. Seppänen
Affiliations:
HIIT Basic Research Unit, Laboratory of Computer and Information Science, P.O. Box 5400, FI-02015 Helsinki University of Technology, Finland
Venue:
Information Processing Letters
Year:
2005

Citing 2
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On two segmentation problems

Journal of Algorithms
Segmentation problems

Journal of the ACM (JACM)

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Abstract

The HYPERCUBE SEGMENTATION problem was recently introduced by Kleinberg et al. [J. ACM 51 (2004) 263-280], along with several algorithms that select each segment's prototype vector from the segment. The algorithms were shown to have an approximation ratio of at least 2(√2 - 1) ≈ 0.828. We show that a lemma used in this proof is tight, and that the asymptotic approximation ratio of no algorithm of this type can exceed 5/6 ≈ 0.833.