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On the parameterized complexity of pooling design.

Yongxi Cheng1, Ding-Zhu Du, Ker-I Ko

  • 1Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada. chengyx@gmail.com

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|September 24, 2009
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Summary
This summary is machine-generated.

Efficient algorithms for DNA library screening using pooling designs are unlikely when the parameter d is small. This study proves that the parameterized complexity of d-separability problems is co-W[2]-complete, implying no sub-exponential time deterministic solutions exist.

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Area of Science:

  • Computational Biology
  • Bioinformatics
  • Algorithm Analysis

Background:

  • DNA library screening is crucial for gene function studies.
  • Pooling designs reduce the number of tests required.
  • Key problems involve determining d-separability (or d-disjunctness) of binary matrices.

Purpose of the Study:

  • To investigate the existence of efficient algorithms for d-separability problems when d is small.
  • To analyze the parameterized complexity of these pooling design problems with d as the parameter.

Main Methods:

  • Parameterized complexity analysis.
  • Investigating coNP-complete problems with a focus on the parameter d.
  • Proving co-W[2]-completeness for the parameterized versions of the three pooling design problems.

Main Results:

  • The parameterized versions of the three d-separability problems are co-W[2]-complete.
  • This implies that efficient (f(d) x (mn)^O(1)) deterministic algorithms are not expected for small d.

Conclusions:

  • No efficient deterministic algorithms can be expected for solving d-separability problems in DNA library screening when d is small.
  • The co-W[2]-completeness result provides a theoretical barrier to developing such algorithms.