Results 1  10
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193
METIS: A software package for partitioning unstructured graphs, partitioning meshes, and computing fillreducing orderings of sparse matrices”,
, 1997
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Multilevel kway Hypergraph Partitioning
, 1999
"... In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on ..."
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Cited by 168 (11 self)
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In this paper, we present a new multilevel kway hypergraph partitioning algorithm that substantially outperforms the existing stateoftheart KPM/LR algorithm for multiway partitioning, both for optimizing local as well as global objectives. Experiments on
Graph mining: laws, generators, and algorithms
 ACM COMPUT SURV (CSUR
, 2006
"... How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in ..."
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Cited by 132 (7 self)
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How does the Web look? How could we tell an abnormal social network from a normal one? These and similar questions are important in many fields where the data can intuitively be cast as a graph; examples range from computer networks to sociology to biology and many more. Indeed, any M: N relation in database terminology can be represented as a graph. A lot of these questions boil down to the following: “How can we generate synthetic but realistic graphs? ” To answer this, we must first understand what patterns are common in realworld graphs and can thus be considered a mark of normality/realism. This survey give an overview of the incredible variety of work that has been done on these problems. One of our main contributions is the integration of points of view from physics, mathematics, sociology, and computer science. Further, we briefly describe recent advances on some related and interesting graph problems.
Asynchronous Variational Integrators
 ARCH. RATIONAL MECH. ANAL.
, 2003
"... We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation t ..."
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Cited by 62 (10 self)
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We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton’s variational principle. As a consequence of this variational structure, the algorithms conserve local momenta and a local discrete multisymplectic structure exactly. To guide the development of the discretizations, a spacetime multisymplectic formulation of elastodynamics is presented. The variational principle used incorporates both configuration and spacetime reference variations. This allows a unified treatment of all the conservation properties of the system. A discrete version of reference configuration is also considered, providing a natural definition of a discrete energy. The possibilities for discrete energy conservation are evaluated. Numerical tests reveal that, even when local energy balance is not enforced exactly, the global and local energy behavior of the AVIs is quite remarkable, a property which can probably be traced to the symplectic nature of the algorithm.
Multilevel Refinement for Combinatorial Optimisation Problems
 SE10 9LS
, 2001
"... Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (some ..."
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Cited by 57 (5 self)
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Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.
Permuting Sparse Rectangular Matrices into BlockDiagonal Form
 SIAM Journal on Scientific Computing
, 2002
"... We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. W ..."
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Cited by 56 (18 self)
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We investigate the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose bipartite graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Our experiments on a wide range of matrices, using stateoftheart graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime.
ACHIEVING HIGH PERFORMANCE ON EXTREMELY LARGE PARALLEL MACHINES: PERFORMANCE PREDICTION AND LOAD BALANCING
, 2005
"... Parallel machines with an extremely large number of processors (at least tens of thousands processors) are now in operation. For example, the IBM BlueGene/L machine with 128K processors is currently being deployed. It is going to be a significant challenge for application developers to write paralle ..."
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Cited by 51 (8 self)
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Parallel machines with an extremely large number of processors (at least tens of thousands processors) are now in operation. For example, the IBM BlueGene/L machine with 128K processors is currently being deployed. It is going to be a significant challenge for application developers to write parallel programs in order to exploit the enormous compute power available and manually scale their applications on such machines. Solving these problems involves finding suitable parallel programming models for such machines and addressing issues like load imbalance. In this thesis, we explore Charm++ programming model and its migratable objects for programming such machines and dynamic load balancing techniques to help parallel applications to easily scale on a large number of processors. We also present a parallel simulator that is capable of predicting parallel performance to help analysis and tuning of the parallel performance and facilitate the development of new load balancing techniques, even before such machines are built. We evaluate the idea of virtualization and its usefulness in helping a programmer to write applications with high degree of parallelism. We demonstrate it by developing several miniapplications with millionway parallelism. We show that Charm++ and AMPI (an extension to MPI) with migratable objects and
A unified algorithm for loadbalancing adaptive scientific simulations
 In Proceedings of the ACM/IEEE Symposium on Supercomputing (SC’00). IEEE Computer
, 2000
"... Adaptive scientific simulations require that periodic repartitioning occur dynamically throughout the course of the computation. The repartitionings should be computed so as to minimize both the interprocessor communications incurred during the iterative meshbased computation and the data redistri ..."
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Cited by 50 (2 self)
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Adaptive scientific simulations require that periodic repartitioning occur dynamically throughout the course of the computation. The repartitionings should be computed so as to minimize both the interprocessor communications incurred during the iterative meshbased computation and the data redistribution costs required to balance the load. Recently developed schemes for computing repartitionings provide the user with only a limited control of the tradeoffs among these objectives. This paper describes a new Unified Repartitioning Algorithm that can tradeoff one objective for the other dependent upon a userdefined parameter describing the relative costs of these objectives. We show that the Unified Repartitioning Algorithm is able to reduce the precise overheads associated with repartitioning as well as or better than other repartitioning schemes for a variety of problems, regardless of the relative costs of performing interprocessor communication and data redistribution. Our experimental results show that this scheme is extremely fast and scalable to large problems.