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Adaptive Partitions

1986; Du, Pan, Shing

  • Reference work entry
Encyclopedia of Algorithms

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Keywords and Synonyms

Technique for constructing approximation      

Problem Definition

Adaptive partition is one of major techniques to design polynomial‐time approximation algorithms, especially polynomial‐time approximation schemes for geometric optimization problems. The framework of this technique is to put the input data into a rectangle and partition this rectangle into smaller rectangles by a sequence of cuts so that the problem is also partitioned into smaller ones. Associated with each adaptive partition, a feasible solution can be constructed recursively from solutions in smallest rectangles to bigger rectangles. With dynamic programming, an optimal adaptive partition is computed in polynomial time.

Historical Background

The adaptive partition was first introduced to the design of an approximation algorithm by Du et al. [5] with a guillotine cut while they studied the minimum edge length rectangular partition (MELRP) problem. They found that if the partition is performed by...

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Recommended Reading

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  5. Du, D.-Z., Pan, L.-Q., Shing, M.-T.: Minimum edge length guillotine rectangular partition. Technical Report 0241886, Math. Sci. Res. Inst., Univ. California, Berkeley (1986)

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, Richardson, TX, USA

    Ping Deng & Weili Wu

  2. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA

    Eugene Shragowitz

Authors
  1. Ping Deng
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  2. Weili Wu
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  3. Eugene Shragowitz
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer ScienceMcCormick School of Engineering and Applied Science, Northwestern University, Evanston, IL, 60208, USA

    Ming-Yang Kao Professor of Computer Science

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© 2008 Springer-Verlag

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Deng, P., Wu, W., Shragowitz, E. (2008). Adaptive Partitions. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-30162-4_2

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