A Linear-Time Algorithm for Finding Locally Connected Spanning Trees on Circular-Arc Graphs

Suppose that T is a spanning tree of a graph G. T is called a locally connected spanning tree of G if for every vertex of T, the set of all its neighbors in T induces a connected subgraph of G. In this paper, given an intersection model of a circular-arc graph, an O(n)-time algorithm is proposed that can determine whether the circular-arc graph contains a locally connected spanning tree or not, and produce one if it exists.     

一个新的二叉树的轮廓线索树构造算法

本文给出了二叉树的轮廓线索树的一个新的构造算法 .与 Reingdd的算法相比 ,该算法简单、高效、便于分析 ,易于推广到 m-叉树的轮廓线索树的构造算法上     

一种求关键路径的新算法

文章提出了一种求关键路径的新算法,该算法数据结构形式简单,求解方便且易于实现,并且算法能求出所有关键路径。用C语言设计了相应的程序验证了此算法。     

一种新的Kth最短路径搜索算法

借助于“背离”路径的概念,论文在2nd最短路径搜索算法的基础上提出了一种新的Kth最短路径搜索算法,并将其应用至实际环境中。通过K-1次2nd最短路径搜索算法的迭代,该算法可以求出网络中任意两个给定节点之间的Kth最短路径,2nd最短路径搜索算法在计算上具有简单性,因而也同样具有简洁、快速的特点。     

A New Approximation Algorithm for Finding Heavy Planar Subgraphs

We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NP-hard problem of finding a heaviest planar subgraph in an edge-weighted graph G . This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had a performance ratio exceeding 1/3 , which is obtained by any algorithm that produces a maximum weight spanning tree in G . Based on the Berman—Ramaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3+1/72 and at most 5/12 . We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8 . Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2 ) for the NP-hard SC MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.     

A New Approximation Algorithm for Finding Heavy Planar Subgraphs

Abstract. We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NP-hard problem of finding a heaviest planar subgraph in an edge-weighted graph G . This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had a performance ratio exceeding 1/3 , which is obtained by any algorithm that produces a maximum weight spanning tree in G . Based on the Berman—Ramaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3+1/72 and at most 5/12 . We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8 . Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2 ) for the NP-hard SC MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.     

所有最短路径的求解算法

本文提出了一种求所有最短路径的算法,能高效地求出一个顶点到其它各顶点的所有最短路径。此外,我们用C语言设计的相应程序验证了此算法。     

一种求解关键路径的新算法

通过定义节点编码图概念,提出一种不需要拓扑排序的求解关键路径的新算法。该算法扩充图的邻接表的存储结构,使图的存储与算法求解过程共享同一存储空间。从图的源节点开始,用加权取极大运算规则,广度优先递归对图中所有节点进行编码。编码图生成后,利用反向搜索求出从源点到汇点的所有关键路径及长度。该算法比现有算法更简单直观,所需的存储空间更小,算法时间复杂度降低到O(n+e),优于现有算法的O(n2)。     

求大素数的一个新算法

讨论了一些关于素数最重要的结果及其性质,同时给出一个新算法,它能快速产生大素数。     

属性约简中一种新的求核算法

属性约简是粗糙集理论中的一个重要内容,其核心任务是得到属性集的核。本文提出了一种基于二进制运算的属性核求解算法,该算法简单直观且易于实现。我们通过设计C语言程序验证了算法的有效性。     

求最短路径的新算法

本文提出了一种求最短路径的新算法,并用C语言设计相应的程序验证了此算法。实验表明,该算法能高效地求出一个顶点到其它各项点的所有最短路径。     

求列表极小值的量子算法

求列表极小值的算法具有广泛的应用。如果能够找到有效的求列表极小值的量子算法,那就可以找到求列表极大值的量子算法,从而与Grover量子搜索算法、求中值量子算法一起构成一套有效的量子算法体系。这些算法将构成用量子计算求解实际应用问题的核心和基础,并为量子算法的进一步研究提供坚实的基础。该文给出了一个时间复杂度为O(N√)的求列表极小值的量子算法。     

查找整系数不可约多项式的新算法与实现程序

本文利用一种独特的映射方法将整系数多项式映射为计算机容易处理的真分数。运用该映射方法建立了一种新的算法，编写了FoxPro程序，找出了整系数不可约多项式，并且可以对这些不可约多项式按需要进行排序或查找。因此，为扩频通信与信道密码等寻找和利用不可约多项式提供了一种可行且实用的算法和程序。     

一种新的二水平多因素系统两两组合覆盖测试数据生成算法

作者系统地研究了使用已有方法对二水平多因素系统（以下简称SM2）生成的两两组合覆盖的测试数据,针对已有方法对该具体问题效果并不理想的情况,利用组合分析方法,给出了一种新的SM2测试数据生成算法,与几种现有的方法相比,生成的测试数据具有数量少、效率高的优点.将其应用于Linux的一些源代码测试以及软件配置测试的测试方案设计,结果表明生成的测试数据具有较高的代码覆盖率和错误检测能力.     

Finding Outbreak Trees in Networks with Limited Information

Real-time control of infectious disease outbreaks represents one of the greatest epidemiological challenges currently faced. In this paper we address the problem of identifying contagion patterns responsible for the spread of a disease in a network, which can be applied in real-time to evaluate an ongoing outbreak. We focus on the scenario where limited information, i.e. infection reports which may or may not include the actual source, is available during an ongoing outbreak and we seek the most likely infection tree that spans at least a set of known infected nodes. This problem can be represented using a maximum likelihood constrained Steiner tree model where the objective is to find a spanning tree with an assignment of integer nodes weights. We propose a novel formulation and solution method based on a two-step heuristic which (1) reduces the initial graph using a polynomial time algorithm designed to find feasible infection paths and (2) solves an exact mixed integer linear programming reformulation of the maximum likelihood model on the resulting subgraph. The proposed methodology can be applied to outbreaks which may evolve from multiple sources. Simulated contagion episodes are used to evaluate the performance of our solution method. Our results show that the approach is computationally efficient and is able to reconstruct a significant proportion of the outbreak, even in the context of low levels of information availability.     

在动态树中寻找祖先

文章提出了有线性预处理时间,在恒定的查询时间内,通过加叶和加根操作对树的祖先进行查找的一种有效算法,这种算法能在O(m+n)时间内进行m次祖先查询及n次增叶操作。     

A Constant-Time Algorithm for Finding Neighbors in Quadtrees

Quadtrees and linear quadtrees are well-known hierarchical data structures to represent square images of size 2^{r} times 2^{r}. Finding the neighbors of a specific leaf node is a fundamental operation for many algorithms that manipulate quadtree data structures. In quadtrees, finding neighbors takes O(r) computational time for the worst case, where r is the resolution (or height) of a given quadtree. Schrack [1] proposed a constant-time algorithm for finding equal-sized neighbors in linear quadtrees. His algorithm calculates the location codes of equal-sized neighbors; it says nothing, however, about their existence. To ensure their existence, additional checking of the location codes is needed, which usually takes O(r) computational time. In this paper, a new algorithm to find the neighbors of a given leaf node in a quadtree is proposed which requires just O(1) (i.e., constant) computational time for the worst case. Moreover, the algorithm takes no notice of the existence or nonexistence of neighbors. Thus, no additional checking is needed. The new algorithm will greatly reduce the computational complexities of almost all algorithms based on quadtrees.     

基于敏捷分桶的频繁项目集生成新算法

指出用于数据挖掘的频繁项目集生成的常规Hash算法存在两个主要缺点：1）难挑选合适的Hash函数,2）易导致Hash冲突。为了克服了这些缺点,提出了一种能动态适应频繁项目集生成实际需要的敏捷分桶新算法,该算法对任何项目集均有按需反应能力,且无需寻找任何Hash函数,更不会导致任何Hash冲突。同时给出了进一步改进和提高新算法效率的研究方向。