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Fast SharedMemory Algorithms for Computing the Minimum Spanning Forest of Sparse Graphs
, 2006
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Practical Parallel Algorithms for Minimum Spanning Trees
 In Workshop on Advances in Parallel and Distributed Systems
, 1998
"... We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns ..."
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Cited by 16 (0 self)
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We study parallel algorithms for computing the minimum spanning tree of a weighted undirected graph G with n vertices and m edges. We consider an input graph G with m=n p, where p is the number of processors. For this case, we show that simple algorithms with dataindependent communication patterns are efficient, both in theory and in practice. The algorithms are evaluated theoretically using Valiant's BSP model of parallel computation and empirically through implementation results.
MST Construction in O(log log n) Communication Rounds
 In Proceedings of the 15 th ACM symposium on Parallel Algorithms and Architectures (SPAA
, 2003
"... We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm that constructs a minimumweight spanning tree in O(log log n) communication rounds, where i ..."
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Cited by 9 (1 self)
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We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm that constructs a minimumweight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to each other process. This result is the first to break the Ω(log n) parallel time complexity barrier with small message sizes. 1.
Emulations Between QSM, BSP and LogP: A Framework for GeneralPurpose Parallel Algorithm Design
, 1998
"... We present workpreserving emulations with small slowdown between LogP and two other parallel models: BSP and QSM. In conjunction with earlier workpreserving emulations between QSM and BSP these results establish a close correspondence between these three generalpurpose parallel models. Our result ..."
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Cited by 8 (1 self)
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We present workpreserving emulations with small slowdown between LogP and two other parallel models: BSP and QSM. In conjunction with earlier workpreserving emulations between QSM and BSP these results establish a close correspondence between these three generalpurpose parallel models. Our results also correct and improve on results reported earlier on emulations between BSP and LogP. In particular we shed new light on the relative power of stalling and nonstalling LogP models. The QSM is a sharedmemory model with only two parameters –p, the number of processors, and g, a bandwidth parameter. These features of the QSM make it a convenient model for parallel algorithm design, and the simple workpreserving emulations of QSM on BSP and LogP show that algorithms designed on the QSM will map well on to these other models. This presents a strong case for the use of QSM as the model of choice for parallel algorithm design. We present QSM algorithms for three basic problems – prefix sums, sample sort and list ranking. Using appropriate cost measures, we analyze the performance of these algorithms and describe simulation results. These results suggest that QSM analysis will predict algorithm performance quite accurately for problem sizes that arise in practice.
Composition of Efficient Nested BSP Algorithms: Minimum Spanning Tree Computation as an Instructive Example
 In International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA
, 2002
"... We report on the results of an automatic configuration approach for implementing complex parallel BSP algorithms. For this approach, a parallel algorithm is described by a sequence of instructions and of subproblems that have to be solved by other parallel algorithms called as subroutines, together ..."
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Cited by 7 (1 self)
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We report on the results of an automatic configuration approach for implementing complex parallel BSP algorithms. For this approach, a parallel algorithm is described by a sequence of instructions and of subproblems that have to be solved by other parallel algorithms called as subroutines, together with a mathematical description of its own running time. There also may be free algorithmic parameters as, e. g., the degree of trees in used data structures that have an impact on the running time. As the running time of an algorithm depends on several machine parameters, on some fixed and on the choice of the free algorithmic parameters and on the choice of the parallel subroutines for which the same statement applies in turn, the actual composition of the parallel program for an actual parallel machine from all these ingredients is a difficult task. We have implemented such a configuration system using the Paderborn University BSP library and present as an instructive example the theoretical and experimental results of implementations of sophisticated minimum spanning tree algorithms. 1
MinimumWeight Spanning Tree Construction in O(log log n) Communication Rounds
 SIAM J. Comput
, 2005
"... Abstract. We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm which constructs a minimumweight spanning tree in O(log log n) communication rou ..."
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Cited by 7 (1 self)
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Abstract. We consider a simple model for overlay networks, where all n processes are connected to all other processes, and each message contains at most O(log n) bits. For this model, we present a distributed algorithm which constructs a minimumweight spanning tree in O(log log n) communication rounds, where in each round any process can send a message to every other process. If message size is Θ(n ɛ) for some ɛ>0, then the number of communication rounds is O(log 1 ɛ).
STUDY OF PARALLEL GRAPH ALGORITHMS FOR MINIMUM SPANNING TREE AND ALLPAIRS SHORTESTPATHS USING A LARGE SCALE CLUSTER APPROVED:
, 2006
"... This research studies two graph problems: minimum spanning tree and allpairs shortestpaths. The minimum spanning tree is a classical network optimization problem that is encountered in the design of physical systems such as computer chips as well as in communication systems that provide the necess ..."
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This research studies two graph problems: minimum spanning tree and allpairs shortestpaths. The minimum spanning tree is a classical network optimization problem that is encountered in the design of physical systems such as computer chips as well as in communication systems that provide the necessary infrastructure to connect geographically dispersed elements. The allpairs shortest path problem is a fundamental problem in computer aided design (CAD) of very large scale integrated (VLSI) circuits, and in the study of transportation and communication networks. This thesis presents parallel implementation of Prim’s minimum spanning tree algorithm and Dijkstra’s allpairs shortestpaths algorithm that are designed directly for message passing network and find out their performances on cluster of workstations containing up to 50processors. From the experimental study, it is found that Prim’s algorithm is not computationaly feasible for our distributed computing model as it is using slower communication backbone. For Dijkstra’s
The Paderborn University BSP (PUB) Library on the Cray T3E
, 2000
"... The Paderborn University BSP (PUB) library is a C communication library based on the BSP model. The basic library supports buered as well as unbuered nonblocking communication between any pair of processors and a mechanism for synchronizing the processors in a barrier style. In addition, it prov ..."
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The Paderborn University BSP (PUB) library is a C communication library based on the BSP model. The basic library supports buered as well as unbuered nonblocking communication between any pair of processors and a mechanism for synchronizing the processors in a barrier style. In addition, it provides routines for collective communication on arbitrary subsets of processors, the ability to partition the processors into independent groups, and a zerocost synchronization mechanism. Techniques which are used to implement PUB on the Cray T3E are presented and the performance compared to MPI and to other BSP libraries are shown. 1 Introduction Most messagepassing libraries are based on pairwise sends and receives. This means that for each send operation, a matching receive has to be issued on the destination processor. Widely available messagepassing libraries like PVM[GBD + 94] and MPI[Mes93] provide the user with this kind of programming model. This approach, however, is ver...