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Algorithmic and Complexity Issues of Three Clustering Methods in Microarray Data Analysis

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Abstract

The complexity, approximation and algorithmic issues of several clustering problems are studied. These non-traditional clustering problems arise from recent studies in microarray data analysis. We prove the following results. (1) Two variants of the Order-Preserving Submatrix problem are NP-hard. There are polynomial-time algorithms for the Order-Preserving Submatrix problem when the condition or gene sets are fixed. (2) Three variants of the Smooth Clustering problem are NP-hard. The Smooth Subset problem is approximable with ratio 0.5, but it cannot be approximable with ratio 0.5 + δ for any δ > 0 unless NP = P. (3) The inferring plaid model problem is NP-hard.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Singapore, 117543, Singapore

    Jinsong Tan & Louxin Zhang

  2. Institute of High Performance Computing, Singapore 117528, Singapore

    Kok Seng Chua

  3. ST Electronics (Satcom & Sensor Systems) Pte. Ltd., Singapore 609602, Singapore

    Song Zhu

Authors
  1. Jinsong Tan
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  2. Kok Seng Chua
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  3. Louxin Zhang
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  4. Song Zhu
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Corresponding authors

Correspondence to Jinsong Tan, Kok Seng Chua, Louxin Zhang or Song Zhu.

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Tan, J., Chua, K., Zhang, L. et al. Algorithmic and Complexity Issues of Three Clustering Methods in Microarray Data Analysis. Algorithmica 48, 203–219 (2007). https://doi.org/10.1007/s00453-007-0040-4

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  • DOI: https://doi.org/10.1007/s00453-007-0040-4

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