Common Graph Research Articles

Multi-View Unsupervised Feature Selection with Adaptive Similarity and View Weight

With the advent of multi-view data, multi-view learning has become an important research direction in both machine learning and data mining. Considering the difficulty of obtaining labeled data in many real applications, we focus on the multi-view unsupervised feature selection problem. Traditional approaches all characterize the similarity by fixed and pre-defined graph Laplacian in each view separately and ignore the underlying common structures across different views. In this paper, we propose an algorithm named Multi-view Unsupervised Feature Selection with Adaptive Similarity and View Weight (ASVW) to overcome the above mentioned problems. Specifically, by leveraging the learning mechanism to characterize the common structures adaptively, we formulate the objective function by a common graph Laplacian across different views, together with the sparse $\ell _{2,p}$ -norm constraint designed for feature selection. We develop an efficient algorithm to address the non-smooth minimization problem and prove that the algorithm will converge. To validate the effectiveness of ASVW, comparisons are made with some benchmark methods on real-world datasets. We also evaluate our method in the real sports action recognition task. The experimental results demonstrate the effectiveness of our proposed algorithm.

Efficient Batched Distance, Closeness and Betweenness Centrality Computation in Unweighted and Weighted Graphs

Distance and centrality computations are important building blocks for modern graph databases as well as for dedicated graph analytics systems. Two commonly used centrality metrics are the compute-intense closeness and betweenness centralities, which require numerous expensive shortest distance calculations. We propose batched algorithm execution to run multiple distance and centrality computations at the same time and let them share common graph and data accesses. Batched execution amortizes the high cost of random memory accesses and presents new vectorization potential on modern CPUs and compute accelerators. We show how batched algorithm execution can be leveraged to significantly improve the performance of distance, closeness, and betweenness centrality calculations on unweighted and weighted graphs. Our evaluation demonstrates that batched execution can improve the runtime of these common metrics by over an order of magnitude.

Forbidden Pairs with a Common Graph Generating Almost the Same Sets

Let $\mathcal{H}$ be a family of connected graphs. A graph $G$ is said to be $\mathcal{H}$-free if $G$ does not contain any members of $\mathcal{H}$ as an induced subgraph. Let $\mathcal{F}(\mathcal{H})$ be the family of connected $\mathcal{H}$-free graphs. In this context, the members of $\mathcal{H}$ are called forbidden subgraphs.In this paper, we focus on two pairs of forbidden subgraphs containing a common graph, and compare the classes of graphs satisfying each of the two forbidden subgraph conditions. Our main result is the following: Let $H_{1},H_{2},H_{3}$ be connected graphs of order at least three, and suppose that $H_{1}$ is twin-less. If the symmetric difference of $\mathcal{F}(\{H_{1},H_{2}\})$ and $\mathcal{F}(\{H_{1},H_{3}\})$ is finite and the tuple $(H_{1};H_{2},H_{3})$ is non-trivial in a sense, then $H_{2}$ and $H_{3}$ are obtained from the same vertex-transitive graph by successively replacing a vertex with a clique and joining the neighbors of the original vertex and the clique. Furthermore, we refine a result in [Combin. Probab. Comput. 22 (2013) 733–748] concerning forbidden pairs.

Crystallographic aspects of hydrated salts of 4,6-diaminopyrimidine with the first five dicarboxylic acids

Abstract The preparation, X-ray single-crystal structure determination and vibrational spectroscopic characterisation of five novel salts, i.e. bis(4,6-diaminopyrimidinium(1+)) oxalate tetrahydrate; 4,6-diaminopyrimidinium(1+) hydrogen malonate monohydrate; bis(4,6-diaminopyrimidinium(1+)) succinate octahydrate; bis(4,6-diaminopyrimidinium(1+)) glutarate dihydrate and bis(4,6-diaminopyrimidinium (1+)) adipate octahydrate, are presented. It is the first crystallographic study with the title cation. All the structures are centrosymmetric. The oxalate, succinate and adipate anions are situated about inversion centres in their respective structures. The dependence on the parity of the number of carbon atoms in the anions is apparent in the interplanar angles of the carboxylate or carboxylic groups. In all of the structures, there are intermolecular N–H···N, N–H···Oacid, N–H···Owater, Owater–H···Oacid and Owater–H···Owater hydrogen-bonds of moderate strength. The most common graph set motif, R 2 2(8), describes the arrangement of the involved carboxylic as well as of the primary- and secondary-amine groups. There is a growing complexity of arrangement of water molecules in the structures with longer anionic molecules. In 4,6-diaminopyrimidinium(1+) hydrogen malonate monohydrate, there is an intramolecular Oacid–H···Oacid bond, and the conformation of the hydrogen malonate ions with non-parallel carboxylic and carboxylate groups is not often observed. The structural parameters of the carboxylic or carboxylate groups in the dicarboxylic acids or their derivatives found in the Cambridge Structural Database (CSD) are compared with the title structures.

Simultaneous Embedding: Edge Orderings, Relative Positions, Cutvertices

A simultaneous embedding (with fixed edges) of two graphs $$G^{\textcircled {1}}$$ and $$G^{\textcircled {2}}$$ with common graph $$G=G^{\textcircled {1}} \cap G^{\textcircled {2}}$$ is a pair of planar drawings of $$G^{\textcircled {1}}$$ and $$G^{\textcircled {2}}$$ that coincide on G. It is an open question whether there is a polynomial-time algorithm that decides whether two graphs admit a simultaneous embedding (problem Sefe). In this paper, we present two results. First, a set of three linear-time preprocessing algorithms that remove certain substructures from a given Sefe instance, producing a set of equivalent Sefe instances without such substructures. The structures we can remove are (1) cutvertices of the union graph $$G^\cup = G^{\textcircled {1}} \cup G^{\textcircled {2}}$$ , (2) most separating pairs of $$G^\cup $$ , and (3) connected components of G that are biconnected but not a cycle. Second, we give an $$O(n^3)$$ -time algorithm solving Sefe for instances with the following restriction. Let u be a pole of a P-node $$\mu $$ in the SPQR-tree of a block of $$G^{\textcircled {1}}$$ or $$G^{\textcircled {2}}$$ . Then at most three virtual edges of $$\mu $$ may contain common edges incident to u. All algorithms extend to the sunflower case, i.e., to the case of more than two graphs pairwise intersecting in the same common graph.

Comparison of Different Generalizations of Clustering Coefficient and Local Efficiency for Weighted Undirected Graphs.

Binary undirected graphs are well established, but when these graphs are constructed, often a threshold is applied to a parameter describing the connection between two nodes. Therefore, the use of weighted graphs is more appropriate. In this work, we focus on weighted undirected graphs. This implies that we have to incorporate edge weights in the graph measures, which require generalizations of common graph metrics. After reviewing existing generalizations of the clustering coefficient and the local efficiency, we proposed new generalizations for these graph measures. To be able to compare different generalizations, a number of essential and useful properties were defined that ideally should be satisfied. We applied the generalizations to two real-world networks of different sizes. As a result, we found that not all existing generalizations satisfy all essential properties. Furthermore, we determined the best generalization for the clustering coefficient and local efficiency based on their properties and the performance when applied to two networks. We found that the best generalization of the clustering coefficient is [Formula: see text], defined in Miyajima and Sakuragawa ( 2014 ), while the best generalization of the local efficiency is [Formula: see text], proposed in this letter. Depending on the application and the relative importance of sensitivity and robustness to noise, other generalizations may be selected on the basis of the properties investigated in this letter.

Analyzing execution traces: critical-path analysis and distance analysis

System designers make trade-offs between metrics of interest such as execution time, functional quality and cost to create a properly balanced system. Execution traces, which are sequences of timestamped start and end events of system tasks, are a general and powerful means to understand the system behavior that gives rise to these trade-offs. Such traces can be produced by, e.g., executable models or prototype systems. Their interpretation, however, often is non-trivial. We present two automated analysis techniques that work on execution traces to help the system designer with interpretation. First, critical-path analysis can be used to answer the typical “what is the bottleneck” question, and we extend earlier work of [16] with a technique that uses application information to refine the analysis. Second, we define a pseudo-metric on execution traces, which is useful for calibration and validation purposes, and which can be used to visualize the differences between traces. Both techniques are based on a common graph representation of execution traces. We have implemented our techniques in the Trace visualization tool [12], and have applied them in a case study from the digital printing domain.

Modeling of decentralized processes in dynamic logistic networks by means of graph-transformational swarms

In this paper, we propose to employ the framework of graph-transformational swarms for the modeling of dynamic logistic networks with decentralized processing and control. The members of a graph-transformational swarm act and interact in a common environment graph with massive parallelism of rule-based activities according to local control conditions and a global cooperation condition. This corresponds directly to the logistic hubs and their processes in a logistic network where the processes run simultaneously and autonomously with a proper way of coordination. This covers also dynamic changes on the network structures as the members of a swarm can change the environment anyhow. The approach is illustrated by the modeling of automated guided vehicles.

Robust graph representation of images with underlying structural networks. Application to the classification of vascular networks of mice’s colon

In this letter, we consider scenes constituted by underlying structural networks. This is an important issue since such scenes appear in many domains of sciences with for instance images of road networks, vascular networks, root systems, etc. The extraction of information from such networks requires characterization methods specifically designed to preserve the topological structure of the network hidden in the image. We propose an entire image processing pipeline for this task with a robust joint segmentation and graph-based representation approach. The proposed method relates, in the closest literature, to the so-called Maximally Stable Extremal Region here extended to extremally stable graph. The method is successfully illustrated with a real world biomedical pattern recognition problem solved with our approach. The robustness of the most common graph parameters is discussed from Monte Carlo simulations on synthetic graphs.

G-SQL

A lot of real-life data are of graph nature. However, it is not until recently that business begins to exploit data's connectedness for business insights. On the other hand, RDBMSs are a mature technology for data management, but they are not for graph processing. Take graph traversal, a common graph operation for example, it heavily relies on a graph primitive that accesses a given node's neighborhood. We need to join tables following foreign keys to access the nodes in the neighborhood if an RDBMS is used to manage graph data. Graph exploration is a fundamental building block of many graph algorithms. But this simple operation is costly due to a large volume of I/O caused by the massive amount of table joins. In this paper, we present G-SQL, our effort toward the integration of a RDBMS and a native in-memory graph processing engine. G-SQL leverages the fast graph exploration capability provided by the graph engine to answer multi-way join queries. Meanwhile, it uses RDBMSs to provide mature data management functionalities, such as reliable data storage and additional data access methods. Specifically, G-SQL is a SQL dialect augmented with graph exploration functionalities and it dispatches query tasks to the in-memory graph engine and its underlying RDMBS. The G-SQL runtime coordinates the two query processors via a unified cost model to ensure the entire query is processed efficiently. Experimental results show that our approach greatly expands capabilities of RDBMs and delivers exceptional performance for SQL-graph hybrid queries.

Graphs with Induced-Saturation Number Zero

Given graphs $G$ and $H$, $G$ is $H$-saturated if $H$ is not a subgraph of $G$, but for all $e \notin E(G)$, $H$ appears as a subgraph of $G + e$. While for every $n \ge |V(H)|$, there exists an $n$-vertex graph that is $H$-saturated, the same does not hold for induced subgraphs. That is, there exist graphs $H$ and values of $n \ge |V(H)|$, for which every $n$-vertex graph $G$ either contains $H$ as an induced subgraph, or there exists $e \notin E(G)$ such that $G + e$ does not contain $H$ as an induced subgraph. To circumvent this Martin and Smith make use of a generalized notion of "graph" when introducing the concept of induced saturation and the induced saturation number of graphs. This allows for edges that can be included or excluded when searching for an induced copy of $H$, and the induced saturation number is the minimum number of such edges that are required.In this paper, we show that the induced saturation number of many common graphs is zero. This yields graphs that are $H$-induced-saturated. That is, graphs such that no induced copy of $H$ exists, but adding or deleting any edge creates an induced copy of $H$. We introduce a new parameter for such graphs, indsat*($n;H$), which is the minimum number of edges in an $H$-induced-saturated graph. We provide bounds on indsat*($n;H$) for many graphs. In particular, we determine indsat*($n;H$) completely when $H$ is the paw graph $K_{1,3}+e$, and we determine indsat*(n;$K_{1,3}$) within an additive constant of four.

Private algorithms for the protected in social network search

Motivated by tensions between data privacy for individual citizens and societal priorities such as counterterrorism and the containment of infectious disease, we introduce a computational model that distinguishes between parties for whom privacy is explicitly protected, and those for whom it is not (the targeted subpopulation). The goal is the development of algorithms that can effectively identify and take action upon members of the targeted subpopulation in a way that minimally compromises the privacy of the protected, while simultaneously limiting the expense of distinguishing members of the two groups via costly mechanisms such as surveillance, background checks, or medical testing. Within this framework, we provide provably privacy-preserving algorithms for targeted search in social networks. These algorithms are natural variants of common graph search methods, and ensure privacy for the protected by the careful injection of noise in the prioritization of potential targets. We validate the utility of our algorithms with extensive computational experiments on two large-scale social network datasets.

Non-linear dynamics of stable carbon and hydrogen isotope signatures based on a biological kinetic model of aerobic enzymatic methane oxidation

The non-linear dynamics of stable carbon and hydrogen isotope signatures during methane oxidation by the methanotrophic bacteria Methylosinus sporium strain 5 (NCIMB 11126) and Methylocaldum gracile strain 14 L (NCIMB 11912) under copper-rich (8.9 µM Cu2+), copper-limited (0.3 µM Cu2+) or copper-regular (1.1 µM Cu2+) conditions has been described mathematically. The model was calibrated by experimental data of methane quantities and carbon and hydrogen isotope signatures of methane measured previously in laboratory microcosms reported by Feisthauer et al. [1] M. gracile initially oxidizes methane by a particulate methane monooxygenase and assimilates formaldehyde via the ribulose monophosphate pathway, whereas M. sporium expresses a soluble methane monooxygenase under copper-limited conditions and uses the serine pathway for carbon assimilation. The model shows that during methane solubilization dominant carbon and hydrogen isotope fractionation occurs. An increase of biomass due to growth of methanotrophs causes an increase of particulate or soluble monooxygenase that, in turn, decreases soluble methane concentration intensifying methane solubilization. The specific maximum rate of methane oxidation υm was proved to be equal to 4.0 and 1.3 mM mM−1 h−1 for M. sporium under copper-rich and copper-limited conditions, respectively, and 0.5 mM mM−1 h−1 for M. gracile. The model shows that methane oxidation cannot be described by traditional first-order kinetics. The kinetic isotope fractionation ceases when methane concentrations decrease close to the threshold value. Applicability of the non-linear model was confirmed by dynamics of carbon isotope signature for carbon dioxide that was depleted and later enriched in 13C. Contrasting to the common Rayleigh linear graph, the dynamic curves allow identifying inappropriate isotope data due to inaccurate substrate concentration analyses. The non-linear model pretty adequately described experimental data presented in the two-dimensional plot of hydrogen versus carbon stable isotope signatures.

Graph and chart aesthetics for experts and laymen in design: The role of familiarity and perceived ease of use

We investigated the relationship between familiarity, perceived ease of use, and attractiveness of graph designs in two target groups: experts and laymen in design. In the first study, we presented them with a variety of more or less common graph designs and asked them without any additional task to evaluate their familiarity, attractiveness, and perceived ease of use. They judged the familiarity and ease of use of the graphs similarly, but they differed in their attractiveness judgments. Familiarity and perceived ease of use appeared to predict attractiveness, but stronger for laymen than for designers. Laymen are attracted to designs they perceive as familiar and easy to use. Designers are attracted to designs between familiar and novel. In the second study, we asked designers and laymen to first perform an information retrieval task with the same graphs and then rate their attractiveness. Laymen’s appreciations remained the same, but the designers’ judgments of attractiveness were different from those in study 1. Correlational analyses suggest that their attractiveness judgments after use were affected not by actual usability but by perceived ease of use of the graphs.

Reconstruction of Gene Regulatory Networks based on Repairing Sparse Low-rank Matrices.

With the growth of high-throughput proteomic data, in particular time series gene expression data from various perturbations, a general question that has arisen is how to organize inherently heterogenous data into meaningful structures. Since biological systems such as breast cancer tumors respond differently to various treatments, little is known about exactly how these gene regulatory networks (GRNs) operate under different stimuli. Challenges due to the lack of knowledge not only occur in modeling the dynamics of a GRN but also cause bias or uncertainties in identifying parameters or inferring the GRN structure. This paper describes a new algorithm which enables us to estimate bias error due to the effect of perturbations and correctly identify the common graph structure among biased inferred graph structures. To do this, we retrieve common dynamics of the GRN subject to various perturbations. We refer to the task as "repairing" inspired by "image repairing" in computer vision. The method can automatically correctly repair the common graph structure across perturbed GRNs, even without precise information about the effect of the perturbations. We evaluate the method on synthetic data sets and demonstrate an application to the DREAM data sets and discuss its implications to experiment design.

Large scale graph processing systems: survey and an experimental evaluation

Graph is a fundamental data structure that captures relationships between different data entities. In practice, graphs are widely used for modeling complicated data in different application domains such as social networks, protein networks, transportation networks, bibliographical networks, knowledge bases and many more. Currently, graphs with millions and billions of nodes and edges have become very common. In principle, graph analytics is an important big data discovery technique. Therefore, with the increasing abundance of large graphs, designing scalable systems for processing and analyzing large scale graphs has become one of the most timely problems facing the big data research community. In general, scalable processing of big graphs is a challenging task due to their size and the inherent irregular structure of graph computations. Thus, in recent years, we have witnessed an unprecedented interest in building big graph processing systems that attempted to tackle these challenges. In this article, we provide a comprehensive survey over the state-of-the-art of large scale graph processing platforms. In addition, we present an extensive experimental study of five popular systems in this domain, namely, GraphChi, Apache Giraph, GPS, GraphLab and GraphX. In particular, we report and analyze the performance characteristics of these systems using five common graph processing algorithms and seven large graph datasets. Finally, we identify a set of the current open research challenges and discuss some promising directions for future research in the domain of large scale graph processing.

Common Divisor Character Degree Graphs of Solvable Groups with Four Vertices

Let G be a finite solvable group. The common divisor graph Γ(G) attached to G is a character degree graph. Its vertices are the degrees of the nonlinear irreducible complex characters of G, and different vertices m, n are adjacent if the greatest common divisor (m, n) > 1. In this article, we classify all graphs with four vertices that may occur as Γ(G) for solvable group G.

BFS-4K: An Efficient Implementation of BFS for Kepler GPU Architectures

Breadth-first search (BFS) is one of the most common graph traversal algorithms and the building block for a wide range of graph applications. With the advent of graphics processing units (GPUs), several works have been proposed to accelerate graph algorithms and, in particular, BFS on such many-core architectures. Nevertheless, BFS has proven to be an algorithm for which it is hard to obtain better performance from parallelization. Indeed, the proposed solutions take advantage of the massively parallelism of GPUs but they are often asymptotically less efficient than the fastest CPU implementations. This paper presents BFS-4K , a parallel implementation of BFS for GPUs that exploits the more advanced features of GPU-based platforms (i.e., NVIDIA Kepler) and that achieves an asymptotically optimal work complexity. The paper presents different strategies implemented in BFS-4K to deal with the potential workload imbalance and thread divergence caused by any actual graph non-homogeneity. The paper presents the experimental results conducted on several graphs of different size and characteristics to understand how the proposed techniques are applied and combined to obtain the best performance from the parallel BFS visits. Finally, an analysis of the most representative BFS implementations for GPUs at the state of the art and their comparison with BFS-4K are reported to underline the efficiency of the proposed solution.

ESTIMATING HETEROGENEOUS GRAPHICAL MODELS FOR DISCRETE DATA WITH AN APPLICATION TO ROLL CALL VOTING.

We consider the problem of jointly estimating a collection of graphical models for discrete data, corresponding to several categories that share some common structure. An example for such a setting is voting records of legislators on different issues, such as defense, energy, and healthcare. We develop a Markov graphical model to characterize the heterogeneous dependence structures arising from such data. The model is fitted via a joint estimation method that preserves the underlying common graph structure, but also allows for differences between the networks. The method employs a group penalty that targets the common zero interaction effects across all the networks. We apply the method to describe the internal networks of the U.S. Senate on several important issues. Our analysis reveals individual structure for each issue, distinct from the underlying well-known bipartisan structure common to all categories which we are able to extract separately. We also establish consistency of the proposed method both for parameter estimation and model selection, and evaluate its numerical performance on a number of simulated examples.

Distinguishing Infections on Different Graph Topologies

The history of infections and epidemics holds famous examples where understanding, containing, and ultimately treating an outbreak began with understanding its mode of spread. Influenza, HIV, and most computer viruses spread person to person, device to device, and through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, do not. In this paper, we study two fundamental questions of detection. First, given a snapshot view of a (perhaps vanishingly small) fraction of those infected, under what conditions is an epidemic spreading via contact (e.g., Influenza), distinguishable from a random illness operating independently of any contact network (e.g., seasonal allergies)? Second, if we do have an epidemic, under what conditions is it possible to determine which network of interactions is the main cause of the spread—the causative network—without any knowledge of the epidemic, other than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We derive sufficient conditions that networks must satisfy for these problems to be identifiable, and produce efficient, highly scalable algorithms that solve these problems. We show that the identifiability condition we give is fairly mild, and in particular, is satisfied by two common graph topologies: the $d$ -dimensional grid, and the Erdos-Renyi graphs.