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).     

Programmable and autonomous computing machine made of biomolecules.

Devices that convert information from one form into another according to a definite procedure are known as automata. One such hypothetical device is the universal Turing machine, which stimulated work leading to the development of modern computers. The Turing machine and its special cases, including finite automata, operate by scanning a data tape, whose striking analogy to information-encoding biopolymers inspired several designs for molecular DNA computers. Laboratory-scale computing using DNA and human-assisted protocols has been demonstrated, but the realization of computing devices operating autonomously on the molecular scale remains rare. Here we describe a programmable finite automaton comprising DNA and DNA-manipulating enzymes that solves computational problems autonomously. The automaton's hardware consists of a restriction nuclease and ligase, the software and input are encoded by double-stranded DNA, and programming amounts to choosing appropriate software molecules. Upon mixing solutions containing these components, the automaton processes the input molecule via a cascade of restriction, hybridization and ligation cycles, producing a detectable output molecule that encodes the automaton's final state, and thus the computational result. In our implementation 1012 automata sharing the same software run independently and in parallel on inputs (which could, in principle, be distinct) in 120 microl solution at room temperature at a combined rate of 109 transitions per second with a transition fidelity greater than 99.8%, consuming less than 10-10 W.     

DNA media storage

In 1994, University of Southern California computer scientist, Dr. Leonard Adleman solved the Hamiltonian path problem using DNA as a computational mechanism. He proved the principle that DNA computing could be used to solve computationally complex problems. Because of the limitations in discovery time, resource requirements, and sequence mismatches, DNA computing has not yet become a commonly accepted practice. However, advancements are continually being discovered that are evolving the field of DNA computing. Practical applications of DNA are not restricted to computation alone. This research presents a novel approach in which DNA could be used as a means of storing files. Through the use of multiple sequence alignment combined with intelligent heu- ristics, the most probabilistic file contents can be determined with minimal errors.     

Solid phase based DNA solution of the coloring problem

DNA computing has the potential to tackle computationally difficult problems that have real-world implications.The parallel search capabilities of DNA make it a valuable tool for approaching intractable computational problems,for which conventional computers have limited potentials.Up to now,many accomplishments have been achieved to improve its performance and increase its reliability.In this paper,the coloring problem has been solved by means of molecular biology techniques.The coloring problem is a well-known NP-complete problem.This work represents further evidence for the ability of DNA computing to solve NP-complete problems.     

DNA media storage

In 1994, University of Southern California computer scientist Dr. Leonard Adleman solved the Hamiltonian path problem using DNA as a computational mechanism. He proved the principle that DNA computing could be used to solve computationally complex problems. Because of the limitations in discovery time, resource requirements, and sequence mismatches, DNA computing has not yet become a commonly accepted practice. However, advancements are continually being discovered that are evolving the field of DNA computing. Practical applications of DNA are not restricted to computation alone. This research presents a novel approach in which DNA could be used as a means of storing files. Through the use of multiple sequence alignment combined with intelligent heuristics, the most probabilistic file contents can be determined with minimal errors.     

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．     

最大权匹配问题的闭环DNA算法

给出并证明了在DNA计算中处理实数问题的策略,即首先在误差限范围内用有理数集合代替实数集合;再取出与有理数集合一一对应的最小的整数集合.针对赋权匹配问题,给出了基于闭环DNA计算模型的赋权匹配问题算法.该算法首先按边进行三组编码并合成初始闭环DNA;再以相邻两条边为约束条件用删除实验获得所有匹配,并用电泳实验得到所有最大权匹配,最后用检测实验输出最优解.证明了算法的正确性,讨论了算法复杂度,并以一个例子说明了算法的有效性.     

Genetic algorithm in DNA computing： A solution to the maximal clique problem

Genetic algorithm is one of the possible ways tobreak the limit of brute-force method in DNA computing.Using the idea of Darwinian evolution, we introduce a geneticDNA computing algorithm to solve the maximal clique prob-lem. All the operations in the algorithm are accessible withtoday‘s molecular biotechnoiogy. Our computer simulationsshow that with this new computing algorithm, it is possible toget a solution from a very small initial data pool, avoidingenumerating all candidate solutions. For randomly generatedproblems, genetic algorithm can give correct solution withina few cycles at high probability. Although the current speedof a DNA computer is slow compared with silicon computers,our simulation indicates that the number of cycles needed inthis genetic algorithm is approximately a linear function ofthe number of vertices in the network. This may make DNAcomputers more powerfully attacking some hard computa-tional problems.     

最大独立集问题的表面计算模型

DNA计算是解决一类难于计算问题的一种新方法,最大独立集问题是一个著名的NP完全问题,最大团问题及最小覆盖问题等价于最大独立集问题。本文中,我们尝试将最大独立集转化为0-1规化问题,利用0-1规化问题的表面计算模型求解最大独立集。本文充分说明了NP-完全问题可以相互转化的性质。     

薄板弯曲问题的基本解及其在断裂力学中的应用

本文基于Betti互等定理,给出一组薄板弯曲问题的基本解;它们都是薄板基本方程的奇异解。将它们应用于薄板弯曲断裂分析时,提供了一个求应力强度因子的新途径。本文引用了Hadamard积分主值概念。最后举了一个算例。     

Linearly programmed DNA-based molecular computer operated on magnetic particle surface in test-tube

The postgenomic era has seen an emergence of new applications of DNA manipulation technologies, including DNA-based molecular computing. Surface DNA computing has already been reported in a number of studies that,however, all employ different mechanisms other than automaton functions. Here we describe a programmable DNA surface-computing device as a Turing machine-like finite automaton. The laboratory automaton is primarily composed of DNA (inputs, output-detectors, transition molecules as software), DNA manipulating enzymes and buffer system that solve artificial computational problems autonomously. When fluoresceins were labeled in the 5‘ end of (-) strand of the input molecule, direct observation of all reaction intermediates along the time scale was made so that the dynamic process of DNA computing could be conveniently visualized. The features of this study are: (i) achievement of finite automaton functions by linearly programmed DNA computer operated on magnetic particle surface and (ii)direct detection of all DNA computing intermediates by capiilary electrophoresis. Since DNA computing has the massive parallelism and feasibility for automation, this achievement sets a basis for large-scale implications of DNA computing for functional genomics in the near future.     

DNA计算技术进展

论述DNA计算技术进展。先介绍DNA计算的基本原理,论述DNA计算的特点方法和存在的问题,接着介绍DNA计算的国内外研究现状,最后指出DNA计算研究中需要解决的问题。     

一种基于禁忌搜索方法的作业车间调度

提出了一种解决作业车间调度最短完工时间问题的启发式算法．该算法中采用了变禁忌表长度策略的禁忌搜索方法．在禁忌搜索过程中利用完工时间（makespan）的一个下界作为判断一个解好坏的辅助量，由于得到该下界所需的计算量远远小于完工时间的，因此大大地减少了禁忌搜索过程的计算时间．从对一组问题基准实例的实验计算结果看，该算法在合理的计算时间内，得到了比当前没有使用转换瓶颈技术的最好的禁忌搜索算法之一的TSAB算法更好的结果．     

基于k-臂分子求解最短路径的DNA计算模型

为有效求解最短路径问题, 避免传统算法计算量大、 求解时间长的问题, 充分发挥DNA(Deoxyribo Nuclec Acid)计算的并行性在求解复杂计算问题的优势, 提出一种基于k-臂分子和粘贴计算求解最短路径问题的DNA计算模型, 阐述了顶点、边及权值的编码方案, 描述了求解最短路径的DNA算法, 经验证, 该模型对求解最短路径问题是有效的。     

一种广义分子计算模型在集合覆盖中的应用

在分子计算原理和传统计算机模型基础上,提出了一种新的基于图灵机的广义分子计算模型,又称广义图灵模型,该模型的具体实现不依赖于特定生物技术. 模型继承分子计算大存储高并行的特点,通过时空复杂度转换,在求解NP完全问题上具有通用性. 模型由一台基本图灵机、一个只写带和一条工作带及读写网络这3部分组成,其中只写带和工作带之间存在一种特殊拓扑映射. 通过数据规模为4的集合覆盖问题,证明该算法能在多项式时间内求解集合覆盖问题,验证了算法和模型的有效性.     

以JIT为目标的柔性调度作业完工期求解算法

由于高度的计算复杂性,柔性调度是NP-hard问题,采用数学规划方法很难求得最优解.智能优化算法(如遗传算法)求解此类问题的近优解的有效性和实用性已被证实.在用GA算法求解此类调度问题时,如何确定一个染色体里所包含的每一个作业的完工期是一个非常关键的问题.该文深入分析了影响作业开工、完工时间的制约因素及其之间的关系,在此基础上,提出一个以JIT为目标的柔性调度作业完工期求解算法;在Matlab平台上进行了仿真.实验结果表明,本算法在求解各作业完工期时是有效和实用的.     

最小生成树DNA算法

为了改进粘贴模型,提出了用生化实验实现求解割集的计算方法,并基于该方法给出了最小生成树DNA算法.首次将分离实验扩展为基于分离板的分离实验和基于电泳技术的分离实验,所提出的最小生成树DNA算法打破了DNA计算的计算模式——用求解割集的最小边的方法逐步产生最小生成树.用该方法求解割集利用了分离实验运算的高度并行性,最小生成树DNA算法的时间复杂度是线性的,从而降低了算法的时间复杂度.     

分子计算机的诞生与现状

介绍了计算机领域的一项最新成果———分子计算机 .分子计算机利用脱氧核糖核酸 (DNA)来进行计算 .腺嘌呤、鸟嘌呤、胞密啶、胸腺密啶 (核苷酸 )在计算中起了重要的作用 .使用限制内切酶、接合酶、转移酶、外切核酸酶、修饰酶来实现计算所需要的各种操作 .介绍了分子计算机完成的第 1个计算———解哈密顿通路问题的方法 ,用这种方法使NP完全问题在很短的时间内就得到解决