Computational meshes for numerical simulation frequently show-at least locally-a structure resembling a triangulated grid. Our goal is to recognize product-like structures in triangular meshes. We define triangulated ...
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Computational meshes for numerical simulation frequently show-at least locally-a structure resembling a triangulated grid. Our goal is to recognize product-like structures in triangular meshes. We define triangulated Cartesian products of graphs and analyze their structural properties. We show how to recognize and factorize graphs that are triangulated products of two factors, when the factors are triangle-free graphs. We also discuss properties of products with more than two factors. (C) 2011 Elsevier B.V. All rights reserved.
The MapReduce framework has been employed in many papers to process the large-scale graph. In this paper, we propose a multi-source message passing model to achieve multi-source traversal of graph in one iterative pro...
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ISBN:
(纸本)9780769546766
The MapReduce framework has been employed in many papers to process the large-scale graph. In this paper, we propose a multi-source message passing model to achieve multi-source traversal of graph in one iterative progress, which largely improve the parallelism efficiency of graph algorithm involving multi-source traversal which occurs in many complex graph algorithms. As the model can traverse the graph from different sources in one iterative progress, the multi-source traversal will finish in much less iteration than before. In this way, the total runtime of the algorithm involves multi-source traversal will be reduced in a large scale. Besides, the message passing model is flexible enough to express a broad set of algorithms. Hence, we design the interface of message passing to facilitate using our model to develop algorithms. Finally, the experiment shows the efficiency and scalability of the model.
Breadth-first search (BFS) is a core primitive for graph traversal and a basis for many higher-level graph analysis algorithms. It is also representative of a class of parallel computations whose memory accesses and w...
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ISBN:
(纸本)9781450311601
Breadth-first search (BFS) is a core primitive for graph traversal and a basis for many higher-level graph analysis algorithms. It is also representative of a class of parallel computations whose memory accesses and work distribution are both irregular and data-dependent. Recent work has demonstrated the plausibility of GPU sparse graph traversal, but has tended to focus on asymptotically inefficient algorithms that perform poorly on graphs with non-trivial diameter. We present a BFS parallelization focused on fine-grained task management constructed from efficient prefix sum that achieves an asymptotically optimal O(|V|+|E|) work complexity. Our implementation delivers excellent performance on diverse graphs, achieving traversal rates in excess of 3.3 billion and 8.3 billion traversed edges per second using single and quad-GPU configurations, respectively. This level of performance is several times faster than state-of-the-art implementations both CPU and GPU platforms.
We present an alternative implementation of the (1 - epsilon) factor NC approximation algorithm for the maximum weight matching by Hougardy et al. [1]. Our implementation, on the EREW PRAM model of computation, achiev...
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We present an alternative implementation of the (1 - epsilon) factor NC approximation algorithm for the maximum weight matching by Hougardy et al. [1]. Our implementation, on the EREW PRAM model of computation, achieves an O(log n) factor improvement on both the execution time and the number of processors.
In a wide array of disciplines, data can be modeled as an interconnected network of entities, where various attributes could be associated with both the entities and the relations among them. Knowledge is often hidden...
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ISBN:
(纸本)9781467300421
In a wide array of disciplines, data can be modeled as an interconnected network of entities, where various attributes could be associated with both the entities and the relations among them. Knowledge is often hidden in the complex structure and attributes inside these networks. While querying and mining these linked datasets are essential for various applications, traditional graph queries may not be able to capture the rich semantics in these networks. With the advent of complex information networks, new graph queries are emerging, including graph pattern matching and mining, similarity search, ranking and expert finding, graph aggregation and OLAP. These queries require both the topology and content information of the network data, and hence, different from classical graph algorithms such as shortest path, reachability and minimum cut, which depend only on the structure of the network. In this tutorial, we shall give an introduction of the emerging graph queries, their indexing and resolution techniques, the current challenges and the future research directions.
Large, real-world graphs are famously difficult to process efficiently. Not only they have a large memory footprint but most graph processing algorithms entail memory access patterns with poor locality, data-dependent...
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ISBN:
(纸本)9781450311823
Large, real-world graphs are famously difficult to process efficiently. Not only they have a large memory footprint but most graph processing algorithms entail memory access patterns with poor locality, data-dependent parallelism, and a low compute-to-memory access ratio. Additionally, most real-world graphs have a low diameter and a highly heterogeneous node degree distribution. Partitioning these graphs and simultaneously achieve access locality and load-balancing is difficult if not impossible. This paper demonstrates the feasibility of graph processing on heterogeneous (i.e., including both CPUs and GPUs) platforms as a cost-effective approach towards addressing the graph processing challenges above. To this end, this work (i) presents and evaluates a performance model that estimates the achievable performance on heterogeneous platforms;(ii) introduces TOTEM - a processing engine based on the Bulk Synchronous Parallel (BSP) model that offers a convenient environment to simplify the implementation of graph algorithms on heterogeneous platforms;and, (iii) demonstrates TOTEM'S efficiency by implementing and evaluating two graph algorithms (PageRank and breadth-first search). TOTEM achieves speedups close to the model's prediction, and applies a number of optimizations that enable linear speedups with respect to the share of the graph offloaded for processing to accelerators.
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to f...
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Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a path that visits the maximum possible number of locations during their time windows. In the second variation, the speeding deliveryman problem, the goal is to find a path that uses the minimum possible speedup to visit all locations during their time windows. For both variations, the time windows are of unit length, and the distance metric is based on a weighted, undirected graph. algorithms with improved approximation ratios are given for the case when the input is defined on a tree rather than a general graph. The algorithms are also extended to handle time windows whose lengths fall in any bounded range.
We consider the sum coloring (chromatic sum) problem and the sum multi-coloring problem for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axis-parallel re...
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We consider the sum coloring (chromatic sum) problem and the sum multi-coloring problem for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axis-parallel rectangles, proper interval graphs, and unit disk graphs. All the above-mentioned graph classes belong to a more general graph class of (k + 1)-clawfree graphs (respectively, for k = 4, 2, 5). We prove that sum coloring is NP-hard for penny graphs and unit square graphs which implies NP-hardness for unit disk graphs and proper intersection graphs of axis-parallel rectangles. We show a 2-approximation algorithm for unit square graphs, with the assumption that the geometric representation of the graph is given. For sum multi-coloring, we confirm that the greedy first-fit coloring, after ordering vertices by their demands, achieves a k-approximation for the preemptive version of sum multi-coloring on (k + 1)-clawfree graphs. Finally, we study priority algorithms as a model for greedy algorithms for the sum coloring problem and the sum multi-coloring problem. We show various inapproximation results under several natural input representations. (C) 2011 Elsevier B.V. All rights reserved.
We propose a combinatorial algorithm to track critical points of 2D time-dependent scalar fields. Existing tracking algorithms such as Feature Flow Fields apply numerical schemes utilizing derivatives of the data, whi...
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We propose a combinatorial algorithm to track critical points of 2D time-dependent scalar fields. Existing tracking algorithms such as Feature Flow Fields apply numerical schemes utilizing derivatives of the data, which makes them prone to noise and involve a large number of computational parameters. In contrast, our method is robust against noise since it does not require derivatives, interpolation, and numerical integration. Furthermore, we propose an importance measure that combines the spatial persistence of a critical point with its temporal evolution. This leads to a time-aware feature hierarchy, which allows us to discriminate important from spurious features. Our method requires only a single, easy-to-tune computational parameter and is naturally formulated in an out-of-core fashion, which enables the analysis of large data sets. We apply our method to synthetic data and data sets from computational fluid dynamics and compare it to the stabilized continuous Feature Flow Field tracking algorithm.
A (k, l)-cocoloring of a graph is a partition of its vertex set into at most k stable sets and at most l cliques. It is known that deciding if a graph is (k, l)-cocolorable is NP-complete. A graph is extended P-4-lade...
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A (k, l)-cocoloring of a graph is a partition of its vertex set into at most k stable sets and at most l cliques. It is known that deciding if a graph is (k, l)-cocolorable is NP-complete. A graph is extended P-4-laden if every induced subgraph with at most six vertices that contains more than two induced P-4's is [2K(2), C-4]-free. Extended P-4-laden graphs generalize cographs, P-4-sparse and P-4-tidy graphs. In this paper, we obtain a linear time algorithm to decide if, given k, l >= 0, an extended P-4-laden graph is (k, l)-cocolorable. Consequently, we obtain a polynomial time algorithm to determine the cochromatic number and the split chromatic number of an extended P-4-laden graph. Finally, we present a polynomial time algorithm to find a maximum induced (k, l)-cocolorable subgraph of an extended P-4-laden graph, generalizing the main results of Bravo et al. (2011) [4] and Demange et al. (2005) [5]. (c) 2012 Elsevier B.V. All rights reserved.
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