基于DNA自组装模型解决图的最小顶点覆盖问题

在分析最小顶点覆盖问题特点的基础上,以5个顶点的图为例,将最小顶点覆盖问题转化为可满足性问题,简化问题的操作难度。再根据DNA自组装的自发性和并行性等优势,通过建立DNA自组装模型解决可满足性问题,从而解决图的最小顶点覆盖问题。相对于传统算法,本算法只应用了凝胶电泳技术,大大的降低了操作难度和误差。     

最小基数箱子覆盖问题

最小基数箱子覆盖问题,是在物件大小满足一定的条件下的装箱问题．给出了一个时间复杂度为O（n）的启发式算法．     

若干NP完全问题的特殊情形

讨论了图算法中若干ＮＰ完全问题在所给的图是一棵树时的特殊情形－ 利用树结构的前序编号表示法提出了解树的最大独立集问题、最小顶点覆盖问题和最小支配集问题的线性时间算法－在渐近意义下这些算法都是最优算法     

广义Petersen图的最小点覆盖集

点覆盖问题是一个著名的NP完全问题.本文对广义Petersen图P(n,2)的精确最小点覆盖数进行研究,讨论并证明了广义Petersen图P(n,2)的最小点覆盖数,给出了最小点覆盖集的构造方法.     

DNA计算在图论中的应用

介绍了DNA计算在图论中应用的一些结果.如中国邮递员问题的DNA计算模型;0-1规划的DNA计算模型最大团问题;图着色问题和最小覆盖问题的表面DNA计算模型等.     

区间图上的并行算法设计

对区间图上的图问题并行求解,给出两种算法设计方法.利用这两种方法,对最小团覆盖、最大团、最大独立集、最小支配集、Hamiltonian 回路、最佳道路覆盖、最小带宽和Steiner 树的计算问题, 在EREW PRAM 模型上给出O(logn) 时间,使用O(n) 处理器的高效并行算法.     

区间图上的并行算法设计

对区间图上的图问题并行求解,给出两种算法设计方法,利用这两种方法,对最小团覆盖,最大团,最大独立集,最小支配集,Hamiltonian回路,最佳道路覆盖,最小带宽和Steiner树的计算问题,在EREW PRAM模型上给出O(logn)时间,使用O（n)处理器的高效并行算法。     

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．     

外部平面图的L(p,q)-标号

对于正整数p,q,n与图G,如果函数φ:V(G)→｛0,1,2, ,n｝满足如下关系:若distG(u,v)=1,则|φ(u)-φ(v)|≥p;若distG(u,v)=2则|φ(u)-φ(v)|≥q,那么称函数φ为图G的L(p,q) 标号.在所有L(p,q) 标号中最小的n称为(p,q) 跨度,记作λ(G;p,q).本文证明了如下结论:设图G是一个最大度为Δ的外部平面图,那么λ(G;p,q)≤qΔ+4p+2q-4.     

DNA计算在电路设计中的应用

讨论了DNA计算的机理,给出了DNA计算的基本生化实验.对电路布线问题,提出了DNA算法,即首先对导线的顺序进行DNA编码,其次通过杂交反应产生所有可行解,最后通过电泳实验得到最优解.对所得结果进行检测时采用了DNA芯片和分子信标技术,对探针进行生物素标记解读出最优解.该算法的核心运算是杂交反应,算法总的操作次数为n 3,其中n为电路布线问题的规模.最后,通过6对接线柱的例子说明了DNA算法的有效性和正确性.     

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).     

Sticker DNA computer model ——PartⅡ: Application

Sticker model is one of the basic models in the DNA computer models. This model is coded with sin-gle-double stranded DNA molecules. It has the following advantages that the operations require no strands extension and use no enzymes; What抯 more, the materials are reusable. Therefore, it arouses attention and interest of scientists in many fields. In this paper, we extend and improve the sticker model, which will be definitely beneficial to the construction of DNA computer. This paper is the second part of our series paper, which mainly focuses on the application of sticker model. It mainly consists of the following three sections: the matrix representation of sticker model is first presented; then a brief review of the past research on graph and com-binatorial optimization, such as the minimal set covering problem, the vertex covering problem, Hamiltonian path or cycle problem, the maximal clique problem, the maximal independent problem and the Steiner spanning tree problem, is described; Finally a DNA algorithm for the graph iso-morphic problem based on the sticker model is given.     

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DNA粘贴模型求解最小集合覆盖问题

运用DNA计算模式中基于粘贴运算的粘贴模型求解最小集合覆盖问题.在粘贴模型中,用存储复合体来表示子集,并利用粘贴运算的巨大并行性,可以有效地求解最小集合覆盖问题.举例说明了基于DNA粘贴模型求解最小集合覆盖问题的过程.     

An Efficient Algorithm for Discovering Co-occurrence Concepts Through Pathfinder Paradigm

The Pathfinder paradigm has been used in generating and analyzing graph models that support clustering similar concepts and minimum-cost paths to provide an associative network structure within a domain. The co-occurrence pathfinder network （ CPFN ） extends the traditional pathfinder paradigm so that co-occurring concepts can be calculated at each sampling time. Existing algorithms take O（n（s）） time to calculate the pathfinder network （PFN） at each sampling time for a non-completed input graph of a CPFN （r = ∞, q = n - 1）, where n is the number of nodes in the input graph, r is the Minkowski exponent and q is the maximum number of links considered in finding a minimum cost path between vertices. To reduce the complexity of calculating the CPFN, we propose a greedy based algorithm, MEC（G） algorithm, which takes shortcuts to avoid unnecessary steps in the existing algorithms, to correctly calculate a CPFN （r = ∞, q= n - 1） in O（klogk） time where k is the number of edges of the input graph. Our example demonstrates the efficiency and correctness of the proposed MEC（G） algorithm, confirming our mathematic analysis on this algorithm.     

具有给定分支数森林的最小能量图

将图G的能量E(G)定义为图G的特征多项式所有特征根的绝对值之和.F_n,q是顶点个数为n,分支个数为q的森林的集合. 对于给定的n和q,给出F_n,q中具有最小能量的图.     

集合覆盖问题降阶算法

集合覆盖问题是运筹学与计算机科学中的一个NP难题.首先将该问题转化为一个等价的二分图,给出该问题的上下界算法;接着给出该问题的数学性质,这些数学性质能降低问题的规模,加快算法的求解速度;然后将数学性质和上下界方法结合起来形成一个降阶算法,并给出了算法的时间复杂度分析.该算法不仅可以单独使用,还可以与其它算法结合起来使用达到更好的效果.最后通过多个示例进一步说明算法的原理及应用情况.     

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.