图数据表示与压缩技术综述

对包含亿万个节点和边的图数据进行高效、紧凑的表示和压缩,是大规模图数据分析处理的基础.图数据压缩技术可以有效地降低图数据的存储空间,同时支持在压缩形式的图数据上进行快速访问.通过深入分析该技术的发展现状,将该技术分为基于传统存储结构的压缩技术、网页图压缩技术、社交网络图压缩技术、面向特定查询的图压缩技术4类.分别对每类技术详细分析了其代表方法并比较了它们之间的性能差异.最后对该技术进行了总结和展望.     

A Framework for Succinct Labeled Ordinal Trees over Large Alphabets

We consider succinct representations of labeled ordinal trees that support a rich set of operations. Our new representations support a much broader collection of operations than previous work. In our approach, labels of nodes are stored in a preorder label sequence, which can be compressed using any succinct representation of strings that supports \(\mathtt{{access}}\) , \({\mathtt{{rank}}}\) and \(\mathtt{{select}}\) operations. Thus, we present a framework for succinct representations of labeled ordinal trees that is able to handle large alphabets. This answers an open problem presented by Geary et al., which asks for representations of labeled ordinal trees that remain space-efficient for large alphabets. We further extend our work and present the first succinct representations for dynamic labeled ordinal trees that support several label-based operations including finding the level ancestor with a given label.     

Succinct Representation, Leaf Languages, and Projection Reductions

In this article, the following results are shown: 1. For succinctly encoded problemss(A), completeness under polynomial time reductions is equivalent to completeness under projection reductions, an extremely weak reduction defined by a quantifier-free projective formula. 2. The succinct versions(Aof a computational problemAis complete under projection reductions for the class of problems characterizable with leaf languageA, but not complete undermonotoneprojections. 3. A strong conversion lemma: IfAis reducible toBin polylogarithmic time, then the succinct version ofAis monotone projection reducible to the succinct version ofB. This result strengthens previous results by Papadimitriou and Yannakakis, and Balcázar and Lozano. It allows iterated application for multiple succinct problems. 4. For all syntactic complexity classes there exist complete problems undermonotoneprojection reductions. This positively answers a question by Stewart for a large number of complexity classes.     

Succinct Palette and Color Model Generation and Manipulation Using Hierarchical Representation

We propose a new method to obtain the representative colors and their distributions of an image. Our intuition is that it is possible to derive the global model from the local distributions. Beginning by sampling pure colors, we build a hierarchical representation of colors in the image via a bottom‐up approach. From the resulting hierarchy, we can obtain satisfactory palettes/color models automatically without a predefined size. Furthermore, we provide interactive operations to manipulate the results which allow the users to reflect their intention directly. In our experiment, we show that the proposed method produces more succinct results that faithfully represent all the colors in the image with an appropriate number of components. We also show that the proposed interactive approach can improve the results of applications such as recoloring and soft segmentation.     

On Succinct Greedy Drawings of Plane Triangulations and 3-Connected Plane Graphs

Geometric routing by using virtual locations is an elegant way for solving network routing problems. In its simplest form, greedy routing, a message is simply forwarded to a neighbor that is closer to the destination. It has been an open conjecture whether every 3-connected plane graph has a greedy drawing in the Euclidean plane R ² (by Papadimitriou and Ratajczak in Theor. Comp. Sci. 344(1):3–14, 2005). Leighton and Moitra (Discrete Comput. Geom. 44(3):686–705, 2010) recently settled this conjecture positively. One main drawback of this approach is that the coordinates of the virtual locations require Ω(nlogn) bits to represent (the same space usage as traditional routing table approaches). This makes greedy routing infeasible in applications. In this paper, we show that the classical Schnyder drawing in R ² of plane triangulations is greedy with respect to a simple natural metric function H(u,v) over R ² that is equivalent to Euclidean metric D _E (u,v) (in the sense that $D_{E}(u,v) \leq H(u,v) \leq2\sqrt{2}D_{E}(u,v)$ ). The drawing uses two integer coordinates between 0 and 2n?5, which can be represented by logn bits. We also show that the classical Schnyder drawing in R ² of 3-connected plane graphs is weakly greedy with respect to the same metric function H(?,?). The drawing uses two integer coordinates between 0 and f (where f is the number of internal faces of G).     

Optimal Polygonal Representation of Planar Graphs

In this paper, we consider the problem of representing planar graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched by an upper bound of six sides with a linear-time algorithm for representing any planar graph by touching hexagons. Moreover, our algorithm produces convex polygons with edges having at most three slopes and with all vertices lying on an O(n)×O(n) grid.     

Succinct representation of dynamic trees

We study the problem of maintaining a dynamic ordered tree succinctly under updates of the following form: insertion or deletion of a leaf, insertion of a node on an edge (edge subdivision) or deletion of a node with only one child (the child becomes a child of its former grandparent). We allow satellite data of a fixed size to be associated to the nodes of the tree.We support update operations in constant amortized time and support access to satellite data and basic navigation operations in worst-case constant time; the basic navigation operations include parent, first/last-child, previous/next-child. These operations are moving from a node to its parent, leftmost/rightmost child, and its previous and next child respectively.We demonstrate that to efficiently support more extended operations, such as determining the i-th child of a node, rank of a child among its siblings, or size of the subtree rooted at a node, one requires a restrictive pattern for update strategy, for which we propose the finger-update model. In this model, updates are performed at the location of a finger that is only allowed to crawl on the tree between a child and a parent or between consecutive siblings. Under this model, we describe how the named extended operations are performed in worst-case constant time.Previous work on dynamic succinct trees (Munro et al., 2001 [17]; Raman and Rao, 2003 [19]) is mainly restricted to binary trees and achieves poly-logarithmic (Munro et al., 2001 [17]) or “poly-log-log” (Raman and Rao, 2003 [19]) update time under a more restricted model, where updates are performed in traversals starting at the root and ending at the root and queries can be answered when the traversal is completed. A previous result on ordinal trees achieves only sublinear amortized update time and “poly-log-log” query time (Gupta et al., 2007 [11]). More recently, the update time has been improved to O(logn/loglogn) while queries can be performed in O(logn/loglogn) time (Sadakane and Navarro, 2010 [20]).     

基于链接实体回放的多源知识图谱终身表示学习

知识图谱存储大量的结构化知识和丰富的语义信息,已被广泛应用于知识驱动的智能软件.随着智能应用的不断发展,它们对知识图谱的需求也在发生变化.而单一知识图谱往往具有数据不完备等缺点,难以满足需求.因此,支持新数据来源、融合多源知识已经成为迫切需求.传统的知识图谱表示学习和应用范式只考虑单一图谱,忽视了不同图谱间的知识迁移.多源知识图谱联合训练虽然可以带来性能提升,但不支持新增知识图谱的拓展表示学习.鉴于此,提出了多源知识图谱终身表示学习的新范式.给定一个知识图谱序列,终身表示学习的目标是在学习新知识图谱的同时,从已学习的知识图谱与模型中获得知识迁移.为实现这一目标,提出了一个基于链接实体回放的多源知识图谱终身表示学习框架.首先,设计一个以Transformer为编码器的知识图谱表示学习模型作为框架核心,利用关系相关性进行实体的链接预测.其次,提出链接子图构造方法,基于实体对齐构建并回放新增知识图谱和已有知识图谱之间的链接子图进行终身学习和知识迁移.最后,采用动态结构方法,为每个知识图谱存储相应的模型参数快照来避免灾难性遗忘.多个链接预测基准数据集上的实验结果表明,所提出的表示学习模型可以取得最先进的性能,且提出的终身表示学习框架可以实现有效的知识迁移.     

Geometric Representation of Graphs in Low Dimension Using Axis Parallel Boxes

An axis-parallel k-dimensional box is a Cartesian product R ₁×R ₂×???×R _k where R _i (for 1≤i≤k) is a closed interval of the form [a _i ,b _i ] on the real line. For a graph G, its boxicity box?(G) is the minimum dimension k, such that G is representable as the intersection graph of (axis-parallel) boxes in k-dimensional space. The concept of boxicity finds applications in various areas such as ecology, operations research etc. A number of NP-hard problems are either polynomial time solvable or have much better approximation ratio on low boxicity graphs. For example, the max-clique problem is polynomial time solvable on bounded boxicity graphs and the maximum independent set problem for boxicity d graphs, given a box representation, has a $\lfloor 1+\frac{1}{c}\log n\rfloor^{d-1}An axis-parallel k-dimensional box is a Cartesian product R ₁×R ₂×⋅⋅⋅×R _k where R _i (for 1≤i≤k) is a closed interval of the form [a _i ,b _i ] on the real line. For a graph G, its boxicity box (G) is the minimum dimension k, such that G is representable as the intersection graph of (axis-parallel) boxes in k-dimensional space. The concept of boxicity finds applications in various areas such as ecology, operations research etc. A number of NP-hard problems are either polynomial time solvable or have much better approximation ratio on low boxicity graphs. For example, the max-clique problem is polynomial time solvable on bounded boxicity graphs and the maximum independent set problem for boxicity d graphs, given a box representation, has a ?1+\frac1clogn?^d-1\lfloor 1+\frac{1}{c}\log n\rfloor^{d-1} approximation ratio for any constant c≥1 when d≥2. In most cases, the first step usually is computing a low dimensional box representation of the given graph. Deciding whether the boxicity of a graph is at most 2 itself is NP-hard.     

Succinct nearest neighbor search

An efficient and universal similarity search solution is a holy grail for multimedia information retrieval. Most similarity indexes work by mapping the original multimedia objects into simpler representations, which are then searched by proximity using a suitable distance function.     

Succinct 2D Dictionary Matching

The dictionary matching problem seeks all locations in a given text that match any of the patterns in a given dictionary. Efficient algorithms for dictionary matching scan the text once, searching for all patterns simultaneously. Existing algorithms that solve the 2-dimensional dictionary matching problem all require working space proportional to the size of the dictionary. This paper presents the first efficient 2-dimensional dictionary matching algorithm that operates in small space. Given d patterns, D={P ₁,…,P _d }, each of size m×m, and a text T of size n×n, our algorithm finds all occurrences of P _i , 1≤i≤d, in T. The preprocessing of the dictionary forms a compressed self-index of the patterns, after which the original dictionary may be discarded. Our algorithm uses O(dmlogdm) extra bits of space. The time complexity of our algorithm is close to linear, O(dm ²+n ² τlogσ), where τ is the time it takes to access a character in the compressed self-index and σ is the size of the alphabet. Using recent results τ is at most sub-logarithmic.     

基于层次信息粒表示的属性图链接预测模型

随着具有结点属性信息的网络图数据的增加,结点属性及结点链接关系越来越复杂,这对复杂网络的链接预测任务带来了一系列的挑战.这些不同来源的原始数据之间存在着不一致性,即结点的属性诱导的潜在链接关系与网络拓扑结构观测到的链接边之间存在着不一致的情况,这一现象将直接影响结点对之间的链接预测准确性与精确性.为了有效处理多源数据的不一致性,融合异构数据的差异,借助粒计算思想,通过对原始数据的多粒度表示,将原始数据在不同层次的粒度进行信息表示建模.最终依据这些数据的粒度表示,寻找最优的粒层结构,并最大化地消除数据内在的不一致性.首先,定义了数据的粒度不同层次表示及粒层关系;其次,对所观测到的链接数据,构建对数似然统计模型,并综合不同粒度层数据特点对模型进行修正;最后,使用多源数据训练统计模型,将学习好的模型用于预测结点对之间的链接概率.实验表明：与现有链接预测模型相比,多源数据经过粒度表示极大地平衡了多源数据的不一致性,有效提升了链接预测任务的准确性.     

Succinct representation of regular languages by boolean automata

Boolean automata are a generalization of finite automata in the sense that the ‘next state’, i.e. the result of the transition function given a state and a letter, is not just a single state (deterministic automata) or a union of states (nondeterministic automata) but a boolean function of states. Boolean automata accept precisely regular languages; furthermore they correspond in a natural way to certain language equations as well as to sequential networks. We investigate the succinctness of representing regular languages by boolean automata. In particular, we show that for every deterministic automaton A with m states there exists a boolean automaton with [log₂m] states which accepts the reverse of the language accepted by A (m≥1). We also show that for every n≥1 there exists a boolean automation with n states such that the smallest deterministic automaton accepting the same language has 2⁽²ⁿ⁾ states; moreover this holds for an alphabet with only two letters.     

论Web2.0网站简洁的视觉风格及成因

Web2.0是当前互联网新的发展形态。由网民提供内容为主,更加注重人际互动和社交化的网站被称为web2.0网站。Web2.0网站在视觉设计上有很多显著的设计创新,体现在版式、导航、配色、字体、图形等方面,这些设计新形式综合发展出一种新的更为简洁的、视觉上更具易读性的网站视觉风格。这是网络互动技术达到新的里程碑的产物,也是互联网模式和理念变化的结果。     

一种简洁单点登录系统设计与实现

阐述了SSO的基本原理,并设计了一个简洁SSO系统,解决了不同Web应用系统之间的互访问题:用户登录一次即可访问所有Web系统。系统设计简单实用,不需要建设昂贵复杂的认证服务器,对现有系统的改动很少,扩展也很容易,具有较高的应用价值。