Alberto Garcia-Robledo

A dual representation simulated annealing algorithm for the bandwidth minimization problem on graphs

A dual representation with neighborhood composed of three perturbation operators.Tuning of DRSA using a full factorial design.Benchmark with 113 instances, 31 improved and the matching of the remaining 82.Wilcoxon signed-rank test used to compare DRSA with GRASP-PR, SA, and VNS. The bandwidth minimization problem on graphs (BMPG) consists of labeling the vertices of a graph with the integers from 1 to n (n is the number of vertices) such that the maximum absolute difference between labels of adjacent vertices is as small as possible. In this work we develop a DRSA (Dual Representation Simulated Annealing) algorithm to solve BMPG. The main novelty of DRSA is an internal dual representation of the problem used in conjunction with a neighborhood function composed of three perturbation operators. The evaluation function of DRSA is able to discriminate among solutions of equal bandwidth by taking into account all absolute differences between labels of adjacent vertices. For better performance, the parameters of DRSA and the probabilities for selecting the perturbation operators were tuned by extensive experimentation carried out using a full factorial design. The benchmark for the proposed algorithm consists of 113 instances of the Harwell-Boeing sparse matrix collection; the results of DRSA included 31 new upper bounds and the matching of 82 best-known solutions (22 solutions are optimal). We used Wilcoxon signed-rank test to compare best solutions produced by DRSA against best solutions produced by three state of the art methods: greedy randomized adaptive search procedure with path relinking, simulated annealing, and variable neighborhood search; according to the comparisons done, the quality of the solutions with DRSA is significantly better than that obtained with the other three algorithms.

Correlation analysis of complex network metrics on the topology of the Internet

We present an experimental study on the linear relationship between a rich set of complex network metrics, to methodologically select a subset of non-redundant and potentially independent metrics that explain different aspects of the topology of the Autonomous System view of the Internet. We followed a data-driven approach based on (1) a correlation study of different properties of evolving Internet networks, and (2) the validation of a non-redundant set of metrics by evaluating the performance of supervised and unsupervised machine learning techniques. We confirm pair-wise metric correlations observed in other types of networks and identify sets of highly correlated metrics that may reveal patterns specific to the topology of the Internet.

Exploring the feasibility of heterogeneous computing of complex networks for big data analysis

We present our experience with exploring the configuration space for accelerating BFSs on large complex networks in the context of a heterogeneous GPU + CPU HPC platform. We study the feasibility of the heterogeneous computing approach by systematically studying different graph partitioning strategies while processing synthetic and real-world complex networks. To achieve this, we exploit the coreness of complex networks for load partitioning.

Partitioning of complex networks for heterogeneous computing: A methodological approach

We present a methodology that guides the design of a multilevel-like unbalanced complex network partitioning framework for load-balance in a graph heterogeneous computing context. Throughout the paper we describe: (1) the design of a topology-aware complex network coarsening process that preserves non-redundant complex network properties, (2) the multilevel partitioning of coarse graphs by the centrality of nodes, and (3) the demonstration of the benefits of the proposed partitioning framework by empirically studying the performance of a BSP-based CPU+GPU heterogeneous computing platform when accelerating the traversal of large real-world and synthetic complex networks.

Accelerating All-Sources BFS Metrics on Multi-core Clusters for Large-Scale Complex Network Analysis

All-Sources BFS (AS-BFS) is the main building block in a variety of complex network metric algorithms, such as the average path length and the betweenness centrality. However, AS-BFS calculations involve as many full BFS traversals as the total number of vertices, rendering AS-BFS impractical on commodity systems for real-world graphs with millions of vertices and links. In this paper we present our experience with the acceleration of AS-BFS graph metrics on multi-core HPC clusters by outlining hybrid coarse-grain parallel algorithms for computing the average path-length, the diameter and the betweenness centrality of complex networks in a lock-free fashion. We report speedups of up to 171\(\times \) on a heterogeneous cluster of 12-core Intel Xeon and 32-core AMD Opteron multi-core nodes; as well as resource utilizations of up to 75%.