Finding a Periodic Attractor of a Boolean Network

Abstract

In this paper, we study the problem of finding a periodic attractor of a Boolean network (BN), which arises in computational systems biology and is known to be NP-hard. Since a general case is quite hard to solve, we consider special but biologically important subclasses of BNs. For finding an attractor of period 2 of a BN consisting of n OR functions of positive literals, we present a polynomial time algorithm. For finding an attractor of period 2 of a BN consisting of n AND/OR functions of literals, we present an O(1:985(n)) time algorithm. For finding an attractor of a fixed period of a BN consisting of n nested canalyzing functions and having constant treewidth w, we present an O(n(2p(w+1))poly(n)) time algorithm.

Robustness and Backbone Motif of a Cancer Network Regulated by miR-17-92 Cluster during the G1/S Transition

“…Recently, various methods have been developed and introduced to investigate the property and the information transition in large Boolean networks. Akutsu et al presented several algorithms to identify periodic attractors and singleton attractors in Boolean networks [41], [42]. By using gene ordering and feedback vertex sets in the algorithms, Zhang and colleagues identified singleton attractors and small attractors in Boolean networks [43].…”

A Fixed-Parameter Algorithm for Detecting a Singleton Attractor in an AND/OR Boolean Network with Bounded Treewidth

“…We further extend the algorithm for detection of a singleton attractor in a constant-depth nested canalyzing function BN with bounded treewidth. Finally, we prove that detection of singleton attractor for a general BN with bounded treewidth is W [1] hard for parameter k (i.e., fixed-parameter intractable for parameter k). The directed graph associated with (a).…”

“…Since it is quite hard to develop such algorithms for general BNs, some restrictions were assumed on types of Boolean functions in all studies. For example, an O(1.587 n )time algorithm and an O(1.985 n )-time algorithm were developed for detection of a singleton attractor [9] and an attractor of period 2 [1], respectively, both for AND/OR BNs which are BNs consisting of Boolean functions restricted to conjunctions and disjunctions of literals.…”

“…An O(n 2p(k+1) poly(n))-time algorithm was also developed for finding an attractor of period p of a BN having bounded treewidth k and consisting of nested canalyzing functions [8], where p and k are constants, and nested canalyzing functions are a super class of AND/OR functions [1]. They also presented a fixed-parameter algorithm (precisely, an algorithm working in O(g(p, k, d)poly(n)) time where g(p, k, d) depends only on p, k, d) for a general BN with bounded degree d and bounded treewidth [1]. However, it is unknown whether there exists a fixed-parameter algorithm even for an AND/OR BN with bounded treewidth but without degree constraint.…”

Dynamics of Random Boolean Networks under Fully Asynchronous Stochastic Update Based on Linear Representation

“…Recent years, many powerful algorithms [3], [17], [20], [35], [45] have been presented to improve the search efficiency and reduce the time complexity. Yet, it should be noted that our main interest in this article is to provide a complete quantitative method and a novel perspective to analyze the dynamics of ARBNs from the view point of theoretical part.…”