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Adaptive Partitions

  • Reference work entry
  • First Online:
Encyclopedia of Algorithms

  • 497 Accesses

Years and Authors of Summarized Original Work

  • 1986; Du, Pan, Shing

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 Note

The adaptive partition was first introduced to the design of an approximation algorithm by Du et al. [4] with a guillotine cut while they studied the minimum edge-length rectangular partition (MELRP) problem. They found that if the partition is performed by a...

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Recommended Reading

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Author information

Authors and Affiliations

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

    Ping Deng, Weili Wu & Ding-Zhu Du

  2. College of Computer Science and Technology, Taiyuan University of Technology, Taiyuan, Shanxi Province, China

    Weili Wu

  3. Department of Computer Science, California State University, Los Angeles, CA, USA

    Weili Wu

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

    Eugene Shragowitz

  5. Computer Science, University of Minnesota, 200 Union Street S.E., 55455, Minneapolis, MN, USA

    Ding-Zhu Du

Authors
  1. Ping Deng
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  2. Weili Wu
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  3. Eugene Shragowitz
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  4. Ding-Zhu Du
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, USA

    Ming-Yang Kao

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Deng, P., Wu, W., Shragowitz, E., Du, DZ. (2016). Adaptive Partitions. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2864-4_2

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