Alessio Arleo

Large graph visualizations using a distributed computing platform

Big Data analytics is recognized as one of the major issues in our current information society, and raises several challenges and opportunities in many fields, including economy and finance, e-commerce, public health and administration, national security, and scientific research. The use of visualization techniques to make sense of large volumes of information is an essential ingredient, especially for the analysis of complex interrelated data, which are represented as graphs. The growing availability of powerful and inexpensive cloud computing services naturally motivates the study of distributed graph visualization algorithms, able to scale to the size of large graphs. We study the problem of designing a distributed visualization algorithm that must be simple to implement and whose computing infrastructure does not require major hardware or software investments. We design, implement, and experiment a force-directed algorithm in Giraph, a popular open source framework for distributed computing, based on a vertex-centric design paradigm. The algorithm is tested both on real and artificial graphs with up to one million edges. The experiments show the scalability and effectiveness of our technique when compared to a centralized implementation of the same force-directed model. Graphs with about one million edges can be drawn in a few minutes, by spending about 1 USD per drawing with a cloud computing infrastructure of Amazon.

A Distributed Multilevel Force-Directed Algorithm

The use of graph visualization approaches to present and analyze complex data is taking a leading role in conveying information and knowledge to users in many application domains. This creates the need of developing efficient and effective algorithms that automatically compute graph layouts. In this respect, force-directed algorithms are arguably among the most popular graph layout techniques. Aimed at leveraging the potential of modern distributed graph algorithms platforms, we present Multi-GiLA, the first multilevel force-directed graph visualization algorithm based on a vertex-centric computation paradigm. We implemented Multi-GiLA using the Apache Giraph platform. Experiments show that it can be successfully applied to compute high quality layouts of very large graphs on inexpensive cloud computing platforms.

A Million Edge Drawing for a Fistful of Dollars

In this paper we study the problem of designing a graph drawing algorithm for large graphs. The algorithm must be simple to implement and the computing infrastructure must not require major hardware or software investments. We report about the experimental analysis of a simple implementation of a spring embedder in Giraph, a vertex-centric open source framework for distributed computing. The algorithm is tested on real graphs of upi¾?to 1 million edges by using a cheap PaaS Platform as a Service infrastructure of Amazon. We can afford drawing graphs with about one million edges in about 8i¾?min, by spending less than 1 USD per drawing for the cloud computing infrastructure.

Visibility representations of boxes in 2.5 dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane \(z=0\) and edges are unobstructed lines of sight parallel to the x- or y-axis. We prove that: (i) Every complete bipartite graph admits a 2.5D-BR; (ii) The complete graph \(K_n\) admits a 2.5D-BR if and only if \(n \leqslant 19\); (iii) Every graph with pathwidth at most 7 admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an n-vertex graph that admits a 2.5D-GBR has at most \(4n - 6 \sqrt{n}\) edges and this bound is tight. Finally, we prove that deciding whether a given graph G admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR \(\varGamma \) is the set of bottom faces of the boxes in \(\varGamma \).

GiViP: A Visual Profiler for Distributed Graph Processing Systems

Analyzing large-scale graphs provides valuable insights in different application scenarios. While many graph processing systems working on top of distributed infrastructures have been proposed to deal with big graphs, the tasks of profiling and debugging their massive computations remain time consuming and error-prone. This paper presents GiViP, a visual profiler for distributed graph processing systems based on a Pregel-like computation model. GiViP captures the huge amount of messages exchanged throughout a computation and provides an interactive user interface for the visual analysis of the collected data. We show how to take advantage of GiViP to detect anomalies related to the computation and to the infrastructure, such as slow computing units and anomalous message patterns.

Visibility Representations of Boxes in 2.5 Dimensions

We initiate the study of 2.5D box visibility representations (2.5D-BR) where vertices are mapped to 3D boxes having the bottom face in the plane \(z=0\) and edges are unobstructed lines of sight parallel to the x- or y-axis. We prove that: (i) Every complete bipartite graph admits a 2.5D-BR; (ii) The complete graph \(K_n\) admits a 2.5D-BR if and only if \(n \leqslant 19\); (iii) Every graph with pathwidth at most 7 admits a 2.5D-BR, which can be computed in linear time. We then turn our attention to 2.5D grid box representations (2.5D-GBR) which are 2.5D-BRs such that the bottom face of every box is a unit square at integer coordinates. We show that an n-vertex graph that admits a 2.5D-GBR has at most \(4n - 6 \sqrt{n}\) edges and this bound is tight. Finally, we prove that deciding whether a given graph G admits a 2.5D-GBR with a given footprint is NP-complete. The footprint of a 2.5D-BR \(\varGamma \) is the set of bottom faces of the boxes in \(\varGamma \).

Profiling distributed graph processing systems through visual analytics

Abstract Analyzing large-scale graphs provides valuable insights in different application scenarios, including social networking, crime detection, content ranking, and recommendations. While many graph processing systems working on top of distributed infrastructures have been proposed to deal with big graphs, the task of profiling their massive computations remains time consuming and error-prone. This paper presents GiViP , a visual profiler for distributed graph processing systems based on a Pregel-like computation model. GiViP captures the huge amount of messages exchanged throughout a computation and provides a powerful user interface for the visual analysis of the collected data. We discuss the effectiveness of our approach and show how to take advantage of GiViP to detect anomalies related to the computation and to the infrastructure, such as slow computing units, anomalous message patterns, unbalanced graph partitions, and links with high latency.