The Generation of a Sort of Fractal Graphs

We present an approach for generating a sort of fractal graphs by a simple probabilistic logic neuron network and show that the graphs can be represented by a set of compressed codings.An algorithm for quickly finding the codings,i.e.,recognizing the corresponding graphs,is given.The codings are shown to be optimal.The results above possibly give us the clue for studying image compression and pattern recognition.     

一种基于神经网络的分形几何图的产生与编码

本文提出用概率逻辑神经网产生一类自（互）相似（分形）图的方法，指出这类图能用一组压缩编码表示，给出快速寻找该编码的算法，既识别该分形几何图的算法，证明该编码是最优的，即码的长度最短，这些成果有希望在图象压缩和模式识别中得到应用。     

Parameterized Complexity of Eulerian Deletion Problems

We study a family of problems where the goal is to make a graph Eulerian, i.e., connected and with all the vertices having even degrees, by a minimum number of deletions. We completely classify the parameterized complexity of various versions: undirected or directed graphs, vertex or edge deletions, with or without the requirement of connectivity, etc. The collection of results shows an interesting contrast: while the node-deletion variants remain intractable, i.e., W[1]-hard for all the studied cases, edge-deletion problems are either fixed-parameter tractable or polynomial-time solvable. Of particular interest is a randomized FPT algorithm for making an undirected graph Eulerian by deleting the minimum number of edges, based on a novel application of the color coding technique. For versions that remain NP-complete but fixed-parameter tractable we consider also possibilities of polynomial kernelization; unfortunately, we prove that this is not possible unless NP?coNP/poly.     

Clustering based on multiple paths

This paper deals with a separation of strongly touching clusters using a concept of n-connectedness between pattern pairs, i.e., the number of paths between patterns. This new concept is similar to the concept of n-connectedness of graphs. Classification algorithms based on the number of independent paths and edge-disjoint paths are presented. It is shown that the latter has a transitivity. Finally, a simpler algorithm, i.e., a classification method based on the total number of paths, is presented. The proposed algorithm may be seen as an intermediate one between the ordinary connectedness algorithm and the maximal complete subgraph (MCS) algorithm.     

面向高效率视频编码标准的快速码率控制算法

在详细分析高效率视频编码标准HEVC现有码率控制算法JCTVC-H0213的基础上,提出了一种快速有效的改进算法。该算法根据前一帧的目标比特和实际比特的比值来确定当前帧量化参数。在恒定比特率情况下将该算法与JCTVC-H0213进行比较,实验结果表明该算法对于大部分内容特性序列峰值信噪比变化值提高2.4dB以上,达到了很好的码率控制效果;并且该算法非常简单,适用于实时的码率控制应用。     

IEH graphs

We propose a new family of interconnection topology that can be used to design communication architecture for distributed systems with an arbitrary number of computing nodes. The design is based on a novel generalization of the well known hypercube graphs. The proposed topology is shown to be incrementally extensible in steps of 1 (cost of restructuring or adding edges is very low), optimally fault tolerant and its diameter is logarithmic in the number of nodes. Moreover, for any given number of nodes, the difference of the maximum and the minimum degree of a node in the graph is ≤1, i.e., the graph is almost regular. A shortest routing algorithm for the proposed family of graphs has been developed.     

Quantized consensus in Hamiltonian graphs

The main contribution of this paper is an algorithm to solve an extended version of the quantized consensus problem over networks represented by Hamiltonian graphs, i.e., graphs containing a Hamiltonian cycle, which we assume to be known in advance. Given a network of agents, we assume that a certain number of tokens should be assigned to the agents, so that the total number of tokens weighted by their sizes is the same for all the agents. The algorithm is proved to converge almost surely to a finite set containing the optimal solution. A worst case study of the expected convergence time is carried out, thus proving the efficiency of the algorithm with respect to other solutions recently presented in the literature. Moreover, the algorithm has a decentralized stop criterion once the convergence set is reached.     

One-to-Many Embeddings of Hypercubes into Cayley Graphs Generated by Reversals

Among Cayley graphs on the symmetric group, some that have a noticeably low diameter relative to the degree of regularity are examples such as the ``star' network and the ``pancake' network, the latter a representative of a variety of Cayley graphs generated by reversals. These diameter and degree conditions make these graphs potential candidates for parallel computation networks. Thus it is natural to investigate how well they can simulate other standard parallel networks, in particular hypercubes. For this purpose, constructions have previously been given for low dilation embeddings of hypercubes into star networks. Developing this theme further, in this paper we construct especially low dilation maps (e.g., with dilation 1, 2, 3, or 4) of hypercubes into pancake networks and related Cayley graphs generated by reversals. Whereas obtaining such results by the use of ``traditional' graph embeddings (i.e., one-to-one or many-to-one embeddings) is sometimes difficult or impossible, we achieve many of these results by using a nontraditional simulation technique known as a ``one-to-many' graph embedding. That is, in such embeddings we allow each vertex in the guest (i.e., domain) graph to be associated with some nonempty subset of the vertex set of the host (i.e., range) graph, these subsets satisfying certain distance and connection requirements which make the simulation possible. Received July 30, 1997, and in revised form July 18, 2001. Online publication October 30, 2001.     

基于规范块半范数的快速分形编码算法

分形图像编码通常需要较长的时间,编码时间主要花费在一个海量码本中搜索每个输入子块的最佳匹配块。在提出的叉迹算法的基础上,提出一种快速编码算法。它主要利用一种新定义的特征——规范块半范数,把搜索范围限制在初始匹配块（在半范数意义下与输入子块最接近的码块）的邻域内。实验显示,与叉迹算法比较,该算法在编码时间和图像质量方面都取得了更好的效果。     

Optimal Reconstruction of Graphs under the Additive Model

We study the problem of reconstructing unknown graphs under the additive combinatorial search model. The main result concerns the reconstruction of bounded degree graphs, i.e., graphs with the degree of all vertices bounded by a constant d . We show that such graphs can be reconstructed in O(dn) nonadaptive queries, which matches the information-theoretic lower bound. The proof is based on the technique of separating matrices. A central result here is a new upper bound for a general class of separating matrices. As a particular case, we obtain a tight upper bound for the class of d -separating matrices, which settles an open question stated by Lindstr?m in [20]. Finally, we consider several particular classes of graphs. We show how an optimal nonadaptive solution of O(n ² / log n) queries for general graphs can be obtained. We also prove that trees with unbounded vertex degree can be reconstructed in a linear number of queries by a nonadaptive algorithm. Received August 1997; revised January 1999.     

Adaptive Algorithms for Join Processing in Distributed Database Systems

Distributed query processing algorithms usually perform data reduction by using a semijoin program, but the problem with these approaches is that they still require an explicit join of the reduced relations in the final phase. We introduce an efficient algorithm for join processing in distributed database systems that makes use of bipartite graphs in order to reduce data communication costs and local processing costs. The bipartite graphs represent the tuples that can be joined in two relations taking also into account the reduction state of the relations. This algorithm fully reduces the relations at each site. We then present an adaptive algorithm for response time optimization that takes into account the system configuration, i.e., the additional resources available and the data characteristics, in order to select the best strategy for response time minimization. We also report on the results of a set of experiments which show that our algorithms outperform a number of the recently proposed methods for total processing time and response time minimization.     

Multirobot Rendezvous With Visibility Sensors in Nonconvex Environments

This paper presents a coordination algorithm for mobile autonomous robots. Relying on distributed sensing, the robots achieve rendezvous, i.e., they move to a common location. Each robot is a point mass moving in a simply connected, nonconvex, unknown environment according to an omnidirectional kinematic model. It is equipped with line-of-sight limited-range sensors, i.e., it can measure the relative position of any object (robots or environment boundary) if and only if the object is within a given distance and there are no obstacles in between. The perimeter minimizing algorithm is designed using the notions of robust visibility, connectivity-preserving constraint sets, and proximity graphs. The algorithm provably achieves rendezvous if the interagent sensing graph is connected at any time during the evolution of the group. Simulations illustrate the theoretical results and the performance of the proposed algorithm in asynchronous setups and with measurement errors, control errors, and nonzero robot size. Simulations to illustrate the importance of visibility constraints and comparisons with the optimal centralized algorithm are also included.     

Acyclic orientation graph coloring for software-managed memory allocation

This paper presents a novel compiler algorithm,called acyclic orientation graph coloring(AOG coloring),for managing data objects in software-managed memory allocation.The key insight is that softwaremanaged memory allocation could be solved as an interval coloring problem,or equivalently,an acyclic orientation problem.We generalize graph coloring register allocation to interval coloring memory allocation by maintaining an acyclic orientation to the currently colored subgraph.This is achieved with some well-crafted heuristics,including Aggressive Simplify that does not necessarily preserve colorability and Best-Fit Select that assigns intervals(i.e.,colors)to nodes by possibly adjusting the colors already assigned to other nodes earlier.Our algorithm generalizes and subsumes as a special case the classical graph coloring register allocation algorithm without notably increased complexity:it deals with memory allocation while preserving the elegance and practicality of traditional graph coloring register allocation.We have implemented our algorithm and tested it on Appel’s 27921 interference graphs for scalars(augmented with node weights).Our algorithm outperforms Memory Coloring,the best in the literature,for software-managed memory allocation,on 98.64%graphs,in which,the gaps are more than 20%on 68.31%graphs and worse only on 0.29%graphs.We also tested it on all the 73 DIMACS weighted benchmarks(weighted graphs),AOG Coloring outperforms Memory Coloring on all of the benchmarks,in which,the gaps are more than 20%on 83.56%graphs.     

Bicriterion cluster analysis

Cluster analysis is concerned with the problem of partitioning a given set of entities into homogeneous and well-separated subsets called clusters. The concepts of homogeneity and of separation can be made precise when a measure of dissimilarity between the entities is given. Let us define the diameter of a partition of the given set of entities into clusters as the maximum dissimilarity between any pair of entities in the same cluster and the split of a partition as the minimum dissimilarity between entities in different clusters. The problems of determining a partition into a given number of clusters with minimum diameter (i.e., a partition of maximum homogeneity) or with maximum split (i.e., a partition of maximum separation) are first considered. It is shown that the latter problem can be solved by the classical single-link clustering algorithm, while the former can be solved by a graph-theoretic algorithm involving the optimal coloration of a sequence of partial graphs, described in more detail in a previous paper. A partition into a given number of clusters will be called efficient if and only if there exists no partition into at most the same number of clusters with smaller diameter and not smaller split or with larger split and not larger diameter. Two efficient partitions are called equivalent if and only if they have the same values for the split and for the diameter.     

H.264草案中的UVLC编码分析

MPEG-1/2/4,H.263中的可变长度码表(VLC)是针对一定码率范围的信道优化设计的,因此它的应用是有限制的。新一代的视频压缩算法要求使用一种新的符号编码技术,使得它既可以节约码流又可以编所有的语法元素。ULVC编码技术正是在这种情况下产生的,它可以处理多种编码条件(从低码率到高码率,不同的应用,不同的图像特性等),各类语法元素使用统一的码表(并且这个码表不需要存储),并且,码字构成的特性使UVLC有许多优于VLC的特点。     

Frequent subgraph mining in outerplanar graphs

In recent years there has been an increased interest in frequent pattern discovery in large databases of graph structured objects. While the frequent connected subgraph mining problem for tree datasets can be solved in incremental polynomial time, it becomes intractable for arbitrary graph databases. Existing approaches have therefore resorted to various heuristic strategies and restrictions of the search space, but have not identified a practically relevant tractable graph class beyond trees. In this paper, we consider the class of outerplanar graphs, a strict generalization of trees, develop a frequent subgraph mining algorithm for outerplanar graphs, and show that it works in incremental polynomial time for the practically relevant subclass of well-behaved outerplanar graphs, i.e., which have only polynomially many simple cycles. We evaluate the algorithm empirically on chemo- and bioinformatics applications.     

On the coding of ordered graphs

Ordered graph and ordered graph isomorphism provide a natural representation of many objects in applications such as computational geometry, computer vision and pattern recognition. In the present paper we propose a coding procedure for ordered graphs that improves an earlier one based on Eulerian circuits of graphs in terms of both simplicity and computational efficiency. Using our coding approach, we show that the ordered graph isomorphism problem can be optimally solved in quadratic time, although no efficient (polynomial-bound) isomorphism algorithm for general graphs exists today. An experimental evaluation demonstrates the superior performance of the new method.     

Random walks for image segmentation

A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension on arbitrary graphs     

Data Mining in Large Databases Using Domain Generalization Graphs

Attribute-oriented generalization summarizes the information in a relational database by repeatedly replacing specific attribute values with more general concepts according to user-defined concept hierarchies. We introduce domain generalization graphs for controlling the generalization of a set of attributes and show how they are constructed. We then present serial and parallel versions of the Multi-Attribute Generalization algorithm for traversing the generalization state space described by joining the domain generalization graphs for multiple attributes. Based upon a generate-and-test approach, the algorithm generates all possible summaries consistent with the domain generalization graphs. Our experimental results show that significant speedups are possible by partitioning path combinations from the DGGs across multiple processors. We also rank the interestingness of the resulting summaries using measures based upon variance and relative entropy. Our experimental results also show that these measures provide an effective basis for analyzing summary data generated from relational databases. Variance appears more useful because it tends to rank the less complex summaries (i.e., those with few attributes and/or tuples) as more interesting.     

权长相合的带权无向图画图算法

针对带权无向图的输出需用边长反映权值大小的问题,提出了一种基于遗传算法的带权无向图画图算法,通过对顶点坐标的编码进行交叉和变异来得到理想的节点坐标,变异算子结合了非一致性变异和单点邻域变异,并在适应度函数中运用顶点平均距离、边交叉数、多度顶点相关边夹角均匀度、边的权值长度比一致程度四个美学标准。实验结果表明,该算法画出的图形连线无交叉,分支清晰,权值—长度相合,能得到清晰、美观且能直观反映权值的可视化输出结果,可应用于带权无向图的可视化输出系统的设计。