微电子学、集成电路

TN4,0224 2004060525图的最大权团的D NA计算/马润年,(2}张强,(4}高琳,(3}许进(空军工程大学)11电子学报一2004,32(1)一13一16给定顶点赋权的无向图,图的最大权团问题是寻找每个顶点都相邻的顶点子集(团)具有最大权.这个问题是寻找无权图的最大团问题的推广.图的最大团和最大权团都是著名的NP一完全问题,没有非常有效的算法.1994年Adieman博士首先提出用DNA计算解决NP一完全问题,使得NP一完全问题的求解可能得到解决.文中给出了基于质粒技术的无向图的最大权团问题的DNA算法,依据HeadT等的实验手段,文中提出的算法是有效并且可行的.…     

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.     

基于恒等子图搜索的点模式匹配算法

点模式匹配问题是计算机视觉和模式识别领域中的一个重要课题,但由于噪声、视场等因素始终难以完全解决.通过构建点模式关系图,把点模式匹配问题转化为关系图最大恒等子图搜索问题,由此给出图、子图、图同构和恒等、支持顶点对及支持顶点对集的概念并对它们满足的一些性质和定理进行了证明,最后提出了一种对最大恒等子图搜索的有效算法,在对...     

基于最小点覆盖和反馈点集的社交网络影响最大化算法

社交网络中的影响最大化问题是指在特定的传播模型下,如何寻找k个最具影响力的节点使得在该模型下社交网络中被影响的节点最多,信息传播的范围最广。该问题是一个优化问题,并且已经被证明是NP-难的。考虑到图的最小点覆盖和反馈点集中的顶点对图的连通性影响较大,该文提出一种基于最小点覆盖和反馈点集的社交网络影响最大化算法(Minimum Vertex Covering and Feedback Vertex Set, MVCFVS),并给出了具体的仿真实验和分析。实验结果表明,与最新的算法比较,该算法得到的节点集在多种模型下都具有优异的传播效果,例如在独立级联模型和加权级联模型中超过当前最好的算法,并且还具有更快的收敛速度。     

一种改进的分布式最大权独立集算法

能快速准确寻找给定图中的最大权独立集的分布式算法,对于解决无线网络中的资源调配、无线骨干网构建等问题具有非常重要的指导意义。该文以基于最大乘信用传播的分布式算法为框架,假设所有节点了解自己邻居节点之间的局部拓扑信息,启发式地提出一种新的相邻节点间交换消息的计算方法以及相应的分布式最大权独立集算法。仿真结果表明,所提算法摆脱了文献中已有算法对图结构必须是树或者二分图的要求,且权和性能优于已有的分布式算法。     

一种基于极大完全子图的最大频繁项集并行挖掘算法

提出一种基于极大完全子图的最大频繁项集并行挖掘算法PMFIM,通过遍历由频繁2-项集构成的用邻-接矩阵表示的图,寻找图的极大完全子图,从而由极大完全子图顶点序列实现对项集的划分,即挖掘子任务的划分.在同类算法中,将找到的最大频繁项划分为局部最大频繁项集LMFI、可能最大频繁项集PMFI和邻接项集的最大频繁项集的超集SMFI,减少了该类算法合并最大频繁项集的开销,并对算法进行了实现和优化.     

一种新的最短路径并行算法

针对两点间最短路径问题,提出一种新的并行求解算法.该算法通过不断消去中间的节点和边以简化图的结构,以局部最优而达到全局最优.相对于经典的串行Dijkstra算法,天然地具有并行特性,对稀疏图更加有效,算法复杂度较低.仿真结果证明:该算法对于任意类型的无向图或有向图,总是可准确求得其最短路径.     

图3-着色问题的O链数DNA计算机算法

随着DNA计算的不断发展,如何克服穷举算法带来的指数爆炸问题已成为DNA计算领域的重要研究目标之一.为减少图3-着色问题DNA计算机算法中的DNA链数,本文将Adleman-Lipton模型生物操作与粘贴模型解空间相结合的DNA计算模型进行扩展,通过设计顶点着色器、稀疏图/稠密图搜索器,提出一种用于求解图3-着色问题的DNA计算模型与算法.将本算法与同类算法对比分析表明:本算法在保持多项式操作时间的条件下,将求解n个顶点的图3-着色问题所需DNA分子链数从O(3ⁿ)减少至O(2ⁿ),改进了3-着色问题同类文献的研究结果.     

多用户对双向中继网络的中继和用户选择策略

通过对多用户对多个可选中继组成的双向中继网络进行权重二部图建模,并利用信道状态信息合理设计权重,从而将以最大化系统总速率为目标的中继和用户对选择策略问题等效为权重二部图的最大权匹配问题。利用图论最大权匹配算法（匈牙利算法）,提出了最大权匹配选择策略。并进一步同时基于最大权匹配算法和用户对公平性,提出了最大权匹配轮询策略和基于数据序列因子的最大权匹配策略。仿真结果证明,3种策略均提升了系统性能。     

基于FPGA的图着色问题求解

图着色问题是在满足相邻顶点不能分配相同颜色且颜色数最少的约束条件下,将图的顶点划分为不相交的集合,且每个集合中的顶点分配相同的颜色。由于图着色问题属于NP-完全问题,求解图着色问题的算法复杂度会随顶点个数的增加呈指数级增长。当顶点个数非常大时,通用处理器求解图着色问题的性能将会显著下降。因此,该文基于现场可编程逻辑门阵列(FPGA)实现求解图着色算法的专用硬件加速器。首先依据FPGA模块化的设计思路提出并实现了基于回溯法的图着色问题求解的硬件架构;其次分析了FPGA内部消耗资源与图着色顶点数之间的关系;最后利用通用异步收发传输器协议实现了通用处理器与FPGA的通信。实验结果表明,相比于在通用处理器上利用软件实现图着色算法,基于FPGA所实现的图着色算法运行时间减少了一个数量级。除此之外,FPGA内部消耗资源数与顶点个数呈线性关系,且每次迭代时FPGA运算所消耗的时间与顶点个数无关。     

Decomposition Algorithms for Solving NP-hard Problems on a Quantum Annealer

NP-hard problems such as the maximum clique or minimum vertex cover problems, two of Karp’s 21 NP-hard problems, have several applications in computational chemistry, biochemistry and computer network security. Adiabatic quantum annealers can search for the optimum value of such NP-hard optimization problems, given the problem can be embedded on their hardware. However, this is often not possible due to certain limitations of the hardware connectivity structure of the annealer. This paper studies a general framework for a decomposition algorithm for NP-hard graph problems aiming to identify an optimal set of vertices. Our generic algorithm allows us to recursively divide an instance until the generated subproblems can be embedded on the quantum annealer hardware and subsequently solved. The framework is applied to the maximum clique and minimum vertex cover problems, and we propose several pruning and reduction techniques to speed up the recursive decomposition. The performance of both algorithms is assessed in a detailed simulation study.

     

The Maximum Throughput of A Wireless Multi-Hop Path

In this paper, the maximum end-to-end throughput that can be achieved on a wireless multi-hop path is investigated analytically. The problem is modeled using the conflict graph, where each link in the multi-hop path is represented uniquely by a vertex in the conflict graph and two vertices are adjacent if and only if the associated links mutually interfere. Using the conflict graph and the linear programming formulations of the problem, we analyzed the maximum end-to-end throughput of a wireless multi-hop path a) in a simple scenario where nodes are optimally placed and each node can only interfere with the transmission of its adjacent nodes along the path, and b) in a more complicated scenario where nodes are randomly placed and each node can interfere with the transmission of any number of nearby nodes along the path in both a) an error free radio environment and b) an erroneous radio environment. The maximum end-to-end throughputs for each of the above four scenarios are obtained analytically. We show that the maximum achievable end-to-end throughput is determined by the throughput of its bottleneck clique, where a clique is a maximal set of mutually adjacent vertices in the associated conflict graph. Further our analysis suggests the optimum scheduling algorithm that can be used to achieve the maximum end-to-end throughput and that it is convenient to use the (maximal) independent sets as the basic blocks for the design of scheduling algorithms. The findings in this paper lay guidelines for the design of optimum scheduling algorithms. They can be used to design computationally efficient algorithms to determine the maximum throughput of a wireless multi-hop path and to design a scheduling algorithm to achieve that throughput.     

Finding Maximum Cliques on the D-Wave Quantum Annealer

This paper assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.

     

The forwarding index of communication networks

A network is defined as an undirected graph and a routing which consists of a collection of simple paths connecting every pair of vertices in the graph. The forwarding index of a network is the maximum number of paths passing through any vertex in the graph. Thus it corresponds to the maximum amount of forwarding done by any node in a communication network with a fixed routing. For a given number of vertices, each having a given degree constraint, we consider the problem of finding networks that minimize the forwarding index. Forwarding indexes are calculated' for cube networks and generalized de Bruijn networks. General bounds are derived which show that de Bruijn networks are asymptotically optimal. Finally, efficient techniques for building large networks with small forwarding indexes out of given component networks are presented and analyzed.     

On a new class of codes for identifying vertices in graphs

We investigate a new class of codes for the optimal covering of vertices in an undirected graph G such that any vertex in G can be uniquely identified by examining the vertices that cover it. We define a ball of radius t centered on a vertex υ to be the set of vertices in G that are at distance at most t from υ. The vertex υ is then said to cover itself and every other vertex in the ball with center υ. Our formal problem statement is as follows: given an undirected graph G and an integer t⩾1, find a (minimal) set C of vertices such that every vertex in G belongs to a unique set of balls of radius t centered at the vertices in C. The set of vertices thus obtained constitutes a code for vertex identification. We first develop topology-independent bounds on the size of C. We then develop methods for constructing C for several specific topologies such as binary cubes, nonbinary cubes, and trees. We also describe the identification of sets of vertices using covering codes that uniquely identify single vertices. We develop methods for constructing optimal topologies that yield identifying codes with a minimum number of codewords. Finally, we describe an application of the theory developed in this paper to fault diagnosis of multiprocessor systems     

Algorithmic Aspects of Topology Control Problems for Ad Hoc Networks

Topology control problems are concerned with the assignment of power values to the nodes of an ad hoc network so that the power assignment leads to a graph topology satisfying some specified properties. This paper considers such problems under several optimization objectives, including minimizing the maximum power and minimizing the total power. A general approach leading to a polynomial algorithm is presented for minimizing maximum power for a class of graph properties called monotone properties. The difficulty of generalizing the approach to properties that are not monotone is discussed. Problems involving the minimization of total power are known to be NP-complete even for simple graph properties. A general approach that leads to an approximation algorithm for minimizing the total power for some monotone properties is presented. Using this approach, a new approximation algorithm for the problem of minimizing the total power for obtaining a 2-node-connected graph is developed. It is shown that this algorithm provides a constant performance guarantee. Experimental results from an implementation of the approximation algorithm are also presented.     

一种计算Ad hoc网络K-终端可靠性的线性时间算法

研究计算Ad hoe网络K-终端可靠性的线性时间算法,可以快速计算Ad hoe网络K-终端可靠性。为了计算Ad hoe网络分级结构尽终端可靠性,可以采用无向概率图表示Ad hoe网络的分级结构。每个簇头由已知失效率的结点表示,并且当且仅当两个簇相邻时,两个结点间的互连由边表示。这个概率图的链路完全可靠,并且已知结点的失效率。此图的K-终端可靠性为给定K-结点集是互连的概率。文中提出了基于合适区间图计算尽终端可靠性的一种线性时间算法。本算法可用来计算Ad hoe网络的K-终端可靠性。其时间复杂度为O（｜V｜＋｜E｜）。     

Generation of K-Trees of undirected graphs

Evaluating the reliability of a network with multiple sources and multiple terminals and unreliable vertices and edges can be converted into a single-source problem and solved using K-Trees. This paper presents an efficient algorithm (GenK-Trees) for enumerating all the K-Trees in an undirected graph. This is the first algorithm with polynomial complexity per K-Tree generated. Formal proofs of the correctness of GenK-Trees and its complexity are given. GenK-Trees is computationally simple, and easy to understand and program; its memory requirements are small, and so it can handle large graphs without running into memory limitations