On the Complexity of Strongly Connected Components in Directed Hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (Sccs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. Sccs which do not reach any components but themselves). Almost linear here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor α(n), where α is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all Sccs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the Sccs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the Sccs is harder in directed hypergraphs than in directed graphs.     

Computing dominators in parallel

We present a fast parallel algorithm for computing the dominators of a directed acyclic graph. The model of computation used in a parallel random access machine that allows simultaneous reads but prohibits simultaneous writes into the same memory location. Let P_t(n) be the processor complexity of computing the transitive closure of an n-vertex directed graph on this model. The only known parallel algorithm for dominators requires O(log²n) time and uses O(nP_t(n)) processors. Our algorithm for dominators has the same time complexity but uses O(P_t(n)) processors, thereby improving the processor complexity of the previously known algorithm by a factor of n.     

A Linear Time Algorithm for the Arc Disjoint Menger Problem in Planar Directed Graphs

Given a graph G=(V,E) and two vertices s,t ∈ V , s\neq t , the Menger problem is to find a maximum number of disjoint paths connecting s and t . Depending on whether the input graph is directed or not, and what kind of disjointness criterion is demanded, this general formulation is specialized to the directed or undirected vertex, and the edge or arc disjoint Menger problem, respectively. For planar graphs the edge disjoint Menger problem has been solved to optimality [W2], while the fastest algorithm for the arc disjoint version is Weihe's general maximum flow algorithm for planar networks [W1], which has running time \bf O (|V| log |V|) . Here we present a linear time, i.e., asymptotically optimal, algorithm for the arc disjoint version in planar directed graphs. Received August 1997; revised January 1999.     

用有向图实现的ATLAS编译系统中的设备分配

ATLAS是测试领域的流行语言，用其编写的测试程序可在任一个具体的自动化测试平台上工作。设备分配是每个ATLAS编译系统都要面临的任务之一。该文提出了将被测设备与自动化测试平台组成的系统看成是有向图，利用图的遍历算法来实现设备分配过程。     

Minimal communication cost software construction in the Internet environment

This paper investigates the issue of building software in the Internet environment, where local area network (LAN) based systems are interconnected by links with different bandwidth and do not share file systems. The software is modeled as a directed acyclic graph. Each node in the graph represents a logical step in processing the software while the edges describe the order of execution. The problem is to construct the software at a particular LAN with minimum Internet communication cost. An optimal polynomial algorithm, SOFTCON, with time complexity is presented, where and are the number of nodes and edges in the graph describing the software respectively, is the number of LANs in the Internet environment, and is the time complexity of the network flow algorithm on the flow network with nodes and edges transformed from the directed acyclic graph of the software. Received: 6 December 1995 / 1 May 1996     

求解最小费用最大流问题的信念传播算法

最小费用最大流问题是一种组合优化问题,在经济、工业等领域具有重要研究意义和应用价值.针对部分最小费用最大流问题求解算法效率较低的情况,依据最小费用最大流问题的线性规划方程,将问题模型映射为对应因子图模型,改进描述函数,给出迭代方程,设计了求解最小费用最大流问题的信念传播算法.利用迭代方程优先对最大可行流特征值进行收敛计算,得到最大流,设置最大流阈值,在此基础上进行最小费用计算,从而求得问题最优解.最后选取若干带权有向图模型进行数值实验,验证了算法的可行性及有效性,且算法在求解效率上优于部分算法.     

More Efficient Topological Sort Using Reconfigurable Optical Buses

Topological sort of an acyclic graph has many applications such as job scheduling and network analysis. Due to its importance, it has been tackled on many models. Dekel et al. [3], proposed an algorithm for solving the problem in O(log² N) time on the hypercube or shuffle-exchange networks with O(N ³) processors. Chaudhuri [2], gave an O(log N) algorithm using O(N ³) processors on a CRCW PRAM model. On the LARPBS (Linear Arrays with a Reconfigurable Pipelined Bus System) model, Li et al. [5] showed that the problem for a weighted directed graph with N vertices can be solved in O(log N) time by using N ³ processors. In this paper, a more efficient topological sort algorithm is proposed on the same LARPBS model. We show that the problem can be solved in O(log N) time by using N ³/log N processors. We show that the algorithm has better time and processor complexities than the best algorithm on the hypercube, and has the same time complexity but better processor complexity than the best algorithm on the CRCW PRAM model.     

Deterministic Resource Discovery in Distributed Networks

The resource discovery problem was introduced by Harchol-Balter, Leighton, and Lewin. They developed a number of algorithms for the problem in the weakly connected directed graph model. This model is a directed logical graph that represents the vertices’ knowledge about the topology of the underlying communication network. The current paper proposes a deterministic algorithm for the problem in the same model, with improved time, message, and communication complexities. Each previous algorithm had a complexity that was higher at least in one of the measures. Specifically, previous deterministic solutions required either time linear in the diameter of the initial network, or communication complexity $O(n^3)$ (with message complexity $O(n^2)$), or message complexity $O(|E_0| \log n)$ (where $E_0$ is the arc set of the initial graph $G_0$). Compared with the main randomized algorithm of Harchol-Balter, Leighton, and Lewin, the time complexity is reduced from $O(\log^2n)$ to\pagebreak[4] $O(\log n )$, the message complexity from $O(n \log^2 n)$ to $O(n \log n )$, and the communication complexity from $O(n^2 \log^3 n)$ to $O(|E_0|\log ^2 n )$. \par Our work significantly extends the connectivity algorithm of Shiloach and Vishkin which was originally given for a parallel model of computation. Our result also confirms a conjecture of Harchol-Balter, Leighton, and Lewin, and addresses an open question due to Lipton.     

Minimal functional routes in directed graphs with dependent edges

Graphs are mathematical structures used to model a set of objects and the relations between them. One of the basic concepts of graph theory, the path, has wide real‐world applications. In classic graph models, edges ending at a node are assumed to be independent. However, many real graphs/networks can only be correctly described by considering a dependency among nodes or edges. Paths in such graphs may not be functional if the conditional dependency is ignored. In this study, we investigate the routing problem in directed graphs with dependent edges represented by general graph models as alternatives to hypergraphs. We define a minimal functional route (MFR) as a minimal set of nodes and edges that can independently perform information transfer between two given nodes, and formulate the determination of MFRs as a graph search problem. A depth‐first‐search (DFS) top‐down algorithm, an iterative integer linear programming (ILP) bottom‐up algorithm, and a subgraph‐growing bottom‐up algorithm are devised subsequently to solve this problem. Numerical experiments verify the effectiveness of the algorithms. The defined MFR problem and the proposed algorithms are expected to find many practical applications.     

基于KGMM改进的动态目标检测算法

针对在线K-均值聚类法初始化混合高斯模型(KGMM)在运行时间、空间复杂度、噪声等方面存在的缺陷,提出了基于KGMM改进的检测方法,采用加入方差因子的C-均值聚类准则来初始化混合高斯模型,有效解决了可能出现的某一像素值属于不同分布类从而概率不同的问题,提高了检测的灵活性;改进了高斯匹配准则,提高了检测算法的准确性;对每个像素点间隔地建立混合高斯分布,减少了高斯模型个数,节省了存储空间,提高了算法的运行速度。实验结果表明改进的检测算法检测效果更理想。     

A novel edge-centric approach for graph edit similarity computation

Graph similarity is an important notion with many applications. Graph edit distance is one of the most flexible graph similarity measures available. The main problem with this measure is that in practice it can only be computed for small graphs due to its exponential time complexity. This paper addresses the high complexity of graph edit distance computations. Specifically, we present CSI_GED, a novel edge-centric approach for computing graph edit distance through common sub-structure isomorphisms enumeration. CSI_GED utilizes backtracking search combined with a number of heuristics to reduce memory requirements and quickly prune away a large portion of the mapping search space. Experiments show that CSI_GED is highly efficient for computing graph edit distance; it outperforms the state-of-the-art methods by over three orders of magnitude. It also shows that CSI_GED scales the computation gracefully to larger and distant graphs on which current methods fail to run. Moreover, we evaluated CSI_GED as a stand-alone graph edit similarity search query method. The experiments show that CSI_GED is effective and scalable, and outperforms the state-of-the-art indexing-based methods by over two orders of magnitude.     

On the Impact of Using Utilities Rather than Costs for Graph Matching

The concept of graph edit distance constitutes one of the most flexible graph matching paradigms available. The major drawback of graph edit distance, viz. the exponential time complexity, has been recently overcome by means of a reformulation of the edit distance problem to a linear sum assignment problem. However, the substantial speed up of the matching is also accompanied by an approximation error on the distances. Major contribution of this paper is the introduction of a transformation process in order to convert the underlying cost model into a utility model. The benefit of this transformation is that it enables the integration of additional information in the assignment process. We empirically confirm the positive effects of this transformation on five benchmark graph sets with respect to the accuracy and run time of a distance based classifier.     

基于动态规划的最小代价路径汉语自动分词

基于最长次长匹配的方法建立汉语切分路径有向图，将汉语自动分词转换为在有向图中选择正确的切分路径，其中有向图中的节点代价对应单词频度，而边代价对应所连接的两个单词的接续频度；运用改进后Dijkstra最小代价路径算法，求出有向图中路径代价最小的切分路径作为切分结果．在切分歧义的处理上采用分步过滤逐步解消的方法，并引入了基于未知词特征词驱动的机制，对未知词进行了前处理，减少了因未知词的出现而导致的切分错误．实验结果表明，该方法有效地提高了汉语分词的精确率和召回率．     

A Cut-Based Algorithm for the Nonlinear Dual of the Minimum Cost Network Flow Problem

We consider a convex, or nonlinear, separable minimization problem with constraints that are dual to the minimum cost network flow problem. We show how to reduce this problem to a polynomial number of minimum s,t-cut problems. The solution of the reduced problem utilizes the technique for solving integer programs on monotone inequalities in three variables, and a so-called proximity-scaling technique that reduces a convex problem to its linear objective counterpart. The problem is solved in this case in a logarithmic number of calls, O(log U), to a minimum cut procedure, where U is the range of the variables. For a convex problem on n variables the minimum cut is solved on a graph with O(n²) nodes. Among the consequences of this result is a new cut-based scaling algorithm for the minimum cost network flow problem. When the objective function is an arbitrary nonlinear function we demonstrate that this constrained problem is solved in pseudopolynomial time by applying a minimum cut procedure to a graph on O(nU) nodes.     

Efficient Parallel Algorithms for Some Graph Theory Problems

In this paper,a sequential algorithm computing the aww vertex pair distance matrix D and the path matrix Pis given.On a PRAM EREW model with p,1≤p≤n^2,processors,a parallel version of the sequential algorithm is shown.This method can also be used to get a parallel algorithm to compute transitive closure array A^* of an undirected graph.The time complexity of the parallel algorithm is O(n^3/p).If D,P and A^* are known,it is shown that the problems to find all connected components,to compute the diameter of an undirected graph,to determine the center of a directed graph and to search for a directed cycle with the minimum(maximum)length in a directed graph can all be solved in O(n^2/p logp)time.     

Searching graphs with A*: applications to job sequencing

The best-first search algorithm A* allows search graphs that are trees, directed acyclic graphs or directed graphs with cycles. In real life applications of A* the search graph is generally implemented as a tree. It is shown here that for certain well known one-machine job sequencing problems that arise in job shops, graph search is much faster than best-first tree search when problem instances are of small and medium size. Moreover, graph search uses less memory and so is able to solve larger problems. Depth-first search needs little memory, and is therefore capable in principle of solving problems of arbitrary size, but is slower than graph search by orders of magnitude for the examples that were studied     

应用模拟植物生长算法求解置换流水车间调度问题*

针对置换流水车间调度问题,提出了一种基于模拟植物生长的调度算法。该算法利用置换流水车间调度的有向图表示,提出了可交换节点集概念,并将其融入模拟植物生长算法中,解决置换流水车间调度问题。采用所提算法对置换流水车间调度问题的基准数据进行测试,并比对标准遗传算法,结果表明算法的有效性。     

Two algorithms for a reachability problem in one-dimensional space

Two algorithms are proposed to solve a reachability problem among time-dependent obstacles in 1D space. In the first approach, the motion planning problem is reduced to a path existence problem in a directed graph. The algorithm is very simple, with running time O(n²), where n is the complexity of obstacles in space-time. The second algorithm uses a sweep-line technique and has running time O(n log₂ n). Besides, the latter algorithm can be easily modified to compute a collision-free trajectory, if such trajectories exist     

多编码树GPU并行轴心子图匹配

子图同构问题是非确定多项式(NP)完全问题,而轴心子图同构是一种特殊的子图同构问题.针对现在已经有许多高效的子图同构算法,然而对于轴心子图同构问题目前并没有基于GPU的搜索算法,且通过改造已有的子图同构算法来解决轴心子图匹配问题会产生大量不必要的中间结果这一问题,提出了一种基于GPU的轴心子图同构算法.首先,通过一种新...     

融合协同知识图谱与优化图注意网络的推荐算法

考虑到推荐算法存在数据稀疏及模型复杂度较高等问题,提出了一种融合协同知识图谱与优化图注意网络的推荐模型。将用户/项目知识图谱与用户-项目交互图结合为协同知识图谱,嵌入到优化的图注意网络模型中,这不仅可以很好地缓解数据稀疏问题,还能更大程度地挖掘用户的潜在兴趣和高阶关系;使用优化的图卷积网络,通过去除特征转换和非线性激活模块,可以在不影响整体推荐性能的基础上极大地降低模型复杂度;结合基于偏差的注意力机制,及时感知候选项目与用户真实感兴趣项目之间的偏差,提升模型的训练效率。在Movielens数据集和Douban数据集上进行仿真实验,结果表明该算法在推荐性能和时间复杂度方面,相比对比算法均得到了有效的提升。