A Genetic Algorithm to Solve the Subset Sum Problem based on Parallel Computing

Abstract: The subset sum problem is to find subsets in a given number set, meanwhile number sum of the subset is equal to appointed value. It is a classical NP-complete problem in graph theory. It can be solved by the electronic computer in exponential time. In this paper, we consider a DNA procedure for solving the subset sum problem in the Adleman-Lipton model. The procedure works in O(n) steps for the subset sum problem of an undirected graph with n vertices. The innovation of the procedure is the ingenious choice of the vertices strands' length, which can get the solution of the problem in proper length range and simultaneity simplify the complexity of the computation

A DNA approach to the Road-Coloring Problem

The Road-Coloring Problem in graph theory can be stated as follows: Is any irreducible aperiodic directed graph with constant outdegree 2 road-colorable? In other words, does such a graph have a synchronizing instruction? That is to say: can we label (or color) the two outgoing edges at each vertex, one with “b” or blue color and the other with “r” or red color, in such a manner that there will be an instruction in the form of a finite sequence in “b”s and “r”s (example: rrbrbbbr) such that this instruction will lead each vertex to the same “target” vertex? This thesis is concerned with writing a DNA algorithm which can be followed in the laboratory to produce an explicit solution of a given Road-Coloring problem. This kind of DNA approach was first introduced by Adleman to find an effective method of finding the solution of a given Hamiltonian Path Problem. The Road-Coloring Problem, though introduced over 30 years ago in 1977 by Adler, Goodwyn, and Weiss was only recently solved by Trahtman. But his solution does not give explicitly the synchronizing instruction

Accelerating DNA Computing via PLP-qPCR Answer Read out to Solve Traveling Salesman Problems

An asymmetric, fully-connected 8-city traveling salesman problem (TSP) was solved by DNA computing using the ordered node pair abundance (ONPA) approach through the use of pair ligation probe quantitative real time polymerase chain reaction (PLP-qPCR). The validity of using ONPA to derive the optimal answer was confirmed by in silico computing using a reverse-engineering method to reconstruct the complete tours in the feasible answer set from the measured ONPA. The high specificity of the sequence-tagged hybridization, and ligation that results from the use of PLPs significantly increased the accuracy of answer determination in DNA computing. When combined with the high throughput efficiency of qPCR, the time required to identify the optimal answer to the TSP was reduced from days to 25 min

A Biomolecular Computing Model in Vivo for Minimum Dominating Set Problem

生物体内分子网络中信息的传输、储存、放大、整合等大量任务可以看成是一种生物分子计算过程.文中提出了一种活体分子计算模型,借助rnA干扰技术和乳糖操纵子调控模型,在细胞内构建了一个基因网络,用于求解图的最小支配集.该模型展示了利用生物体自身的信息处理能力进行计算的能力,在生物体内建立具有一定智能的分子机器,这将在计算科学、生物学、医学上有着深远的应用前景.Biomolecular computing models in vivo are an emerging computing model inspired from the biological phenomena that the biochemical molecular in living perform computation,communications,and signal processing collaboratively.In this paper,a biomolecular computing model in vivo for minimum dominating set problem is presented,a synthetic gene network is constructed by RNAi and lactose operon in living cell.This model explores further the ability to solve hard problems based on organism processing signal,and try to construct an intelligent molecule machine in cell.It may be widely and further used in computing science,biology,and medicine.国家自然科学基金(60910002;60974112;60971085;30970969);国家“八六三”高技术研究发展计划项目基金(2009AA012413);教育部博士点基金(20070001020);中国博士后基金(20080440257)资

Self-Assembly of DNA Graphs and Postman Tours

DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and the Windy Postman Problem

On functional module detection in metabolic networks

Functional modules of metabolic networks are essential for understanding the metabolism of an organism as a whole. With the vast amount of experimental data and the construction of complex and large-scale, often genome-wide, models, the computer-aided identification of functional modules becomes more and more important. Since steady states play a key role in biology, many methods have been developed in that context, for example, elementary flux modes, extreme pathways, transition invariants and place invariants. Metabolic networks can be studied also from the point of view of graph theory, and algorithms for graph decomposition have been applied for the identification of functional modules. A prominent and currently intensively discussed field of methods in graph theory addresses the Q-modularity. In this paper, we recall known concepts of module detection based on the steady-state assumption, focusing on transition-invariants (elementary modes) and their computation as minimal solutions of systems of Diophantine equations. We present the Fourier-Motzkin algorithm in detail. Afterwards, we introduce the Q-modularity as an example for a useful non-steady-state method and its application to metabolic networks. To illustrate and discuss the concepts of invariants and Q-modularity, we apply a part of the central carbon metabolism in potato tubers (Solanum tuberosum) as running example. The intention of the paper is to give a compact presentation of known steady-state concepts from a graph-theoretical viewpoint in the context of network decomposition and reduction and to introduce the application of Q-modularity to metabolic Petri net models