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...f vertices does not contain any two vertices having an edge between them; such a set is said to be maximal if no other vertices can be added to that set while keeping it independent. Luby’s algorithm =-=[18]-=- starts by assigning a random number to each vertex; then it finds a vertex such that its random number is larger than all of the neighbors, removes it and removes its neighbors. Instead of removing t...

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...nt in many scientific computing applications such as automatic differentiation [1], printed circuit testing [2], parallel numerical computation problems [3], register allocation [4], and optimization =-=[5]-=-. Today’s large scientific computing applications are typically executed on large scale parallel machines for mainly two reasons: to reduce the execution time by leveraging parallelism, and to process...

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... Instead of removing that vertex, one can give it the smallest color, and the algorithm becomes a parallel graph coloring algorithm. Many of distributed memory parallel graph coloring algorithms [3], =-=[19]-=-, [20] relies on this technique. The second category of coloring algorithms relies on speculative coloring technique [21], [22], [6], [23]. In the simplest form [21], each processor tentatively colors...

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...lors assigned to the vertices. The problem has been known to be NP-Complete [13] and recently, it has shown that for all ɛ > 0, it is NP-Hard to approximate the graph coloring problem within |V | 1−ɛ =-=[14]-=-. Yet simple algorithms are known to provide almost optimal coloring for a majority of common graphs [5]. The sequential greedy coloring presented in Algorithm 1 is the most popular technique for grap...

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...t every two adjacent vertices have a different color. The graph coloring problem has been shown to be a critical ingredient in many scientific computing applications such as automatic differentiation =-=[1]-=-, printed circuit testing [2], parallel numerical computation problems [3], register allocation [4], and optimization [5]. Today’s large scientific computing applications are typically executed on lar...

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... have a different color. The graph coloring problem has been shown to be a critical ingredient in many scientific computing applications such as automatic differentiation [1], printed circuit testing =-=[2]-=-, parallel numerical computation problems [3], register allocation [4], and optimization [5]. Today’s large scientific computing applications are typically executed on large scale parallel machines fo...

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...red for scalable hybrid processing, which will be the main focus of this work. The reason to undertake such a challenging task is that distributed systems are not ideal platforms for graph algorithms =-=[10]-=-, furthermore, distributed memory graph coloring techniques (in fact almost all graph algorithms) suffer severe performance drawbacks when trying to use all the processing units of multicore clusters ...

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... vertex the smallest permissible color. The order of traversal of the graph is known to be of importance for reducing the number of colors used and many heuristics have been developed on that premise =-=[17]-=-, [1]. Algorithm 1: Sequential greedy coloring. Data: G = (V, E) for each v ∈ V do for each w ∈ adj (v) do forbiddenColors[color[w]] ← v color[v] ← min{i > 0 : forbiddenColors[i] ̸= v} B. Parallel Gra...

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...e algorithms are known to provide almost optimal coloring for a majority of common graphs [5]. The sequential greedy coloring presented in Algorithm 1 is the most popular technique for graph coloring =-=[15]-=-, [16]. This algorithm simply visits the vertices of the graph in some order and assign to each vertex the smallest permissible color. The order of traversal of the graph is known to be of importance ...

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...ithm. Many of distributed memory parallel graph coloring algorithms [3], [19], [20] relies on this technique. The second category of coloring algorithms relies on speculative coloring technique [21], =-=[22]-=-, [6], [23]. In the simplest form [21], each processor tentatively colors parts of the graph independently of the other ones using the sequential greedy algorithm. Once the graph has been fully colore...

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...roblem has been shown to be a critical ingredient in many scientific computing applications such as automatic differentiation [1], printed circuit testing [2], parallel numerical computation problems =-=[3]-=-, register allocation [4], and optimization [5]. Today’s large scientific computing applications are typically executed on large scale parallel machines for mainly two reasons: to reduce the execution...

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...pn 1 ppn The experiments are run on six real-world graphs which come from various application areas including linear car analysis, finite element, structural engineering and automotive industry [22], =-=[27]-=-. They have been obtained from the University of Florida Sparse Matrix Collection3 and the Parasol project. The list of the graphs and their main properties are summarized in Table I. The number of co...

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...ad of removing that vertex, one can give it the smallest color, and the algorithm becomes a parallel graph coloring algorithm. Many of distributed memory parallel graph coloring algorithms [3], [19], =-=[20]-=- relies on this technique. The second category of coloring algorithms relies on speculative coloring technique [21], [22], [6], [23]. In the simplest form [21], each processor tentatively colors parts...

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...ecute a sequential version of the algorithm. Or execute a distributed memory version of the graph algorithm. In many cases, the former is either infeasible due to memory limitations, or not efficient =-=[6]-=-. The advent of multicore architectures significantly increased the number of processing units within a single machine. Most supercomputers nowadays provide more than four processing cores per node, a...

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... hardware specific intrinsics to be efficient which does not exists on the architectures targeted in this study. C. Hybrid Algorithms Many algorithms have been developed for hybrid systems [7], [25], =-=[26]-=-, [8]. Baker et al. [7] experiments algebraic multigrid on a hybrid platform and discusses the challenges faced. They introduce the first comprehensive study of the performance of algebraic multigrid ...

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...rithms are known to provide almost optimal coloring for a majority of common graphs [5]. The sequential greedy coloring presented in Algorithm 1 is the most popular technique for graph coloring [15], =-=[16]-=-. This algorithm simply visits the vertices of the graph in some order and assign to each vertex the smallest permissible color. The order of traversal of the graph is known to be of importance for re...

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...cessing units within a single node. Hybrid systems have flourished in computation-intensive areas such as linear algebra [7], multiple sequence alignment [8] and parallel matrix-vector multiplication =-=[9]-=- which report significant performance improvements. To the best of our knowledge, graph algorithms have not been considered for scalable hybrid processing, which will be the main focus of this work. T...

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... algorithm. Many of distributed memory parallel graph coloring algorithms [3], [19], [20] relies on this technique. The second category of coloring algorithms relies on speculative coloring technique =-=[21]-=-, [22], [6], [23]. In the simplest form [21], each processor tentatively colors parts of the graph independently of the other ones using the sequential greedy algorithm. Once the graph has been fully ...

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...y graph coloring techniques (in fact almost all graph algorithms) suffer severe performance drawbacks when trying to use all the processing units of multicore clusters using message passing libraries =-=[11]-=-. In this paper, we present the design and the development of a hybrid coloring algorithm. We provide a thorough experimental performance analysis of a careful implementation on a multicore cluster. O...

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...of distributed memory parallel graph coloring algorithms [3], [19], [20] relies on this technique. The second category of coloring algorithms relies on speculative coloring technique [21], [22], [6], =-=[23]-=-. In the simplest form [21], each processor tentatively colors parts of the graph independently of the other ones using the sequential greedy algorithm. Once the graph has been fully colored, all the ...

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...explained in details in Section III. The third category, which includes most recent development in coloring algorithms, is dataflow coloring algorithms which has been originally designed for Cray XMT =-=[24]-=-. The main difference of dataflow coloring algorithm is how the coloring of a vertex is initiated or triggered (and in some versions, how these coloring tasks are assigned to a processing element). By...

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...provement made possible by having multiple processing units within a single node. Hybrid systems have flourished in computation-intensive areas such as linear algebra [7], multiple sequence alignment =-=[8]-=- and parallel matrix-vector multiplication [9] which report significant performance improvements. To the best of our knowledge, graph algorithms have not been considered for scalable hybrid processing...

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...-level hardware specific intrinsics to be efficient which does not exists on the architectures targeted in this study. C. Hybrid Algorithms Many algorithms have been developed for hybrid systems [7], =-=[25]-=-, [26], [8]. Baker et al. [7] experiments algebraic multigrid on a hybrid platform and discusses the challenges faced. They introduce the first comprehensive study of the performance of algebraic mult...