Polynomial Time Reachability Analysis in Discrete State Chemical Reaction Networks Obeying Conservation Laws

IF 2.9 2区 化学 Q2 CHEMISTRY, MULTIDISCIPLINARY
Gergely Szlobodnyik, G. Szederkényi
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引用次数: 0

Abstract

In this paper the reachability problem of discrete state Chemical Reaction Networks (d-CRNs) is studied. We consider sub-classes of sub-and superconservative d-CRN network structures and prove that the reachability relation can be decided in polynomial time. We make use of the result that in the studied d-CRN sub-classes, the reachability relation is equivalent to the existence of a non-negative integer solution of the d-CRN state equation. The equivalence implies the reformulation of the reachability problem as integer linear programming decision problem. We show that in the studied classes of d-CRN structures, the state equation has a totally unimodular coefficient matrix. As the reachability relation is equivalent to the non-negative integer solution of the state equation, the resulting integer programming decision program can be relaxed to a simple linear program having polynomial time complexity. Hence, in the studied sub-classes of sub and superconservative reaction network structures, the reachability relation can be decided in polynomial time and the number of continuous decision variables is equal to the number of reactions of the d-CRN.
服从守恒定律的离散态化学反应网络的多项式时间可达性分析
研究了离散态化学反应网络(d-CRNs)的可达性问题。考虑了子保守和超保守d-CRN网络结构的子类,证明了可达性关系可以在多项式时间内确定。利用在所研究的d-CRN子类中,可达性关系等价于d-CRN状态方程非负整数解的存在性。等效性意味着将可达性问题重新表述为整数线性规划决策问题。结果表明,在所研究的d-CRN结构中,状态方程具有完全非模系数矩阵。由于可达性关系等价于状态方程的非负整数解,由此得到的整数规划决策方案可以简化为时间复杂度为多项式的简单线性规划。因此,在研究的亚保守和超保守反应网络结构的子类中,可达性关系可以在多项式时间内确定,并且连续决策变量的个数等于d-CRN的反应个数。
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来源期刊
CiteScore
4.40
自引率
26.90%
发文量
71
审稿时长
2 months
期刊介绍: MATCH Communications in Mathematical and in Computer Chemistry publishes papers of original research as well as reviews on chemically important mathematical results and non-routine applications of mathematical techniques to chemical problems. A paper acceptable for publication must contain non-trivial mathematics or communicate non-routine computer-based procedures AND have a clear connection to chemistry. Papers are published without any processing or publication charge.
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