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Programming Parallel Algorithms
, 1996
"... In the past 20 years there has been treftlendous progress in developing and analyzing parallel algorithftls. Researchers have developed efficient parallel algorithms to solve most problems for which efficient sequential solutions are known. Although some ofthese algorithms are efficient only in a th ..."
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Cited by 237 (11 self)
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In the past 20 years there has been treftlendous progress in developing and analyzing parallel algorithftls. Researchers have developed efficient parallel algorithms to solve most problems for which efficient sequential solutions are known. Although some ofthese algorithms are efficient only in a theoretical framework, many are quite efficient in practice or have key ideas that have been used in efficient implementations. This research on parallel algorithms has not only improved our general understanding ofparallelism but in several cases has led to improvements in sequential algorithms. Unf:ortunately there has been less success in developing good languages f:or prograftlftling parallel algorithftls, particularly languages that are well suited for teaching and prototyping algorithms. There has been a large gap between languages
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 47 (13 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.
Can a SharedMemory Model Serve as a Bridging Model for Parallel Computation?
, 1999
"... There has been a great deal of interest recently in the development of generalpurpose bridging models for parallel computation. Models such as the BSP and LogP have been proposed as more realistic alternatives to the widely used PRAM model. The BSP and LogP models imply a rather different style fo ..."
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Cited by 40 (12 self)
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There has been a great deal of interest recently in the development of generalpurpose bridging models for parallel computation. Models such as the BSP and LogP have been proposed as more realistic alternatives to the widely used PRAM model. The BSP and LogP models imply a rather different style for designing algorithms when compared with the PRAM model. Indeed, while many consider data parallelism as a convenient style, and the sharedmemory abstraction as an easytouse platform, the bandwidth limitations of current machines have diverted much attention to messagepassing and distributedmemory models (such as the BSP and LogP) that account more properly for these limitations. In this paper we consider the question of whether a sharedmemory model can serve as an effective bridging model for parallel computation. In particular, can a sharedmemory model be as effective as, say, the BSP? As a candidate for a bridging model, we introduce the Queuing SharedMemory (QSM) model, which accounts for limited communication bandwidth while still providing a simple sharedmemory abstraction. We substantiate the ability of the QSM to serve as a bridging model by providing a simple workpreserving emulation of the QSM on both the BSP, and on a related model, the (d, x)BSP. We present evidence that the features of the QSM are essential to its effectiveness as a bridging model. In addition, we describe scenarios
Fast SharedMemory Algorithms for Computing the Minimum Spanning Forest of Sparse Graphs
, 2006
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Accounting for memory bank contention and delay in highbandwidth multiprocessors
 In Proc. 7th ACM Symp. on Parallel Algorithms and Architectures
, 1997
"... Abstract—For years, the computation rate of processors has been much faster than the access rate of memory banks, and this divergence in speeds has been constantly increasing in recent years. As a result, several sharedmemory multiprocessors consist of more memory banks than processors. The object ..."
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Cited by 30 (4 self)
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Abstract—For years, the computation rate of processors has been much faster than the access rate of memory banks, and this divergence in speeds has been constantly increasing in recent years. As a result, several sharedmemory multiprocessors consist of more memory banks than processors. The object of this paper is to provide a simple model (with only a few parameters) for the design and analysis of irregular parallel algorithms that will give a reasonable characterization of performance on such machines. For this purpose, we extend Valiant’s bulksynchronous parallel (BSP) model with two parameters: a parameter for memory bank delay, the minimum time for servicing requests at a bank, and a parameter for memory bank expansion, the ratio of the number of banks to the number of processors. We call this model the (d, x)BSP. We show experimentally that the (d, x)BSP captures the impact of bank contention and delay on the CRAY C90 and J90 for irregular access patterns, without modeling machinespecific details of these machines. The model has clarified the performance characteristics of several unstructured algorithms on the CRAY C90 and J90, and allowed us to explore tradeoffs and optimizations for these algorithms. In addition to modeling individual algorithms directly, we also consider the use of the (d, x)BSP as a bridging model for emulating a very highlevel abstract model, the Parallel Random Access Machine (PRAM). We provide matching upper and lower bounds for emulating the EREW and QRQW PRAMs on the (d, x)BSP.
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 27 (10 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
Parallel Implementation of Algorithms for Finding Connected Components in Graphs
, 1997
"... In this paper, we describe our implementation of several parallel graph algorithms for finding connected components. Our implementation, with virtual processing, is on a 16,384processor MasPar MP1 using the language MPL. We present extensive test data on our code. In our previous projects [21, 22, ..."
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Cited by 25 (1 self)
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In this paper, we describe our implementation of several parallel graph algorithms for finding connected components. Our implementation, with virtual processing, is on a 16,384processor MasPar MP1 using the language MPL. We present extensive test data on our code. In our previous projects [21, 22, 23], we reported the implementation of an extensible parallel graph algorithms library. We developed general implementation and finetuning techniques without expending too much effort on optimizing each individual routine. We also handled the issue of implementing virtual processing. In this paper, we describe several algorithms and finetuning techniques that we developed for the problem of finding connected components in parallel; many of the finetuning techniques are of general interest, and should be applicable to code for other problems. We present data on the execution time and memory usage of our various implementations.
A Comparison of Parallel Algorithms for Connected Components
 in the Symposium on Parallel Algorithms and Architectures
, 1994
"... This paper presents a comparison of the pragmatic aspects of some parallel algorithms for finding connected components, together with optimizations on these algorithms. The algorithms being compared are two similar algorithms by ShiloachVishkin [22] and AwerbuchShiloach [2], a randomized contracti ..."
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Cited by 23 (1 self)
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This paper presents a comparison of the pragmatic aspects of some parallel algorithms for finding connected components, together with optimizations on these algorithms. The algorithms being compared are two similar algorithms by ShiloachVishkin [22] and AwerbuchShiloach [2], a randomized contraction algorithm based on algorithms by Reif [21] and Phillips [20], and a hybrid algorithm [11]. Improvements are given for the first two to improve performance significantly, although without improving their asymptotic complexity. The hybrid combines features of the others and is generally the fastest of those tested. Timings were made using NESL [4] code as executed on a Connection Machine 2 and Cray YMP/C90. 1 Introduction The complexity of various PRAM algorithms has received much attention, but there has been relatively little work on the implementation and pragmatic efficiency of many of these algorithms. Moreover, much of this work has been for algorithms having regular communication ...
Connected Components Algorithms For MeshConnected Parallel Computers
 PARALLEL ALGORITHMS: 3RD DIMACS IMPLEMENTATION CHALLENGE OCTOBER 1719, 1994, VOLUME 30 OF DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1995
"... We present a new CREW PRAM algorithm for finding connected components. For a graph G with n vertices and m edges, algorithmA 0 requires at most O(logn) parallel steps and performs O((n+m) log n) work in the worst case. The advantage our algorithm has over others in the literature is that it can be ..."
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Cited by 14 (0 self)
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We present a new CREW PRAM algorithm for finding connected components. For a graph G with n vertices and m edges, algorithmA 0 requires at most O(logn) parallel steps and performs O((n+m) log n) work in the worst case. The advantage our algorithm has over others in the literature is that it can be adapted to a 2D meshconnected communication model in which all CREW operations are replaced by O(logn) parallel row and column operations without increasing the time complexity. We present the mapping of A 0 to a meshconnected computer and describe two implementations, A 1 and A 2 . Algorithm A 1 , which uses an adjacency matrix to represent the graph, performs O(n 2 log n) work. Hence, it only achieves work efficiency on dense graphs. The second implementation, A 2 , uses a sparse representation of the adjacency matrix and again performs O(logn) row and column operations but reduces the work to O((m + n) log n) on all graphs. We report MasPar MP1 performance figures for implementati...
Practical Parallel DivideandConquer Algorithms
, 1997
"... Nested data parallelism has been shown to be an important feature of parallel languages, allowing the concise expression of algorithms that operate on irregular data structures such as graphs and sparse matrices. However, previous nested dataparallel languages have relied on a vector PRAM impleme ..."
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Cited by 7 (2 self)
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Nested data parallelism has been shown to be an important feature of parallel languages, allowing the concise expression of algorithms that operate on irregular data structures such as graphs and sparse matrices. However, previous nested dataparallel languages have relied on a vector PRAM implementation layer that cannot be efficiently mapped to MPPs with high interprocessor latency. This thesis shows that by restricting the problem set to that of dataparallel divideandconquer algorithms I can maintain the expressibility of full nested dataparallel languages while achieving good efficiency on current distributedmemory machines. Specifically, I define