Open Access

Algorithms for Finding Small Attractors in Boolean Networks

  • Shu-Qin Zhang1Email author,
  • Morihiro Hayashida2,
  • Tatsuya Akutsu2,
  • Wai-Ki Ching1 and
  • Michael K Ng3
EURASIP Journal on Bioinformatics and Systems Biology20072007:20180

https://doi.org/10.1155/2007/20180

Received: 29 June 2006

Accepted: 13 February 2007

Published: 12 April 2007

Abstract

A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.

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Authors’ Affiliations

(1)
Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong
(2)
Bioinformatics Center, Institute for Chemical Research, Kyoto University
(3)
Department of Mathematics, Hong Kong Baptist University

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Copyright

© Shu-Qin Zhang et al. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.