CAM中一类新的NP完全问题

本文提出了计算机辅助制造(CAM)中的一类作业调度问题并证明了它的NP完全性。     

MSP问题NP完全性研究

针对文献[1,2]提出的MSP问题,研究了MSP问题与着色问题、子图同构问题的对应关系,揭示了MSP问题所反映的NP完全问题的共性;分析了MSP问题的相变现象,为文献[1,2]提出的多项式时间算法框架的测试提供了难例产生方法。     

Complexity and design of QoS routing algorithms in wireless mesh networks

Quality of service (QoS) provisioning in wireless mesh networks (WMNs) is an open issue to support emerging multimedia services. In this paper, we study the problem of QoS provisioning in terms of end-to-end bandwidth allocation in WMNs. It is challenging due to interferences in the networks. We consider widely used interference models and show that except a few special cases, the problem of finding a feasible path is NP-complete under the models. We propose a k-shortest path based algorithmic framework to solve this problem. We also consider the problem of optimizing network performance by on-line dynamic routing, and adapt commonly used conventional QoS routing metrics to be used in WMNs. We find the optimal solutions for these problems through formulating them as optimization models. A model is developed to check the existence of a feasible path and another to find the optimal path for a demand; moreover, an on-line optimal QoS routing algorithm is developed. Comparing the algorithms implemented by the proposed framework with the optimization models shows that our solution can find existing feasible paths with high probability, efficiently optimizes path lengths, and has a comparable performance to the optimal QoS routing algorithm. Furthermore, our results show that contrary to wireline networks, minimizing resource consumption should be preferred over load distribution even in lightly loaded WMNs.     

Guarding a set of line segments in the plane

We consider the following problem: Given a finite set of straight line segments in the plane, find a set of points of minimum size, so that every segment contains at least one point in the set. This problem can be interpreted as looking for a minimum number of locations of policemen, guards, cameras or other sensors, that can observe a network of streets, corridors, tunnels, tubes, etc. We show that the problem is strongly NP-complete even for a set of segments with a cubic graph structure, but in P for tree structures.     

Elimination of Boolean variables for probabilistic coherence

 In this paper we deal with the computational complexity problem of checking the coherence of a partial probability assessment (called CPA). The CPA problem, like its analogous PSAT, is NP-complete so we look for an heuristic procedure to make tractable reasonable instances of the problem. Starting from the characteristic feature of de Finetti's approach (i.e. the explicit distinction between the probabilistic assessment and the logical relations among the sentences) we introduce several rules for a sequential “elimination” of Boolean variables from the domain of the assessment. The procedure resembles the well-known Davis-Putnam rules for the satisfiability, however we have, as a drawback, the introduction of constraints (among real variables) whose satisfiability must be checked. In simple examples we test the efficiency of the procedure respect to the “traditional” approach of solving a linear system with a huge coefficient matrix built from the atoms generated by the domain of the assessment.     

Solving multiple processor and multiple resource constrained scheduling problems using a genetic algorithm approach

We consider the multiprocessor scheduling of unit time tasks with precedence constraints and finite set of limited resources. Each task demands some amount of resources for its execution and the total demand for each kind of resources must not exceed a certain limit at any instant of time. Our objective is to find out the minimum time schedule which satisfies the partial orders and the resource usage constraints. We have applied Genetic Algorithm for the present problem. We have shown that the Genetic Algorithm is quite superior to the First Fit Decreasing method.     

DNA计算的原理及研究进展

阐述了DNA计算的机理及其数学原理,介绍了Adleman实验,指出了DNA计算目前的应用领域和存在的问题,并对DNA计算的发展前景进行了展望。     

图的顶点着色问题的DNA算法

图的顶点着色问题是指无向图中任意两个相邻顶点都分配到不同的颜色,这个问题是著名的NP-完全问题,没有非常有效的算法.但在1994年Adleman^[1]首次提出用DNA计算解决NP-完全问题,设计出一种全新的计算模式—模拟生物分子DNA的结构并借助于分子生物技术进行计算,使得NP-完全问题的求解可能得到解决.本文首先提出了基于分子生物技术的图的顶点着色问题的DNA算法,算法的关键是对图中的顶点和顶点的颜色进行恰当的编码,以便于使用常规的生物操作及生物酶完成解的产生及最终解的分离,依据分子生物学的实验方法,本文提出的算法是有效和可行的;其次指出了该算法的优点、存在的问题及将来进一步的研究方向.     

随机算法异步并行化的效率分析

随机算法的执行时间具有不确定性,这种不确定性为随机算法的异步并行提供了良好的基础,已有许多计算实验表明了随机算法的异步并行可以达到线性甚至超线性的加速.对于求解SAT问题的随机算法RDP,研究了异步并行效率与运行时间分布和处理器数目之间的关系.应用一种单峰分布──分段线性分布模型来模拟随机算法的运行时间分布.理论分析和计算结果均表明:当处理器数目k较小和单峰位于分布的前部时,随机算法的异步并行具有近线性加速.