James Abello

Massive Quasi-Clique Detection

We describe techniques that are useful for the detection of dense subgraphs (quasi-cliques) in massive sparse graphs whose vertex set, but not the edge set, fits in RAM. The algorithms rely on efficient semi-external memory algorithms used to preprocess the input and on greedy randomized adaptive search procedures (GRASP) to extract the dense subgraphs. A software platform was put together allowing graphs with hundreds of millions of nodes to be processed. Computational results illustrate the effectiveness of the proposed methods.

ASK-GraphView: A Large Scale Graph Visualization System

We describe ASK-GraphView, a node-link-based graph visualization system that allows clustering and interactive navigation of large graphs, ranging in size up to 16 million edges. The system uses a scalable architecture and a series of increasingly sophisticated clustering algorithms to construct a hierarchy on an arbitrary, weighted undirected input graph. By lowering the interactivity requirements we can scale to substantially bigger graphs. The user is allowed to navigate this hierarchy in a top down manner by interactively expanding individual clusters. ASK-GraphView also provides facilities for filtering and coloring, annotation and cluster labeling

Handbook of massive data sets

Preface.- Part I: Internet and the World Wide Web.- Part II: Massive Graphs.- Part III: String Processing and Data Compression.- Part IV: External Memory Algorithms and Data Structures.- Part V: Optimization.- Part VI: Data Management.- Part VII: Architecture Issues.- Part VIII: Applications.- Index.

A functional approach to external graph algorithms

AbstractWe present a new approach for designing external graph algorithms and use it to design simple, deterministic and randomized external algorithms for computing connected components, minimum spanning forests, bottleneck minimum spanning forests, maximal independent sets (randomized only), and maximal matchings in undirected graphs. Our I/ O bounds compete with those of previous approaches. We also introduce a semi-external model, in which the vertex set but not the edge set of a graph fits in main memory. In this model we give an improved connected components algorithm, using new results for external grouping and sorting with duplicates. Unlike previous approaches, ours is purely functional—without side effects—and is thus amenable to standard checkpointing and programming language optimization techniques. This is an important practical consideration for applications that may take hours to run.

Axes-based visualizations with radial layouts

In the analysis of multidimensional data sets questions involving detection of extremal events, correlations, patterns and trends play an increasingly important role in a variety of applications. Axes-based visualizations like Parallel or Star Coordinates are useful tools for the analysis of multidimensional data sets. In this paper, we present several interactive axes, which can be used to analyze data in an intuitive manner. Furthermore, we present two novel radial visual arrangements of such axes - the TimeWheel and the MultiComb. They focus on data sets with one variable of reference. TimeWheel and MultiComb in combination with interactive axes are part of an interactive framework called VisAxes, which can be used for enhanced multidimensional data browsing and analysis.

MGV: a system for visualizing massive multidigraphs

Describes MGV (Massive Graph Visualizer), an integrated visualization and exploration system for massive multidigraph navigation. It adheres to the visual information-seeking mantra: overview first, zoom and filter, then details on demand. MGVs only assumption is that the vertex set of the underlying digraph corresponds to the set of leaves of a pre-determined tree T. MGV builds an out-of-core graph hierarchy and provides mechanisms to plug in arbitrary visual representations for each graph hierarchy slice. Navigation from one level to another of the hierarchy corresponds to the implementation of a drill-down interface. In order to provide the user with navigation control and interactive response, MGV incorporates a number of visualization techniques like interactive pixel-oriented 2D and 3D maps, statistical displays, color maps, multi-linked views and a zoomable label-based interface. This makes the association of geographic information and graph data very natural. To automate the creation of the vertex set hierarchy for MGV, we use the notion of graph sketches. They can be thought of as visual indices that guide the navigation of a multigraph too large to fit on the available display. MGV follows the client-server paradigm and it is implemented in C and Java-3D. We highlight the main algorithmic and visualization techniques behind the tools and, along the way, point out several possible application scenarios. Our techniques are being applied to multigraphs defined on vertex sets with sizes ranging from 100 million to 250 million vertices.

Fisheye Tree Views and Lenses for Graph Visualization

We present interactive visual aids to support the exploration and navigation of graph layouts. They include fisheye tree views and composite lenses. These views provide, in an integrated manner, overview+detail and focus+context. Fisheye tree views are novel applications of the well known fisheye distortion technique. They facilitate the exploration of the hierarchy trees associated with clustered graphs. Composite lenses are the result of the integration of several lens techniques. They facilitate the display of local graph information that may be otherwise difficult to grasp in large and dense graph layouts

Technical Section: CGV-An interactive graph visualization system

Previous work on graph visualization has yielded a wealth of efficient graph analysis algorithms and expressive visual mappings. To support the visual exploration of graph structures, a high degree of interactivity is required as well. We present a fully implemented graph visualization system, called CGV (Coordinated Graph Visualization), whose particular emphasis is on interaction. The system incorporates several interactive views that address different aspects of graph visualization. To support different visualization tasks, view ensembles can be created dynamically with the help of a flexible docking framework. Several novel techniques, including enhanced dynamic filtering, graph lenses, and edge-based navigation are presented. The main graph canvas interactions are augmented with several visual cues, among which the infinite grid and the radar view are novel. CGV provides a history mechanism that allows for undo/redo of interaction. CGV is a general system with potential application in many scenarios. It has been designed as a dual-use system that can run as a stand-alone application or as an applet in a web browser. CGV has been used to evaluate graph clustering results, to navigate topological structures of neuronal systems, and to perform analysis of some time-varying graphs.

Finding independent sets in a graph using continuous multivariable polynomial formulations

Two continuous formulations of the maximum independent set problem on a graph G=(V,E) are considered. Both cases involve the maximization of an n-variable polynomial over the n-dimensional hypercube, where n is the number of nodes in G. Two (polynomial) objective functions F(x) and H(x) are considered. Given any solution to x0 in the hypercube, we propose two polynomial-time algorithms based on these formulations, for finding maximal independent sets with cardinality greater than or equal to F(x0) and H(x0), respectively. A relation between the two approaches is studied and a more general statement for dominating sets is proved. Results of preliminary computational experiments for some of the DIMACS clique benchmark graphs are presented.

Visualizing large graphs with compound-fisheye views and treemaps

Compound-fisheye views are introduced as a method for the display and interaction with large graphs. The method relies on a hierarchical clustering of the graph, and a generalization of the traditional fisheye view, together with a treemap representation of the cluster tree.