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16
Efficient parallel graph algorithms for coarse grained multicomputers and BSP (Extended Abstract)
 in Proc. 24th International Colloquium on Automata, Languages and Programming (ICALP'97
, 1997
"... In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and bulksynchronous parallel computer (BSP) models which solve the following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and s ..."
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Cited by 62 (22 self)
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In this paper, we present deterministic parallel algorithms for the coarse grained multicomputer (CGM) and bulksynchronous parallel computer (BSP) models which solve the following well known graph problems: (1) list ranking, (2) Euler tour construction, (3) computing the connected components and spanning forest, (4) lowest common ancestor preprocessing, (5) tree contraction and expression tree evaluation, (6) computing an ear decomposition or open ear decomposition, (7) 2edge connectivity and biconnectivity (testing and component computation), and (8) cordal graph recognition (finding a perfect elimination ordering). The algorithms for Problems 17 require O(log p) communication rounds and linear sequential work per round. Our results for Problems 1 and 2, i.e.they are fully scalable, and for Problems hold for arbitrary ratios n p 38 it is assumed that n p,>0, which is true for all commercially
CGMgraph/CGMlib: Implementing and Testing CGM Graph Algorithms on PC Clusters
 International Journal of High Performance Computing Applications
, 2003
"... In this paper, we present CGMgraph, the first integrated library of parallel graph methods for PCclu8(T9 based on CGM algo rithms. CGMgraph implements parallel methods for variou graph prob lems. Ou implementations of deterministic list ranking, Eu er tou con nected components, spanning forest, and ..."
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Cited by 25 (2 self)
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In this paper, we present CGMgraph, the first integrated library of parallel graph methods for PCclu8(T9 based on CGM algo rithms. CGMgraph implements parallel methods for variou graph prob lems. Ou implementations of deterministic list ranking, Eu er tou con nected components, spanning forest, and bipartite graph detection are, to ou r knowledge, the first e#cient implementations for PC clu sters.Ou library also inclu des CGMlib, a library of basic CGM tools su ch as sort ing, prefix su m, one to all broadcast, all to one gather, h Relation, all to all broadcast, array balancing, and CGM partitioning. Both libraries are available for download at http://cgm.dehne.net. 1
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 21 (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.
A Range Minima Parallel Algorithm for Coarse Grained Multicomputers
, 1999
"... Given an array of n real numbers A = (a1 , a2 , ..., an ), define MIN(i, j) = min{a i , ..., a j }. The range minima problem consists of preprocessing array A such that queries MIN(i, j), for any 1 i j n, can be answered in constant time. Range minima is a basic problem that appears in many other im ..."
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Cited by 3 (2 self)
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Given an array of n real numbers A = (a1 , a2 , ..., an ), define MIN(i, j) = min{a i , ..., a j }. The range minima problem consists of preprocessing array A such that queries MIN(i, j), for any 1 i j n, can be answered in constant time. Range minima is a basic problem that appears in many other important problems such as lowest common ancestor, Euler tour, pattern matching with scaling, etc. In this work we present a parallel algorithm under the CGM model (Coarse Grained Multicomputer), that solves the range minima problem in O( n p ) time and constant number of communication rounds.
Parallel Range Minima on Coarse Grained Multicomputers
, 1999
"... Given an array of n real numbers A = (a0 , a1 , ..., an 1 ), define MIN(i, j) = min{a i , ..., a j }. The range minima problem consists of preprocessing array A such that queries MIN(i, j), for any 0 i j n 1 can be answered in constant time. ..."
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Cited by 2 (2 self)
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Given an array of n real numbers A = (a0 , a1 , ..., an 1 ), define MIN(i, j) = min{a i , ..., a j }. The range minima problem consists of preprocessing array A such that queries MIN(i, j), for any 0 i j n 1 can be answered in constant time.
Sequential Random Permutation, List Contraction and Tree Contraction are Highly Parallel
"... We show that simple sequential randomized iterative algorithms for random permutation, list contraction, and tree contraction are highly parallel. In particular, if iterations of the algorithms are run as soon as all of their dependencies have been resolved, the resulting computations have logarit ..."
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Cited by 1 (1 self)
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We show that simple sequential randomized iterative algorithms for random permutation, list contraction, and tree contraction are highly parallel. In particular, if iterations of the algorithms are run as soon as all of their dependencies have been resolved, the resulting computations have logarithmic depth (parallel time) with high probability. Our proofs make an interesting connection between the dependence structure of two of the problems and random binary trees. Building upon this analysis, we describe linearwork, polylogarithmicdepth algorithms for the three problems. Although asymptotically no better than the many prior parallel algorithms for the given problems, their advantages include very simple and fast implementations, and returning the same result as the sequential algorithm. Experiments on a 40core machine show reasonably good performance relative to the sequential algorithms. 1
List Ranking on a Coarse Grained Multiprocessor
, 1999
"... We present a deterministic algorithm for the List Ranking Problem on a Coarse Grained p Multiprocessor (CGM) that is only a factor of log (p) away from optimality. This statement holds as well for counting communication rounds where it achieves O(log(p)log (p)) and for the required communicat ..."
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Cited by 1 (1 self)
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We present a deterministic algorithm for the List Ranking Problem on a Coarse Grained p Multiprocessor (CGM) that is only a factor of log (p) away from optimality. This statement holds as well for counting communication rounds where it achieves O(log(p)log (p)) and for the required communication cost and total computation time where it achieves O(nlog (p)). We report on experimental studies of that algorithm on a variety of platforms that show the validity of the chosen CGMmodel, and also show the possible gains and limits of such an algorithm. Finally, we suggest to extend CGM model by the communication blow up to allow better a priori predictions of communication costs of algorithms.
Fullyscalable faulttolerant simulations for BSP and CGM
 in: Proceedings of the 13th International Parallel Processing Symposium & 10th Symposium on Parallel Distributed Processing
, 1999
"... In this paper we consider general simulations of algorithms designed for fully operational BSP and CGM machines on machines with faulty processors. The faults are deterministic (i.e., worstcase distributions of faults are considered) and static (i.e., they do not change in the course of computati ..."
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Cited by 1 (0 self)
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In this paper we consider general simulations of algorithms designed for fully operational BSP and CGM machines on machines with faulty processors. The faults are deterministic (i.e., worstcase distributions of faults are considered) and static (i.e., they do not change in the course of computation). We assume that a constant fraction of processors are faulty. We present a deterministic simulation (resp. a randomized simulation) that achieves constant slowdown per local computations and O((log h p)
Feasibility, Portability, . . . Grained Graph Algorithms
, 2000
"... We study the relationship between the design and analysis of graph algorithms in the coarsed grained parallel models and the behavior of the resulting code on todays parallel machines and clusters. We conclude that the coarse grained multicomputer model (CGM) is well suited to design competitive al ..."
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We study the relationship between the design and analysis of graph algorithms in the coarsed grained parallel models and the behavior of the resulting code on todays parallel machines and clusters. We conclude that the coarse grained multicomputer model (CGM) is well suited to design competitive algorithms, and that it is thereby now possible to aim to develop portable, predictable and efficient parallel algorithms code for graph problems.