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).     

图的最小顶点覆盖问题的质粒DNA计算模型

给出了图的最小顶点覆盖问题的质粒DNA算模型及其实现算法．算法的时间复杂性是O(q),编码最小覆盖问题所需的核苷酸片段种类为n,其中n,q分别是图的规模和边数．在算法中,所用酶的种类也等于图的规模．而且,算法不需要复杂的单链DNA自身退火反应和PCR扩增．     

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.     

基于生物芯片技术的地图四着色问题的DNA算法

基于先进的生物芯片技术、多种荧光标记技术和DNA计算理论提出了解决地图四着色问题的DNA算法,通过一个实例阐述了具体的DNA操作步骤,并对生化实验进行了计算机模拟,给出了所有可行的着色方案,证明了该算法的可行性。与已有的模型相比,该模型在解的准确性、计算复杂度以及操作的自动化方面都表现出了很强的优势。     

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.     

关于图染色的算法

本文给出了图上顶点染色,边染色的算法.其中边染色算法是一个非多项式时间的精确算法,该算法是先求出所有极大匹配,然后再求极小匹配覆盖,最后得出最优边染色.顶点染色算法是一个多项式时间的近似算法,该算法的时间复杂性为O(n~3logn),空间复杂性为O(n~3)的近似算法,它是由贪吃策略得到的.对于任意的图,该算法所用的期望颜色数为「log(n 1)」.     

Modified PSO algorithm for solving planar graph coloring problem

The graph coloring is a classic NP-complete problem. Presently there is no effective method to solve this problem. Here we propose a modified particle swarm optimization （PSO） algorithm in which a disturbance factor is added to a particle swarm optimizer for improving its performance. When the current global best solution cannot be updated in a certain time period that is longer than the disturbance factor, a certain number of particles will be chosen according to probability and their velocities will be reset to force the particle swarm to get rid of local minimizers. It is found that this operation is helpful to improve the performance of particle swarm. Classic planar graph coloring problem is resolved by using modified particle swarm optimization algorithm. Numerical simulation results show that the performance＇of the modified PSO is superior to that of the classical PSO.     

解决图着色问题的膜进化算法

图着色问题是图论中比较热门的NP难问题之一。针对该问题,有许多启发式求解算法,但都存在求解的质量不高,计算时间较长等问题。近些年提出的膜进化算法,在处理NP难问题中展现出了独特的优势。基于膜进化算法框架,提出了解决图着色问题的膜进化算法,把图着色问题和膜结合,设计了复制、融合、分裂、溶解、融合分裂、禁忌搜索6种膜进化算子。这些算子在演变的过程中使膜和膜结构发生进化,从而找到更优解,最后求得解决方案。在DIMACS的40个挑战数据集上面进行了实验,与3个最新的图着色算法比较的结果表明：在保证解的质量的情况下,文中提出的膜进化算法能有效降低求解的时间,其中有58%的实例占优。     

Modified PSO algorithm for solving planar graph coloring problem

The graph coloring is a classic NP-complete problem. Presently there is no effective method to solve this problem. Here we propose a modified particle swarm optimization (PSO) algorithm in which a disturbance factor is added to a particle swarm optimizer for improving its performance. When the current global best solution cannot be updated in a certain time period that is longer than the disturbance factor, a certain number of particles will be chosen according to probability and their velocities will be reset to force the particle swarm to get rid of local minimizers. It is found that this operation is helpful to improve the performance of particle swarm. Classic planar graph coloring problem is resolved by using modified particle swarm optimization algorithm. Numerical simulation results show that the performance of the modified PSO is superior to that of the classical PSO.     

Algorithm of graph isomorphism with threedimensional DNA graph structures

ResearchonDNAcomputingwasinitializedin1994 ,whenAdleman[1] proposedamethodofsolvingasmallinstanceoftheHamiltonianPathproblembyalaboratoryexperimentinvolvingDNAmolecules .Later,Lipton[2 ] demonstratedhowalargeclassofNP completeproblemscouldbesolvedbyencodingtheprobleminDNAmolecules .Inparticular ,LiptonshowedonefamousNP problem ,theso called“satisfiability”problem (SAT)andsubsequentlytheotherNP problemscouldbeencodedandsolvedusingmolecules .TheadvantagesofDNAcomputingareitsmassivepa…     

Algorithm of graph isomorphism with three dimensional DNA graph structures

An algorithm for solving the graph isomorphism problem with 3-D DNA structures is proposed in this paper. The karmed branched junction molecules are used to code k-degree vertices. Double stranded molecules are used to code edges. Then the molecules are mixed in a tube to be ligated. The result can be detected by gel electrophoresis. The time complexity of the algorithm is O(n2), where n is the number of vertices of the graph.     

求解最短路径问题的一种改进的人工蜂群算法

针对传统算法在计算大规模路网的优化问题时所表现出来的计算时间长、存储空间大等缺点,提出了一种改进的人工蜂群算法来求解最优路径选择的方法．试验结果表明,对于有向图和无向图,该算法都具有较好的全局寻优能力,即能获得满足条件的最优路径．     

并行环境下基于图着色理论的空间数据部署

在面向计算部署到数据节点端执行的分布式并行环境下,提出一种基于图着色理论的适用于矢量空间数据的部署方法,将空间数据粒度的部署问题转化为图顶点着色的过程,提高了任意空间区域的信息查询效率.给出基于图着色理论的数据部署方法,并通过节点的任务量进一步改进算法,使得该算法可实现海量空间数据粒度的离散化部署,提高了空间数据检索和查询的并行化程度,充分利用了并行计算资源.     

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.     

一种改进的自适应蚁群算法及其应用研究

蚁群算法作为一种新型的模拟进化算法,具有分布计算和信息正反馈等优点,但蚁群算法与其他进化算法一样存在收敛速度慢,易陷于局部最优等缺陷。针对这一问题,提出一种改进的蚁群算法,结合遗传算法和图论中的最邻近算法,并自适应地初始化信息素和限定信息素的大小范围。将该算法应用于旅行商问题(traveling salesman problem,TSP)求解,与基本蚁群算法比较,数值实验结果表明,这种改进算法能有效抑制算法陷入局部最优的缺陷,从而提高了解的全局搜索能力和解的质量。     

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.     

图着色问题的逆序蚁群算法研究

针对经典的图着色问题,依据传统图着色算法中逆序图着色的着色思想,结合蚁群算法的搜索机制,给出了逆序蚁群着色算法.根据着色进度和未着色点的相邻点度数随机动态逆序选择新的着色点,使得算法具有较强的搜索全局最优解的能力.利用计算机生产大量随机图作为测试实例,对比逆序着色算法和逆序蚁群算法,实验结果说明逆序蚁群着色算法提高了求解质量,加快了收敛速度,证明了其优良特性.同时算法效率的提高,也保证了该算法可适用于较大规模的着色问题求解.此外,还进行了一系列对比试验,得出了关键参数的合理取值范围.     

分组遗传算法用于图的着色

图的着色算法是一种典型的NP 完全问题 在系统地讨论了图的正常顶点着色、边着色以及全着色的有关理论的基础上 ,提出了基于分组遗传算法和启发式搜索的图的正常 k 点着色 ,正常k 边着色以及正常k 全着色的新型混合算法 ,提出了评价算法性能的标准 实验仿真结果表明 ,新型混合算法可以获得问题高质量的解 ,即对图进行着色所使用的颜色数接近图的色数     

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.     

基于遗传和启发式算法的混合顶点着色算法

图的着色问题是一种典型的NP-完全问题.提出了基于遗传算法和启发式算法的新型混合顶点着色算法,该算法在实现过程中涉及到染色体的编码方法、适应度函数的设计以及遗传算子的选择等.实验仿真结果表明此算法改善了求解的时间复杂度,可以获得问题高质量的解.