Book of Abstracts of the Sixth SIAM Workshop on Combinatorial Scientific Computing

Book of Abstracts of CSC14 edited by Bora UçarInternational audienceThe Sixth SIAM Workshop on Combinatorial Scientific Computing, CSC14, was organized at the Ecole Normale Supérieure de Lyon, France on 21st to 23rd July, 2014. This two and a half day event marked the sixth in a series that started ten years ago in San Francisco, USA. The CSC14 Workshop's focus was on combinatorial mathematics and algorithms in high performance computing, broadly interpreted. The workshop featured three invited talks, 27 contributed talks and eight poster presentations. All three invited talks were focused on two interesting fields of research specifically: randomized algorithms for numerical linear algebra and network analysis. The contributed talks and the posters targeted modeling, analysis, bisection, clustering, and partitioning of graphs, applied in the context of networks, sparse matrix factorizations, iterative solvers, fast multi-pole methods, automatic differentiation, high-performance computing, and linear programming. The workshop was held at the premises of the LIP laboratory of ENS Lyon and was generously supported by the LABEX MILYON (ANR-10-LABX-0070, Université de Lyon, within the program ''Investissements d'Avenir'' ANR-11-IDEX-0007 operated by the French National Research Agency), and by SIAM

Improving the scalability of parallel N-body applications with an event driven constraint based execution model

The scalability and efficiency of graph applications are significantly constrained by conventional systems and their supporting programming models. Technology trends like multicore, manycore, and heterogeneous system architectures are introducing further challenges and possibilities for emerging application domains such as graph applications. This paper explores the space of effective parallel execution of ephemeral graphs that are dynamically generated using the Barnes-Hut algorithm to exemplify dynamic workloads. The workloads are expressed using the semantics of an Exascale computing execution model called ParalleX. For comparison, results using conventional execution model semantics are also presented. We find improved load balancing during runtime and automatic parallelism discovery improving efficiency using the advanced semantics for Exascale computing.Comment: 11 figure

Automated problem scheduling and reduction of synchronization delay effects

It is anticipated that in order to make effective use of many future high performance architectures, programs will have to exhibit at least a medium grained parallelism. A framework is presented for partitioning very sparse triangular systems of linear equations that is designed to produce favorable preformance results in a wide variety of parallel architectures. Efficient methods for solving these systems are of interest because: (1) they provide a useful model problem for use in exploring heuristics for the aggregation, mapping and scheduling of relatively fine grained computations whose data dependencies are specified by directed acrylic graphs, and (2) because such efficient methods can find direct application in the development of parallel algorithms for scientific computation. Simple expressions are derived that describe how to schedule computational work with varying degrees of granularity. The Encore Multimax was used as a hardware simulator to investigate the performance effects of using the partitioning techniques presented in shared memory architectures with varying relative synchronization costs

On partitioning problems with complex objectives

Hypergraph and graph partitioning tools are used to partition work for efficient parallelization of many sparse matrix computations. Most of the time, the objective function that is reduced by these tools relates to reducing the communication requirements, and the balancing constraints satisfied by these tools relate to balancing the work or memory requirements. Sometimes, the objective sought for having balance is a complex function of the partition. We describe some important class of parallel sparse matrix computations that have such balance objectives. For these cases, the current state of the art partitioning tools fall short of being adequate. To the best of our knowledge, there is only a single algorithmic framework in the literature to address such balance objectives. We propose another algorithmic framework to tackle complex objectives and experimentally investigate the proposed framework.Les outils de partitionnement de graphes et d'hypergraphes interviennent pour paralléliser efficacement de nombreux algorithmes liés aux matrices creuses. La plupart du temps, la fonction objectif minimisée par ces outils est liée au besoin de réduire les coûts de communication, tandis que les contraintes d'équilibre à satisfaire sont elles liées à l'équilibrage de la charge ou de la consommation mémoire. Parfois, l'objectif d'équilibre est une fonction complexe du partitionnement. Nous décrivons plusieurs applications majeures de calcul parallèle sur des matrices creuses où de telles contraintes d'équilibre apparaissent. Pour ces exemples, même les outils de partitionnement les plus pointus sont loin d'être adéquats. Pour autant que nous sachions, il n'existe dans la littérature qu'un seul cadre algorithmique qui traite ces problèmes. Nous proposons ici une nouvelle approche algorithmique et fournissons des résultats d'expériences la mettant en œuvre

Semi-Distributed Load Balancing for Massively Parallel Multicomputer Systems

This paper presents a semi-distributed approach, for load balancing in large parallel and distributed systems, which is different from the conventional centralized and fully distributed approaches. The proposed strategy uses a two-level hierarchical control by partitioning the interconnection structure of a distributed or multiprocessor system into independent symmetric regions (spheres) centered at some control points. The central points, called schedulers, optimally schedule tasks within their spheres and maintain state information with low overhead. We consider interconnection structures belonging to a number of families of distance transitive graphs for evaluation, and using their algebraic characteristics, show that identification of spheres and their scheduling points is, in general, an NP-complete problem. An efficient solution for this problem is presented by making an exclusive use of a combinatorial structure known as the Hadamard Matrix. Performance of the proposed strategy has been evaluated and compared with an efficient fully distributed strategy, through an extensive simulation study. In addition to yielding high performance in terms of response time and better resource utilization, the proposed strategy incurs less overhead in terms of control messages. It is also shown to be less sensitive to the communication delay of the underlying network

Parallel implementation of the finite element method on shared memory multiprocessors

PhD ThesisThe work presented in this thesis concerns parallel methods for finite element analysis. The research has been funded by British Gas and some of the presented material involves work on their software. Practical problems involving the finite element method can use a large amount of processing power and the execution times can be very large. It is consequently important to investigate the possibilities for the parallel implementation of the method. The research has been carried out on an Encore Multimax, a shared memory multiprocessor with 14 identical CPU's. We firstly experimented on autoparallelising a large British Gas finite element program (GASP4) using Encore's parallelising Fortran compiler (epf). The par- allel program generated by epj proved not to be efficient. The main reasons are the complexity of the code and small grain parallelism. Since the program is hard to analyse for the compiler at high levels, only small grain parallelism has been inserted automatically into the code. This involves a great deal of low level syn- chronisations which produce large overheads and cause inefficiency. A detailed analysis of the autoparallelised code has been made with a view to determining the reasons for the inefficiency. Suggestions have also been made about writing programs such that they are suitable for efficient autoparallelisation. The finite element method consists of the assembly of a stiffness matrix and the solution of a set of simultaneous linear equations. A sparse representation of the stiffness matrix has been used to allow experimentation on large problems. Parallel assembly techniques for the sparse representation have been developed. Some of these methods have proved to be very efficient giving speed ups that are near ideal. For the solution phase, we have used the preconditioned conjugate gradient method (PCG). An incomplete LU factorization ofthe stiffness matrix with no fill- in (ILU(O)) has been found to be an effective preconditioner. The factors can be obtained at a low cost. We have parallelised all the steps of the PCG method. The main bottleneck is the triangular solves (preconditioning operations) at each step. Two parallel methods of triangular solution have been implemented. One is based on level scheduling (row-oriented parallelism) and the other is a new approach called independent columns (column-oriented parallelism). The algorithms have been tested for row and red-black orderings of the nodal unknowns in the finite element meshes considered. The best speed ups obtained are 7.29 (on 12 processors) for level scheduling and 7.11 (on 12 processors) for independent columns. Red-black ordering gives rise to better parallel performance than row ordering in general. An analysis of methods for the improvement of the parallel efficiency has been made.British Ga

Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author