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A Fast, Parallel Spanning Tree Algorithm for Symmetric Multiprocessors (SMPs) (Extended Abstract)
, 2004
"... Our study in this paper focuses on implementing parallel spanning tree algorithms on SMPs. Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial probl ..."
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Cited by 31 (11 self)
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Our study in this paper focuses on implementing parallel spanning tree algorithms on SMPs. Spanning tree is an important problem in the sense that it is the building block for many other parallel graph algorithms and also because it is representative of a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but often have no known efficient parallel implementations. In this paper we present a new randomized algorithm and implementation with superior performance that for the firsttime achieves parallel speedup on arbitrary graphs (both regular and irregular topologies) when compared with the best sequential implementation for finding a spanning tree. This new algorithm uses several techniques to give an expected running time that scales linearly with the number p of processors for suitably large inputs (n> p 2). As the spanning tree problem is notoriously hard for any parallel implementation to achieve reasonable speedup, our study may shed new light on implementing PRAM algorithms for sharedmemory parallel computers. The main results of this paper are 1. A new and practical spanning tree algorithm for symmetric multiprocessors that exhibits parallel speedups on graphs with regular and irregular topologies; and 2. An experimental study of parallel spanning tree algorithms that reveals the superior performance of our new approach compared with the previous algorithms. The source code for these algorithms is freelyavailable from our web site hpc.ece.unm.edu.
Fast SharedMemory Algorithms for Computing the Minimum Spanning Forest of Sparse Graphs
, 2006
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On the architectural requirements for efficient execution of graph algorithms
 In Proc. 34th Int’l Conf. on Parallel Processing (ICPP
, 2005
"... Combinatorial problems such as those from graph theory pose serious challenges for parallel machines due to noncontiguous, concurrent accesses to global data structures with low degrees of locality. The hierarchical memory systems of symmetric multiprocessor (SMP) clusters optimize for local, conti ..."
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Cited by 15 (7 self)
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Combinatorial problems such as those from graph theory pose serious challenges for parallel machines due to noncontiguous, concurrent accesses to global data structures with low degrees of locality. The hierarchical memory systems of symmetric multiprocessor (SMP) clusters optimize for local, contiguous memory accesses, and so are inefficient platforms for such algorithms. Few parallel graph algorithms outperform their best sequential implementation on SMP clusters due to long memory latencies and high synchronization costs. In this paper, we consider the performance and scalability of two graph algorithms, list ranking and connected components, on two classes of sharedmemory computers: symmetric multiprocessors such as the Sun Enterprise servers and multithreaded architectures
Randomized Minimum Spanning Tree Algorithms Using Exponentially Fewer Random Bits
"... For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel mi ..."
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Cited by 1 (0 self)
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For many fundamental problems there exist randomized algorithms that are asymptotically optimal and are superior to the best known deterministic algorithm. Among these are the minimum spanning tree (MST) problem, the MST sensitivity analysis problem, the parallel connected components and parallel minimum spanning tree problems, and the local sorting and set maxima problems. (For the first two problems there are provably optimal deterministic algorithms with unknown, and possibly superlinear running times.) One downside of the randomized methods for solving these problems is that they use a number of random bits linear in the size of the input. In this paper we develop some general methods for reducing exponentially the consumption of random bits in comparison based algorithms. In some cases we are able to reduce the number of random bits from linear to nearly constant without affecting the expected running time. Most of our results are obtained by adjusting or reorganizing existing randomized algorithms to work well with a pairwise or O(1)wise independent sampler. The prominent exception — and the main focus of this paper — is a lineartime randomized minimum spanning tree algorithm that is not derived from the well known KargerKleinTarjan algorithm. In many ways it resembles more closely the deterministic minimum spanning tree algorithms based on Soft Heaps. Further,
Parametric Control of Captured Mesh Sequences for Realtime Animation
"... Abstract. In this paper we introduce an approach to highlevel parameterisation of captured mesh sequences of actor performance for realtime interactive animation control. Highlevel parametric control is achieved by nonlinear blending between multiple mesh sequences exhibiting variation in a part ..."
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Abstract. In this paper we introduce an approach to highlevel parameterisation of captured mesh sequences of actor performance for realtime interactive animation control. Highlevel parametric control is achieved by nonlinear blending between multiple mesh sequences exhibiting variation in a particular movement. For example walking speed is parameterised by blending fast and slow walk sequences. A hybrid nonlinear mesh sequence blending approach is introduced to approximate the natural deformation of nonlinear interpolation techniques whilst maintaining the realtime performance of linear mesh blending. Quantitative results show that the hybrid approach gives an accurate realtime approximation of offline nonlinear deformation. Results are presented for single and multidimensional parametric control of walking (speed/direction), jumping (heigh/distance) and reaching (height) from captured mesh sequences. This approach allows continuous realtime control of highlevel parameters such as speed and direction whilst maintaining the natural surface dynamics of captured movement.
International Journal of Soft Computing, Mathematics and Control (IJSCMC),Vol.2,No.2,May 2013 A NEW PARALLEL ALGORITHM FOR COMPUTING MINIMUM SPANNING TREE
"... Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to red ..."
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Computing the minimum spanning tree of the graph is one of the fundamental computational problems. In this paper, we present a new parallel algorithm for computing the minimum spanning tree of an undirected weighted graph with n vertices and m edges. This algorithm uses the cluster techniques to reduce the number of processors by fraction 1/() f n and the parallel work by the fraction O ( 1 lo g(()) f n),where f() n is an arbitrary function. In the case f() n 1 = , the algorithm runs in logarithmictime and use super linear work on EREWPRAM model. In general, the proposed algorithm is the simplest one.