Parameterized algorithms for feedback set problems and their duals in tournaments

The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournaments, a well studied class of directed graphs. We consider both weighted and unweighted versions.     

Black-white pebbles and graph separation

Summary We exhibit a close relationship between two topics in computational complexity. One topic is the analysis of storage requirements for nondeterministic computations. The corresponding mathematical model is a well known black-white pebble game on directed acyclic graphs. The other topic is the search for small separators of undirected graphs. We model a dynamic version of the concept of a separator with a vertex separator game. This game is closely related to graph layout and searching problems. We show that instances of the black-white pebble game and the vertex separator game can easily be transformed into each other. As an application of this result both games are shown to be NP-complete.     

An algorithmic study of switch graphs

We derive a variety of results on the algorithmics of switch graphs. On the negative side we prove hardness of the following problems: Given a switch graph, does it possess a bipartite/planar/triangle-free/Eulerian configuration? On the positive side we design fast algorithms for several connectivity problems in undirected switch graphs, and for recognizing acyclic configurations in directed switch graphs.     

Improved Lower Bounds on Time and Processors for Scheduling Precedence Graphs on Multicomputer Systems

This paper improves lower bounds on the minimum number of processors and minimum time to execute a given directed acyclic task graph with communication delays. The given task graph is partitioned into a number of independent task graphs to arrive at sharper bounds. A drawback of the earlier best method is pointed out and corrected. The time taken to calculate the bounds is also less in comparison to the corrected method. These bounds are useful in comparing heuristic algorithms used for scheduling directed acyclic task graphs and as compiler tools in static scheduling-on parallel computers.     

Algorithms for P<Subscript>4</Subscript>-Comparability Graph Recognition and Acyclic P<Subscript>4</Subscript>-Transitive Orientation

We consider two problems pertaining to P₄-comparability graphs, namely, the problem of recognizing whether a simple undirected graph is a P₄-comparability graph and the problem of producing an acyclic P₄-transitive orientation of a P₄-comparability graph. These problems have been considered by Hoàng and Reed who described O(n⁴)- and O(n⁵)-time algorithms for their solution, respectively, where n is the number of vertices of the input graph. Faster algorithms have recently been presented by Raschle and Simon, and by Nikolopoulos and Palios; the time complexity of these algorithms for either problem is O(n + m²), where m is the number of edges of the graph. In this paper we describe O(n m)-time and O(n + m)-space algorithms for the recognition and the acyclic P₄-transitive orientation problems on P₄-comparability graphs. The algorithms rely on properties of the P₄-components of a graph, which we establish, and on the efficient construction of the P₄-components by means of the BFS-trees of the complement of the graph rooted at each of its vertices, without however explicitly computing the complement. Both algorithms are simple and use simple data structures.     

基于遗传算法的有向无环图画图算法

在研究了现有画有向无环图的主要方法的基础上提出一种基于遗传算法的有向无环图画图算法,将一般有向无环图的画图问题转换为函数优化问题,用遗传算法求目标函数最优解的近似值。实验表明此算法具有算法统一、方法简单、容易实现、易于修改,并且具有自适应、自学习和易于并行化的特点。     

Answering Reachability Queries on Incrementally Updated Graphs by Hierarchical Labeling Schema

We proposed a novel solution schema called the Hierarchical Labeling Schema (HLS) to answer reachability queries in directed graphs. Different from many existing approaches that focus on static directed acyclic graphs (DAGs), our schema focuses on directed cyclic graphs (DCGs) where vertices or arcs could be added to a graph incrementally. Unlike many of the traditional approaches, HLS does not require the graph to be acyclic in constructing its index. Therefore, it could, in fact, be applied to both DAGs and DCGs. When vertices or arcs are added to a graph, the HLS is capable of updating the index incrementally instead of re-computing the index from the scratch each time, making it more efficient than many other approaches in the practice. The basic idea of HLS is to create a tree for each vertex in a graph and link the trees together so that whenever two vertices are given, we can immediately know whether there is a path between them by referring to the appropriate trees. We conducted extensive experiments on both real-world datasets and synthesized datasets. We compared the performance of HLS, in terms of index construction time, query processing time and space consumption, with two state-of-the-art methodologies, the path-tree method and the 3-hop method. We also conducted simulations to model the situation when a graph is updated incrementally. The performance comparison of different algorithms against HLS on static graphs has also been studied. Our results show that HLS is highly competitive in the practice and is particularly useful in the cases where the graphs are updated frequently.     

Access graphs: a model for investigating memory consistency

Computer architectures supporting shared memory continue to increase in complexity as designers seek to improve memory performance. This is especially true of proposals for massively parallel systems with distributed, yet shared, memory. The need to maintain a reasonably simple memory model for programmers, in spite of enhancements like caches and access pipelining, is responsible for many of the complications. We develop a novel graph model, access graphs, for visualizing processor/memory interaction. Access graphs symbolically represent the causal relationships between load, store, and synchronization events. The focus is on two classes of access graphs: pseudo and real. A pseudo access graph describes an execution in terms of abstract events familiar to the programmer. If the pseudo access graph is acyclic, then memory consistency is preserved during the execution. A real access graph describes an execution in terms of physical events known to the hardware designer. A real access graph must be acyclic since hardware cannot violate causality. Memory consistency can be verified for a given computer system by proving that for any acyclic real access graph describing a program's execution on that computer, an acyclic pseudo access graph can be derived describing the same execution     

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     

Parallel directed graph algorithms on directional processor arrays with reconfigurable bus systems

Processors arrays with reconfigurable bus systems (abbreviated to PARBS) have been received a lot of attention in the last decade, and many undirected graph algorithms with constant time complexity have been proposed on PARBS. However, for a directed graph, it will be proved that connecting PARBS in the way proposed for undirected graphs generates paths which do not exist in the directed graph. This result may lead to incorrect solution for directed graph problems. Therefore, in this paper, a model named D-PARBS (Directional PARBS) is proposed for eliminating the non-existent paths. This model can be used to correctly identifying redundant arcs on directed graphs in constant time. Furthermore, by modifying the D-PARBS architecture, constant time algorithms with O(n ³) processors are developed to solve topological sort, transitive closure, cyclic graph checking, and strongly connected component problems on directed graphs. Chi-Jung Kuo: He is currently an operation officer of the Information Processing Department in the Taipei Branch of Bangkok Bank. His research interests include parallel processing and graph theory. He received his B.S. and M.S. degree in Information Management from National Taiwan University of Science and Technology in 1993 and 1995, respectively. He was a teacher in the Chin Min Junior College from 1995 to 1996. Chiun-Chieh Hsu, Ph.D.: He is currently a full professor of Information Management Department at National Taiwan University of Science and Technology. His current research interests include fault-tolerant computing, parallel and distributed processing, networks, and graph theory. He received his B.E., M.E., and Ph.D. degrees all in Electrical Engineering from National Taiwan University in 1983, 1987, and 1990, respectively. He worked as a software and firmware design engineer of Research and Development in Acer Computer Company from 1983 to 1985. Wei-Chen Fang: He received the BS degree in MIS from Tamkang University and the MS degree in Information Management from National Taiwan University of Science and Technology. Currently, he is a Ph.d student and works as an assistant researcher with the Advanced Technology research group for Chunghwa Telecommunication Laboratory. His research interests include multi-processor architecture, fault-tolerant computing, and parallel and distributed processing.     

On a game in directed graphs

Inspired by recent algorithms for electing a leader in a distributed system, we study the following game in a directed graph: each vertex selects one of its outgoing arcs (if any) and eliminates the other endpoint of this arc; the remaining vertices play on until no arcs remain. We call a directed graph lethal if the game must end with all vertices eliminated and mortal if it is possible that the game ends with all vertices eliminated. We show that lethal graphs are precisely collections of vertex-disjoint cycles, and that the problem of deciding whether or not a given directed graph is mortal is NP-complete (and hence it is likely that no “nice” characterization of mortal graphs exists).     

The directed subgraph homeomorphism problem

The set of pattern graphs for which the fixed directed subgraph homeomorphism problem is NP-complete is characterized. A polynomial time algorithm is given for the remaining cases. The restricted problem where the input graph is a directed acyclic graph is in polynomial time for all pattern graphs and an algorithm is given.     

知识图谱划分算法研究综述

知识图谱是人工智能的重要基石,因其包含丰富的图结构和属性信息而受到广泛关注.知识图谱可以精确语义描述现实世界中的各种实体及其联系,其中顶点表示实体,边表示实体间的联系.知识图谱划分是大规模知识图谱分布式处理的首要工作,对知识图谱分布式存储、查询、推理和挖掘起基础支撑作用.随着知识图谱数据规模及分布式处理需求的不断增长,...     

同构计算环境中一种快速有效的静态任务调度算法

快速有效的调度任务是多处理器计算环境中的一个关键问题．目前任务调度算法中刻画任务依赖关系最流行的模型是DAG,在以前的文献中,提出了一种新的更实际、更普遍的TTIG模型及其相应的MATE算法(基于同构计算环境)．延伸了TTIG模型,并提出基于同构系统的新的算法及两种启发式方法(GBHA1和GBHA2)．GBHA以组的形式尽量消除图中回路,因而能获得任务图的全局信息,具有更好的调度性能．在模拟实验中,将此算法与MATE和其他同构环境中基于DAG的有效调度算法,在不同测试条件下进行了比较,结果显示GBHA在性能上明显优于MATE,与基于DAG模型的调度算法比较而言,在性能方面各有千秋,但在算法时间复杂度方面具有显著的优势．     

Searching networks with unrestricted edge costs

Best-first and depth-first heuristic search algorithms often assume underlying search graphs with only nonnegative edge costs and attempt to optimize simple objective functions. Applicability of these algorithms to graphs with both positive and negative edge costs is not completely studied. In the paper, two new problems are identified: one in computational geometry and the other in the layout design of very large scale integrated (VLSI) circuits. The former problem relates to a weight-balanced bipartitioning of a given set of points in a plane. The goal of the second problem is to find an area-balanced staircase path in a VLSI floorplan. Formulations of these problems lead to an interesting directed acyclic search graph with positive, zero and negative edge costs and an objective function of general nature. These problems are NP-hard. To solve such general problems optimally, search schemes are proposed. Experimental results reveal the efficacy and versatility of the proposed schemes, the depth-first scheme being the better choice. It is shown that the classical number-partitioning problem can also be formulated in this framework     

Heuristic algorithms for scheduling iterative task computations ondistributed memory machines

Many partitioned scientific programs can be modeled as iterative executions of computational tasks and represented by iterative task graphs (ITGs). An ITG may or may not have dependence cycles. In this paper, we consider the symbolic scheduling of ITGs on distributed memory architectures with nonzero communication overhead and propose heuristic algorithms for scheduling both cyclic and acyclic ITGs without searching an entire iteration space. Our approach incorporates techniques of software pipelining, graph unfolding, directed acyclic graph (DAG) scheduling, and load balancing. We analyze the asymptotic optimality of the algorithms to show that the derived schedules are competitive to optimal solutions. We also study the sensitivity of scheduling performance on inaccurate weights. Finally, we present experimental results to demonstrate the effectiveness of the optimization techniques     

Gibbs and Markov properties of graphs

Directed acyclic graphs (DAG's) and, more generally, chain graphs have in recent years been widely used for statistical modelling. Their Gibbs and Markov properties are now well understood and are exploited, e.g., in reducing the complexity encountered in estimating the joint distribution of many random variables. The scope of the models has been restricted to acyclic or recursive processes and this restriction was long considered imperative, due to the supposed fundamentally different nature of processes involving reciprocal interactions between variables. Recently however it was shown independently by Spirtes (Spirtes, 1995) and Koster (Koster, 1996) that graphs containing directed cycles may be given a proper Markov interpretation. This paper further generalizes the scope of graphical models. It studies a class of conditional independence (CI) probability models determined by a general graph which may have directed and undirected edges, and may contain directed cycles. This class of graphical models strictly includes the well-known class of graphical chain models studied by Frydenberg et al., and the class of probability models determined by a directed cyclic graph or a reciprocal graph, studied recently by Spirtes and Koster. It is shown that the Markov property determined by a graph is equivalent to the existence of a Gibbs-factorization of the density (assumed positive). To better understand the structural aspects of the Gibbs and Markov properties embodied by graphs the notion of lattice conditional independence (LCI), introduced by Andersson and Perlman (Andersson and Perlman, 1993), is needed. The Gibbs-factorization has an outer ‘skeleton’ which is determined by the ring of all anterior sets of the graph. This revised version was published online in June 2006 with corrections to the Cover Date.     

Evaluating the performance of table processing algorithms

While techniques for evaluating the performance of lower-level document analysis tasks such as optical character recognition have gained acceptance in the literature, attempts to formalize the problem for higher-level algorithms, while receiving a fair amount of attention in terms of theory, have generally been less successful in practice, perhaps owing to their complexity. In this paper, we introduce intuitive, easy-to-implement evaluation schemes for the related problems of table detection and table structure recognition. We also present the results of several small experiments, demonstrating how well the methodologies work and the useful sorts of feedback they provide. We first consider the table detection problem. Here algorithms can yield various classes of errors, including non-table regions improperly labeled as tables (insertion errors), tables missed completely (deletion errors), larger tables broken into a number of smaller ones (splitting errors), and groups of smaller tables combined to form larger ones (merging errors). This leads naturally to the use of an edit distance approach for assessing the results of table detection. Next we address the problem of evaluating table structure recognition. Our model is based on a directed acyclic attribute graph, or table DAG. We describe a new paradigm, “graph probing,” for comparing the results returned by the recognition system and the representation created during ground-truthing. Probing is in fact a general concept that could be applied to other document recognition tasks as well. Received July 18, 2000 / Accepted October 4, 2001     

Independency relationships and learning algorithms for singly connected networks

Graphical structures such as Bayesian networks or Markov networks are very useful tools for representing irrelevance or independency relationships, and they may be used to efficiently perform reasoning tasks. Singly connected networks are important specific cases where there is no more than one undirected path connecting each pair of variables. The aim of this paper is to investigate the kind of properties that a dependency model must verify in order to be equivalent to a singly connected graph structure, as a way of driving automated discovery and construction of singly connected networks in data. The main results are the characterizations of those dependency models which are isomorphic to singly connected graphs (either via the d-separation criterion for directed acyclic graphs or via the separation criterion for undirected graphs), as well as the development of efficient algorithms for learning singly connected graph representations of dependency models.     

基于LT+模型的社交网络影响力最大化研究

影响力最大化问题的目标是寻找社交网络中一组种子结点集合,在给定的传播模型下,使得这些结点最终传播的影响范围最大。Kempe和Kleinberg提出的贪心算法可以获得很好的影响范围,但是因复杂度太高而并不适用于大型社交网络。Chen和Yuan等人基于线性阈值(LT)模型提出了构造局部有向无环图的启发式算法,但是LT模型只考虑了邻居结点的直接影响力,忽略了结点之间存在的间接影响力。因此,在LT模型的基础上,结合网络中结点之间存在的间接影响力,提出了LT⁺影响力模型,并利用构造局部有向无环图的启发式算法求解LT⁺模型的影响力最大化,称为LT⁺DAG算法。真实数据集上的对比实验表明,LT⁺DAG算法具有更好的影响范围以及较好的可扩展性。