二部图的所有极大匹配

二部图作为一种非常重要的数据结构有很多特殊性质,针对文献[4]中的二部图的所有极大匹配求解算法,给出了反例证明了该算法是错误的,同时证明了二部图的所有极大匹配的求解是NP难问题.     

基于极大极小准则的Hopfield联想记忆学习算法*

基于联想记忆各记忆模式的吸引域之间应保持大小平衡的思想．提出了设计Hopfield联想记忆网络的极大极小准则,即设计出的对称连接权阵应使得网络最小的记忆模式吸引域达到最大．首先提出了一种快速学习算法;再发展了一个启发性迭代学习算法,称为约束感知器优化学习算法．大量实验结果表明了本文学习算法的优越性．     

二部图所有极大匹配的求解算法

二部图是一种十分重要的数据结构。在对二部图及匹配的概念进行了阐述后。给出了求二部图所有极大匹配的算法。该算法也可用于求二部图的所有最大匹配和完全匹配。用C语言程序验证了此算法的有效性。     

极大限制边连通网络的充分条件

限制边连通度是度量网络可靠性的重要参数。设[G]是一个边集为[E]的连通网络。称一个边集合[S?E]是一个限制边割,如果[G-S]是不连通的且每个分支至少有两个顶点。网络[G]的限制边连通度,记为[λ'],定义为[G]的最小限制边割的基数。设[d(v)]表示顶点[v]的度,[ξ=min{d(u)+d(v)-2:uv∈E}]表示[G]的最小边度。称网络[G]是极大限制边连通的,如果[λ'=ξ]。给出了网络是极大限制边连通的一些充分条件。     

基于二分图极大权值匹配的SOC故障定位算法研究*

针对故障传播给故障定位带来的影响,考虑SOC功能测试系统中的故障源和故障事件之间的不确定性,提出一种基于二分图的故障定位算法。首先从SOC中抽象出特定的硬件模块,由这些模块构成故障源。然后故障源结合相应的故障事件组合成二分图,在二分图的基础上生成一种适用于SOC故障定位的故障传播模型(Fault Propagation Model,FPM)。最后将SOC故障定位的问题转化成二分图极大权值匹配的求解问题,从概率上保证结果的正确性。实验结果表明,故障定位准确率提高了0~21%,误报率下降了0~15%,更加适用于小型系统的故障定位。     

无向图在计算机绘图中的应用

本文把笔式绘图仪绘图过程时间最少的调度问题转换为在加权无向图中求解最优H-回路,并且利用最小生成树、欧拉回路、非二部图赋权匹配的算法给出了一种近似调度算法,旨在减少绘图仪移动空走时间和换笔时间,从而提高绘图效率。本算法经RP-MF160等绘图仪应用,效率提高约15%。     

并行程序的流程图分析法*

本文给出一种对Ada并行程序的流程图分析法．该方法不仅给出在并行程序中,并发多任务之间相互通信的一种可视化的表示,同时可检查出并行程序中存在的死锁,并能启发如何消除死锁．并行流程图在检查死锁的方便性、消除死锁的启发性、实际应用的可行性和对并行算法思想的描述性等方面明显优于已知的Petri网分析法。     

无存储器冲突的并行快速排序算法*

本文在一个EREW PRAM(exclusive read exclusive write paralled random accessmachine)上提出一个并行快速排序算法,这个算法用k个处理器可将n个项目在平均O((n/k+logn)logn)时间内排序．所以平均来说算法的时间和处理器数量的乘积对任何k≤n/logn是O(nlogn)．     

基于边映射表连接的匹配算法

针对面向语义网络图匹配的特殊性, 在基于状态回溯搜索算法的基础上提出一种新的称为基于边映射表连接的匹配算法, 利用语义网络图的有向性, 将图匹配问题转换为对搜索路径的规划, 并采用深度优先算法形成搜索步, 同时对目标图的所有边建立索引, 加快以边匹配为中心形成边映射表的过程, 最后对边映射表进行连接形成结果集。在真实数据集上的实验结果表明, 该算法具有较高的执行效率。     

混合图在无向图割集生成中的应用

为了进一步提高生成无向图割集的递归收缩算法的执行效率,将无向图转换为一类特殊的混合图,并将转换结果代替无向图输入递归收缩算法进行处理,修改了递归收缩算法中相应的算法步骤,使得改进算法可以更高效地生成无向图的割集.在理论上论证了改进算法的正确性,并通过理论分析和实验比较了改进算法和现有算法的时间复杂度和空间复杂度.理论分析结果和实验比较结果均表明改进算法明显比现有算法高效.     

高效异步并行图算法及ADA的实现

本文给出了计算图的所有顶点间的距离矩阵Ｄ及最短路径矩阵Ｐ的一串行和异步并行算法．利用上述结果,又得到其他图论问题的高效异步并行算法,并介绍了用ＡＤＡ语言对异步并行算法实现的主要步骤．     

Parallel strong orientation of an undirected graph

A dominating set of an undirected graph G is a set D of nodes such that every node of G either is in D or is adjacent to some node of D. It is shown that the problem of finding a minimum cardinality dominating set is NP-complete for split graphs (a subclass of chordal graphs) and bipartite graphs.     

Finding the k Shortest Paths in Parallel

A concurrent-read exclusive-write PRAM algorithm is developed to find the k shortest paths between pairs of vertices in an edge-weighted directed graph. Repetitions of vertices along the paths are allowed. The algorithm computes an implicit representation of the k shortest paths to a given destination vertex from every vertex of a graph with n vertices and m edges, using O(m+nk log ² k) work and O( log^3k log ^*k+ log n( log log k+ log ^*n)) time, assuming that a shortest path tree rooted at the destination is pre-computed. The paths themselves can be extracted from the implicit representation in O( log k + log n) time, and O(n log n +L) work, where L is the total length of the output. Received July 2, 1997; revised June 18, 1998.     

An adjustable linear time parallel algorithm for maximum weight bipartite matching

We present a parallel algorithm for finding a maximum weight matching in general bipartite graphs with an adjustable time complexity of using O(nmax(2ω,4+ω)) processing elements for ω?1. Parameter ω is not bounded. This is the fastest known strongly polynomial parallel algorithm to solve this problem. This is also the first adjustable parallel algorithm for the maximum weight bipartite matching problem in which the execution time can be reduced by an unbounded factor. We also present a general approach for finding efficient parallel algorithms for the maximum matching problem.     

Parallel coloring of graphs: two approximate algorithms

Graph coloring is an abstraction of scheduling problems. Using an exclusive-read and exclusive-write (EREW) parallel random access machine (PRAM) model, two approximate coloring algorithms are parallelized. The performance analysis reveals that the parallel largest-degree-first algorithm is efficient for regular or near-regular graphs; while the second, a costlier but more easily parallelizable algorithm, yields optimal speedup for graphs of widely varying densities.     

Efficient parallel term matching and anti-unification

In this paper we present optimal processor x time parallel algorithms for term matching and anti-unification of terms represented as trees. Term matching is the special case of unification in which one of the terms is restricted to contain no variables. It has wide applicability to logic programming, term rewriting systems and symbolic pattern matching. Anti-unification is the dual problem of unification in which one computes the most specific generalization of two terms. It has application to inductive inference and theorem proving. Our algorithms run in O(log² N) time using N/log² N processors on a shared-memory model of computation that prohibits simultaneous reads or writes (EREW PRAM). These algorithms are the first polylogarithmic-time EREW algorithms with a processor x time product of the same order as that of their sequential counterparts, thereby permitting optimal speed-ups using any number of processors up to N/log² N. We also use the techniques developed in the paper to provide an N/log N-processor, O(log N)-time algorithm for a shared-memory model that allows both simultaneous reads and simultaneous writes (CRCW PRAM).Supported by NSF Grant IRI-88-09324 and NSF/DARPA Grant CCR-8908092.     

Hardness and approximation of minimum maximal matchings

In this paper, we consider the minimum maximal matching problem in some classes of graphs such as regular graphs. We show that the minimum maximal matching problem is NP-hard even in regular bipartite graphs, and a polynomial time exact algorithm is given for almost complete regular bipartite graphs. From the approximation point of view, it is well known that any maximal matching guarantees the approximation ratio of 2 but surprisingly very few improvements have been obtained. In this paper we give improved approximation ratios for several classes of graphs. For example any algorithm is shown to guarantee an approximation ratio of (2-o(1)) in graphs with high average degree. We also propose an algorithm guaranteeing for any graph of maximum degree Δ an approximation ratio of (2?1/Δ), which slightly improves the best known results. In addition, we analyse a natural linear-time greedy algorithm guaranteeing a ratio of (2?23/18k) in k-regular graphs admitting a perfect matching.     

求极大独立集的程序实现研究

独立集有着广泛的应用,尤其广泛应用于系统故障诊断领域。在求简单图极大独立集的程序实现方面,目前开展的研究工作还比较少。介绍简单图极大独立集的一种求取算法,剖析了该算法在使用面向对象程序设计模式中的实现方式,提出在定长字符串模式匹配中采用异或运算的运算法则来进行字符串模式匹配,由此作为多元式代数运算的基础对这个算法进行程序实现,并分析了这种字符串模式匹配的时间效率。