最短路径问题的DNA算法

最短路径问题是在一个带权图的两个顶点之间找出一条具有最小权和路径的问题,它是图论中一个经典的NP完全问题,用电子计算机需要指数级的时间内才能得到解决,本文基于分子生物技术并利用Adleman-Lipton模型给出最短路径问题的DNA算法,这个DNA算法理论上能在多项式的时间内解决这个NP完全问题。具体地对个城市的最短路径问题,首先将它视为一个具有顶点和边的图,并将顶点,边分别用DNA链编码表示,边的方向通过顶点的编码获得;再将这些DNA链投放在试管中进行生物化学反应,利用DNA计算的高效并行性,通过基本的生物实验操作最后得到最短路径问题的解,其过程的复杂度为O(n)。该算法的创新之处在于表示城市和路径的DNA链长度的设计以及在操作中巧妙的消除了路径途经城市数目不同的影响,能使我们在合理小的范围内寻找最短路径问题的解,较大地简化了问题的复杂度。     

DNA计算原理与发展

DNA计算是一种摸拟生物分子DNA的结构并借助分子生物技术进行计算的新方法,为NP完全问题的解决提供了一种全新的途径,具有广阔的应用前景。本文首先介绍了DNA计算的基本思想;然后综述了DNA算例及其模型;指出了DNA计算的应用及目前存在的问题;最后对DNA计算的发展前景进行展望。     

QoS路由技术的新方法

多约束QoS路由问题是NP完全问题，一般采用启发式算法求解。量子遗传算法和DNA计算技术是新型的软计算方法．是解决NP完全问题的有效途径。文章在介绍量子遗传算法和DNA计算基本原理的基础上．给出了利用量子遗传算法求解多约束QoS路由问题的算法过程以及利用DNA计算技术解决QoS路由问题的算法模型，为多约束QoS路由技术的求解提供了新方法和新思路。     

DNA计算中编码问题的研究

编码是DNA计算的开始,对DNA计算尤为的重要。编码的好坏直接影响计算反应过程的质量。本文简要描述了DNA编码的理论,总结了编码的约束条件和几个模型的DNA序列的设计。最后,指出了编码问题的研究方向。     

图的k着色问题的DNA计算模型

DNA计算是一种新的并行计算模式,在解决NP完全问题等方面具有很大的优越性．利用DNA计算的计算特性给出了一个图的k着色问题的DNA计算模型,该算法最多需要3kn（n-1）/2＋6个生物操作即可求出图的色数及相应的着色模式．     

三维DNA自组装在多维背包问题中的应用研究

利用DNA自组装执行计算的思想已从实验上被证明了其可行性．已有多种理论模型被提出用以解决各种NP问题．基于DNA Tile自组装模型理论在二维下的扩展,本文设计了可以实现这一算法的三维DNA Tile组装系统,提出了一种用于解决多维背包问题的三维DNA自组装模型．该模型可以非确定性的输出可行性解决方案．分析表明系统可以在线性组装步骤内完成计算,所需的Tile种类数与问题维数无关．为探索三维DNA自组装的计算能力进行了一次有意义的尝试．     

最大团问题的三链DNA计算模型

本文研究利用三链DNA求解最大团问题。首先将最大团问题中的顶点编码为DNA片段,进行生化反应,组合成所有可能的情况,然后利用三链模型对解进行筛选,最终得到图的最大团。该模型降低了编码的复杂度,提高了检测效率,其他的NP(Non-deterministic Polynomial)问题也可用此方法来求解。     

背包问题的三链DNA计算模型

背包问题是组合优化中很重要的NP问题。因为三链DNA的特殊结构在参与反应时可以减少计算模型的错解率,且在生化反应中利用磁珠分离法对解进行分离较方便准确,文章利用三链模型求解0-1背包问题和完全背包问题。首先将背包问题的约束条件进行分解,再将物品质量编码为DNA片段,链接反应后,利用凝胶电泳技术和三链模型检测所包含的物品组合,得到满足约束条件的物品组合,再利用此方法检测价值最大的组合,即问题的解。其他的背包问题也可用此方法来解决。     

基于DNA链置换的可满足性问题的计算模型

可满足性问题是经典的NP完全问题之一。本文建立了一个基于DNA链置换的可满足性问题的计算模型,可满足性问题的约束条件被映射成计算模型上的荧光个数,将可满足性问题中变量的两种取值(0和1)分别设计成不同的DNA链,通过DNA链置换反应,最后观察反应后的计算模型上荧光个数找出可满足性问题的可行解。该模型具有操作简单,结果便于观察和检测的优点。     

最大匹配问题的DNA试管计算模型

最大匹配问题是找给定图G中任意两条边都没有公共端点的最大边集,是NP完全问题.算法的关键是将数学问题转换到DNA链上,对图中的每条边进行适当的编码,利用生物操作及生物酶产生链及最终链的分离.给出了基于分子生物技术的图的匹配问题的DNA计算的试管方式.结果表明,提出的算法是有效可行的.     

New field of cryptography： DNA cryptography

The vast parallelism, exceptional energy efficiency and extraordinary information density inherent in DNA molecules are being explored for computing, data stor- age and cryptography. In such research area, novel computers, data storage and cryptography mi…     

DNA计算及DNA计算机的研究进展

概述了DNA计算的基本原理、DNA计算的应用和DNA计算机的研究进展及存在问题，基于DNA生化反应的计算机称为DNA计算机，由于其采用一种完全不同于传统计算机的运算逻辑与存贮方式，DNA计算机在解决某些复杂问题时具有传统计算机无法比拟的优势，目前国际上关于DNA计算和DNA分子生物计算机的研究方兴未艾，极大地推进了DNA计算机的研究过程。     

A molecular cryptography model based on structures of DNA self-assembly

With the progress of DNA computing, DNA- based cryptography becomes an emerging interdisciplinary research field. In this paper, we present a novel DNA cryptography that takes advantage of DNA self assembled structure. Making use of the toehold strands recognition and strand displacement, the bit-wise exclusive-or （XOR） operation is carried out to fulfill the information encryption and decryption in the form of a one-time-pad. The security of this system mainly comes from the physical isolation and specificity of DNA molecules. The system is con- structed by using complex DNA self-assembly, in which technique of fluorescent detection is utilized to implement the signal processing. In the proposed DNA cryptography, the XOR operation at each bit is carried out individually, thus the encryption and decryption process could be con- ducted in a massive, parallel way. This work may dem- onstrate that DNA cryptography has the great potential applications in the field of inRwmation security.     

A surface-based DNA algorithm for the minimal vertex cover problem

Abstract DNA computing was proposed for solving a class of intractable computational problems, of which the computing timewill grow exponentially with the problem size. Up to now, many achievements have been made to improve its performance and increase itsreliability. It has been shown many times that the surface-based DNA computing technique has very low error rate, but the technique hasnot been widely used in the DNA computing algorithms design. In this paper, a surface-based DNA computing algorithm for minimal ver-tex cover problem, a problem well-known for its exponential difficulty, is introduced. This work provides further evidence for the abilityof surface-based DNA computing in solving NP-complete problems.     

A new DNA algorithm to solve graph coloring problem

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).     

A new DNA algorithm to solve graph coloring problem

Using a small quantity of DNA molecules and little experimental time to solve complex problems successfully is a goal of DNA computing. Some NP-hard problems have been solved by DNA computing with lower time complexity than conventional computing. However, this advantage often brings higher space complexity and needs a large number of DNA encoding molecules. One example is graph coloring problem. Current DNA algorithms need exponentially increasing DNA encoding strands with the growing of problem size. Here we propose a new DNA algorithm of graph coloring problem based on the proof of four-color theorem. This algorithm has good properties of needing a relatively small number of operations in polynomial time and needing a small number of DNA encoding molecules (we need only 6R DNA encoding molecules if the number of regions in a graph is R).     

DNA计算研究的新进展

DNA计算(DNA computing)是伴随着分子生物学的兴起和发展而出现的．作为一种全新的算法，DNA计算显示了其进行复杂运算的可行性．该文介绍DNA计算的机理，探讨了目前DNA计算的研究进展，并介绍了表面固定的生物计算和由输入DNA分子同时提供数据和燃料的生物分子自动机．     

A novel DNA computing model based on RecA-mediated triple-stranded DNA structure

The field of DNA computing emerged in 1994 after Adleman’s paper was published. Henceforth,a few scholars solved some noted NP-complete problems in this way. And all these methods of DNA computing are based on conventional Watson-Crick hydrogen bond of doublehelical DNA molecule. In this paper, we show that the triple-stranded DNA structure mediated by RecA protein can be used for solving computational problems. Sequence-specific recognition of double-stranded DNA by oligonucleotide-directed triple helix (triplex) formation is used to carry out the algorithm. We present procedure for the 3-vertex-colorability problems. In our proposed procedure, it is suggested that it is possible to solve more complicated problems with more variables by this model.