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16
Combinatorial preconditioners for sparse, symmetric, diagonally dominant linear systems
, 1996
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Performance Evaluation of a New Parallel Preconditioner
 In Proceedings of the Ninth International Parallel Processing Symposium
, 1995
"... The linear systems associated with large, sparse, symmetric, positive definite matrices are often solved iteratively using the preconditioned conjugate gradient method. We have developed a new class of preconditioners, support tree preconditioners, that are based on the connectivity of the graphs co ..."
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Cited by 22 (2 self)
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The linear systems associated with large, sparse, symmetric, positive definite matrices are often solved iteratively using the preconditioned conjugate gradient method. We have developed a new class of preconditioners, support tree preconditioners, that are based on the connectivity of the graphs corresponding to the matrices and are wellstructured for parallel implementation. In this paper, we evaluate the performance of support tree preconditioners by comparing them against two common types of preconditioners: diagonal scaling, and incomplete Cholesky. Support tree preconditioners require less overall storage and less work per iteration than incomplete Cholesky preconditioners. In terms of total execution time, support tree preconditioners outperform both diagonal scaling and incomplete Cholesky preconditioners. 1
Dynamic parallel tree contraction
 In Proceedings 5th Annual ACM Symp. on Parallel Algorithms and Architectures
, 1994
"... Parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of problems with incremental changes in the data. In dynamic tree contraction problems, we are ..."
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Cited by 16 (2 self)
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Parallel tree contraction has been found to be a useful and quite powerful tool for the design of a wide class of efficient graph algorithms. We propose a corresponding technique for the parallel solution of problems with incremental changes in the data. In dynamic tree contraction problems, we are given an initial tree T, and then an online algorithm processes requests regarding T. Requests may be either incremental changes to T or requests for certain values computed using the tree. A simple example is maintaining the preorder numbering on a tree. The online algorithm would then have to handle incremental changes to the tree, and would also have to quickly answer queries about the preorder number of any tree node. Our dynamic algorithms are based on the prior parallel tree contraction algorithms, and hence we call such algorithms incremental tree contraction algorithms. By maintaining the connection between our incremental algorithms and the parallel tree contraction algorithm, we create incremental algorithms for tree contraction. We consider a dynamic binary tree T of ≤ n nodes and unbounded depth. We describe a procedure, which we call the dynamic parallel tree contraction algorithm, which incrementally processes various parallel modification requests and queries: (1) parallel requests to add or delete leaves of T, or modify labels of internal nodes or leaves of T, and also (2) parallel tree contraction queries which require recomputing values at specified nodes. Each modification or query is with respect to a set of nodes U in T. We make use of a random splitting tree as an aid
Graph partitioning into isolated, high conductance clusters: theory, computation and . . .
, 2008
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The Design and Analysis of BulkSynchronous Parallel Algorithms
, 1998
"... The model of bulksynchronous parallel (BSP) computation is an emerging paradigm of generalpurpose parallel computing. This thesis presents a systematic approach to the design and analysis of BSP algorithms. We introduce an extension of the BSP model, called BSPRAM, which reconciles sharedmemory s ..."
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Cited by 10 (1 self)
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The model of bulksynchronous parallel (BSP) computation is an emerging paradigm of generalpurpose parallel computing. This thesis presents a systematic approach to the design and analysis of BSP algorithms. We introduce an extension of the BSP model, called BSPRAM, which reconciles sharedmemory style programming with efficient exploitation of data locality. The BSPRAM model can be optimally simulated by a BSP computer for a broad range of algorithms possessing certain characteristic properties: obliviousness, slackness, granularity. We use BSPRAM to design BSP algorithms for problems from three large, partially overlapping domains: combinatorial computation, dense matrix computation, graph computation. Some of the presented algorithms are adapted from known BSP algorithms (butterfly dag computation, cube dag computation, matrix multiplication). Other algorithms are obtained by application of established nonBSP techniques (sorting, randomised list contraction, Gaussian elimination without pivoting and with column pivoting, algebraic path computation), or use original techniques specific to the BSP model (deterministic list contraction, Gaussian elimination with nested block pivoting, communicationefficient multiplication of Boolean matrices, synchronisationefficient shortest paths computation). The asymptotic BSP cost of each algorithm is established, along with its BSPRAM characteristics. We conclude by outlining some directions for future research.
On the Parallel Complexity of Model Checking in the Modal MuCalculus
 In Proceedings, Ninth Annual IEEE Symposium on Logic in Computer Science
, 1994
"... The modal mucalculus is an expressive logic that can be used to specify safety and liveness properties of concurrent systems represented as labeled transition systems (LTSs). We show that Model Checking in the Modal MuCalculus (MCMMC)  the problem of checking whether an LTS is a model of a form ..."
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Cited by 9 (1 self)
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The modal mucalculus is an expressive logic that can be used to specify safety and liveness properties of concurrent systems represented as labeled transition systems (LTSs). We show that Model Checking in the Modal MuCalculus (MCMMC)  the problem of checking whether an LTS is a model of a formula of the propositional modal mucalculus  is Phard even for a very restrictive version of the problem involving the alternationfree fragment. In particular, MCMMC is Phard even if the formula is fixed and alternationfree, and the LTS is deterministic, acyclic, and has fanin and fanout bounded by 2. The reduction used is from a restricted version of the circuit value problem known as Synchronous Alternating Monotone Fanout 2 Circuit Value Problem. Our Phardness result is tight in the sense that placing any further nontrivial restrictions on either the formula or the LTS results in membership in NC for MCMMC. Specifically, we exhibit NCalgorithms for two potentially useful versio...
Parallel External Memory Graph Algorithms
"... In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one of the privatecache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to solutions for many problems on trees, such as computing the Euler to ..."
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Cited by 8 (3 self)
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In this paper, we study parallel I/O efficient graph algorithms in the Parallel External Memory (PEM) model, one of the privatecache chip multiprocessor (CMP) models. We study the fundamental problem of list ranking which leads to solutions for many problems on trees, such as computing the Euler tour, preorder and postorder numbering of the vertices, the depth of each vertex and the sizes of subtrees rooted at each vertex of the tree. We also study the problems of computing the connected components of a graph and minimum spanning tree of a connected graph. All our solutions provide an optimal speedup of O(p) in parallel I/O complexity compared to the singleprocessor external memory versions of the algorithms. 1
Nbody Simulation I: Fast Algorithms for Potential Field Evaluation and Trummer's Problem
, 1996
"... In this paper, we describe a new approximation algorithm for the nbody problem. The algorithm is a nontrivial modification of the fast multipole method that works in both two and three dimensions. Due to the equivalence between the twodimensional nbody problem and Trummer's problem, our algorith ..."
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Cited by 7 (5 self)
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In this paper, we describe a new approximation algorithm for the nbody problem. The algorithm is a nontrivial modification of the fast multipole method that works in both two and three dimensions. Due to the equivalence between the twodimensional nbody problem and Trummer's problem, our algorithm also gives the fastest known approximation algorithm for Trummer's problem. Let A be the sum of the absolute values of the particle charges in the nbody problem under consideration (or the sum of the masses if the simulation is gravitational). To approximate the particle potentials with error bound ffl, we let p = dlog(A=ffl)e and give complexity bounds in terms of p. Note that, under reasonable assumptions on the particle charges, if we desire the output to be accurate to b bits, then p = \Theta(b). In two dimensions, our algorithm runs in time O(n log 2 p), which is a substantial improvement over the previous best algorithm which requires \Theta(np log p) time. We also apply our new ...
Reconstructing a Minimum Spanning Tree after Deletion of Any Node
 Algorithmica
, 1999
"... Updating a minimum spanning tree (MST) is a basic problem for communication networks. In this paper, we consider single node deletions in MSTs. Let G = (V; E) be an undirected graph with n nodes and m edges, and let T be the MST of G. For each node v in V , the node replacement for v is the minim ..."
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Cited by 6 (0 self)
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Updating a minimum spanning tree (MST) is a basic problem for communication networks. In this paper, we consider single node deletions in MSTs. Let G = (V; E) be an undirected graph with n nodes and m edges, and let T be the MST of G. For each node v in V , the node replacement for v is the minimum weight set of edges R(v) that connect the components of T \Gamma v. We present a sequential algorithm and a parallel algorithm that find R(v) for all V simultaneously. The sequential algorithm takes O(m log n) time, but only O(mff(m; n)) time when the edges of E are presorted by weight. The parallel algorithm takes O(log 2 n) time using m processors on a CREW PRAM. 2 1 INTRODUCTION For communication networks, minimum spanning trees (MSTs) are used for basic network tasks such as broadcast, leader election, and synchronization. Updating the MST after changes in network topology is a fundamental problem. In this paper, we update MSTs after single node deletions. In a graph G with ...
Parallel Priority Queue and List Contraction: The BSP Approach
 In Proc. EuroPar 97. LNCS
, 1997
"... . In this paper we present efficient and practical extensions of the randomized Parallel Priority Queue (PPQ) algorithms of Ranade et al., and efficient randomized and deterministic algorithms for the problem of list contraction on the BulkSynchronous Parallel (BSP) model. We also present an experi ..."
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Cited by 5 (0 self)
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. In this paper we present efficient and practical extensions of the randomized Parallel Priority Queue (PPQ) algorithms of Ranade et al., and efficient randomized and deterministic algorithms for the problem of list contraction on the BulkSynchronous Parallel (BSP) model. We also present an experimental study of their performance. We show that our algorithms are communication efficient and achieve small multiplicative constant factors for a wide range of parallel machines. 1 Introduction We present an architecture independent study of the computation and communication requirements of an efficient Parallel Priority Queue (PPQ) implementation and list contraction algorithms along with an experimental study. The computational model adopted is the BulkSynchronous Parallel (BSP) model, proposed by L. G. Valiant [20], which deals explicitly with the notion of communication and synchronization among computational threads. A detailed discussion of the BSP model appears in [20]. The first a...