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22
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
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Cited by 1173 (16 self)
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Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering
, 1996
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Analysis of multilevel graph partitioning
, 1995
"... Recently, a number of researchers have investigated a class of algorithms that are based on multilevel graph partitioning that have moderate computational complexity, and provide excellent graph partitions. However, there exists little theoretical analysis that could explain the ability of multileve ..."
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Cited by 107 (14 self)
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Recently, a number of researchers have investigated a class of algorithms that are based on multilevel graph partitioning that have moderate computational complexity, and provide excellent graph partitions. However, there exists little theoretical analysis that could explain the ability of multilevel algorithms to produce good partitions. In this paper we present such an analysis. We show under certain reasonable assumptions that even if no refinement is used in the uncoarsening phase, a good bisection of the coarser graph is worse than a good bisection of the finer graph by at most a small factor. We also show that the size of a good vertexseparator of the coarse graph projected to the finer graph (without performing refinement in the uncoarsening phase) is higher than the size of a good vertexseparator of the finer graph by at most a small factor.
An Efficient Partitioning Algorithm for Distributed Virtual Environment Systems
 IEEE TRANS. PARALLEL AND DISTRIBUTED SYSTEMS
, 2002
"... Distributed virtual environment (DVE) systems model and simulate the activities of thousands of entities interacting in a virtual world over a wide area network. Possible applications for DVE systems are multiplayer video games, military and industrial trainings, and collaborative engineering. In ge ..."
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Cited by 72 (0 self)
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Distributed virtual environment (DVE) systems model and simulate the activities of thousands of entities interacting in a virtual world over a wide area network. Possible applications for DVE systems are multiplayer video games, military and industrial trainings, and collaborative engineering. In general, a DVE system is composed of many servers and each server is responsible to manage multiple clients who want to participate in the virtual world. Each server receives updates from different clients (such as the current position and orientation of each client) and then delivers this information to other clients in the virtual world. The server also needs to perform other tasks, such as object collision detection and synchronization control. A large scale DVE system needs to support many clients and this imposes a heavy requirement on networking resources and computational resources. Therefore, how to meet the growing requirement of bandwidth and computational resources is one of the major challenges in designing a scalable and costeffective DVE system. In this paper, we propose an efficient partitioning algorithm that addresses the scalability issue of designing a large scale DVE system. The main idea is to dynamically divide the virtual world into different partitions and then efficiently assign these partitions to different servers. This way, each server will process approximately the same amount of workload. Another objective of the partitioning algorithm is to reduce the servertoserver communication overhead. The theoretical foundation of our dynamic partitioning algorithm is based on the linear optimization principle. We also illustrate how one can parallelize the proposed partitioning algorithm so that it can efficiently partition a very large scale DVE system. Lastly, experiments are carried out to illustrate the effectiveness of the proposed partitioning algorithm under various settings of the virtual world.
A CoarseGrain Parallel Formulation of Multilevel kway Graph Partitioning Algorithm
 PARALLEL PROCESSING FOR SCIENTIFIC COMPUTING. SIAM
, 1997
"... In this paper we present a parallel formulation of a multilevel kway graph partitioning algorithm, that is particularly suited for messagepassing libraries that have high latency. The multilevel kway partitioning algorithm reduces the size of the graph by successively collapsing vertices and edge ..."
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Cited by 45 (0 self)
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In this paper we present a parallel formulation of a multilevel kway graph partitioning algorithm, that is particularly suited for messagepassing libraries that have high latency. The multilevel kway partitioning algorithm reduces the size of the graph by successively collapsing vertices and edges (coarsening phase), finds a kway partitioning of the smaller graph, and then it constructs a kway partitioning for the original graph by projecting and refining the partition to successively finer graphs (uncoarsening phase). Our algorithm is able to achieve a high degree of concurrency, while maintaining the high quality partitions produced by the serial algorithm.
Multilevel Graph Partitioning Schemes
 Proc. 24th Intern. Conf. Par. Proc., III
, 1995
"... Abstract – In this paper we present experiments with a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph. We investigate the effectiveness of ma ..."
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Cited by 40 (0 self)
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Abstract – In this paper we present experiments with a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph. We investigate the effectiveness of many different choices for all three phases: coarsening, partition of the coarsest graph, and refinement. In particular, we present a new coarsening heuristic (called heavyedge heuristic) for which the size of the partition of the coarse graph is within a small factor of the size of the final partition obtained after multilevel refinement. We also present a new scheme for refining during uncoarsening that is much faster than the KernighanLin refinement. We test our scheme on a large number of graphs arising in various domains including finite element methods, linear programming, VLSI, and transportation. Our experiments show that our scheme consistently produces partitions that are better than those produced by spectral partitioning schemes in substantially smaller timer (10 to 35 times faster than multilevel spectral bisection). Also, when our scheme is used to compute fill reducing orderings for sparse matrices, it substantially outperforms the widely used multiple minimum degree algorithm. 1
Architecture aware partitioning algorithms
, 2006
"... Existing partitioning algorithms provide limited support for load balancing simulations that are performed on heterogeneous parallel computing platforms. On such architectures, effective load balancing can only be achieved if the graph is distributed so that it properly takes into account the availa ..."
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Cited by 10 (0 self)
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Existing partitioning algorithms provide limited support for load balancing simulations that are performed on heterogeneous parallel computing platforms. On such architectures, effective load balancing can only be achieved if the graph is distributed so that it properly takes into account the available resources (CPU speed, network bandwidth). With heterogeneous technologies becoming more popular, the need for suitable graph partitioning algorithms is critical. We developed such algorithms that can address the partitioning requirements of scientific computations, and can correctly model the architectural characteristics of emerging hardware platforms.
A Scalable Diffusion Algorithm For Dynamic Mapping And Load Balancing On Networks Of Arbitrary Topology
, 1997
"... The problems of mapping and load balancing applications on arbitrary networks are considered. A novel diffusion algorithm is presented to solve the mapping problem. It complements the well known diffusion algorithms for load balancing which have enjoyed success on massively parallel computers (MPPs) ..."
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Cited by 6 (5 self)
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The problems of mapping and load balancing applications on arbitrary networks are considered. A novel diffusion algorithm is presented to solve the mapping problem. It complements the well known diffusion algorithms for load balancing which have enjoyed success on massively parallel computers (MPPs). Mapping is more difficult on interconnection networks than on MPPs because of the variations which occur in network topology. Popular mapping algorithms for MPPs which depend on recursive topologies are not applicable to irregular networks. The most celebrated of these MPP algorithms use information from the Laplacian matrix of a graph of communicating processes. The diffusion algorithm presented in this paper is also derived from this Laplacian matrix. The diffusion algorithm works on arbitrary network topologies and is dramatically faster than the celebrated MPP algorithms. It is delay and fault tolerant. Time to convergence depends on initial conditions and is insensitive to problem sca...
Analysis of Scalable Algorithms for Dynamic Load Balancing and Mapping with Application to Photorealistic Rendering
, 1998
"... This thesis presents and analyzes scalable algorithms for dynamic load balancing and mapping in distributed computer systems. The algorithms are distributed and concurrent, have no central thread of control, and require no centralized communication. They are derived using spectral properties of grap ..."
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Cited by 4 (0 self)
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This thesis presents and analyzes scalable algorithms for dynamic load balancing and mapping in distributed computer systems. The algorithms are distributed and concurrent, have no central thread of control, and require no centralized communication. They are derived using spectral properties of graphs: graphs of physical network links among computers in the load balancing problem, and graphs of logical communication channels among processes in the mapping problem. A distinguishing characteristic of these algorithms is that they are scalable: the expected cost of execution does not increase with problem scale. This is proven in a scalability theorem which shows that, for several simple disturbance models, the rate of convergence to a solution is independent of scale. This property is extended through simulated examples and informal argument to general and random disturbances. A worst case disturbance is presented and shown to occur with vanishing probability as the problem scale increas...