Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While ...
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Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been devoted to analyzing these, with most analyzing them based on programming models, less research focuses on understanding their challenges in distributed environments. Applying graph tasks to distributed environments is not easy, often facing numerous challenges through our analysis, including parallelism, load balancing, communication overhead, and bandwidth. In this article, we provide an extensive overview of the current state-of-the-art in this field by outlining the challenges and solutions of distributed graph algorithms. We first conduct a systematic analysis of the inherent challenges in distributed graph processing, followed by presenting an overview of existing general solutions. Subsequently, we survey the challenges highlighted in recent distributed graph processing papers and the strategies adopted to address them. Finally, we discuss the current research trends and identify potential future opportunities.
graphs and their algorithms are fundamental to computer science, but they can be difficult to formalise, especially in dependently-typed proof assistants. Part of the problem is that graphs aren't as well-behaved ...
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Recent years have seen significant progress in the study of dynamic graph algorithms, and most notably, the introduction of strong lower bound techniques for them (e.g., Henzinger, Krinninger, Nanongkai and Saranurak,...
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Specifying and verifying graph-manipulating programs is a well-known and persistent challenge in separation logic. We show that the obstacles in dealing with graphs are removed if one represents graphs as partial comm...
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For computations on large-scale graphs, one often resorts to parallel algorithms. However, parallel algorithms are difficult to write, debug and analyze. Worse still, it is difficult to make algorithms parallelly scal...
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For computations on large-scale graphs, one often resorts to parallel algorithms. However, parallel algorithms are difficult to write, debug and analyze. Worse still, it is difficult to make algorithms parallelly scalable, such that the more machines are used, the faster the algorithms run. Indeed, it is not yet known whether any PTIME computational problems admit parallelly scalable algorithms on shared-nothing *** it possible to parallelize sequential graph algorithms and guarantee convergence at the correct results as long as the sequential algorithms are correct? Moreover, does a PTIME parallelly scalable problem exist on shared-nothing systems? This position paper answers both questions in the affirmative.
With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researcher...
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With the ubiquitous presence of next-generation sequencing in modern biological, genetic, pharmaceutical and medical research, not everyone pays attention to the underlying computational methods. Even fewer researchers know what were the origins of the current models for DNA assembly. We present original graph models used in DNA sequencing by hybridization, discuss their properties and connections between them. We also explain how these graph models evolved to adapt to the characteristics of next generation sequencing. Moreover, we present a practical comparison of state-of-the-art DNA de novo assembly tools representing these transformed models, i.e. overlap and decomposition-based graphs. Even though the competition is tough, some assemblers perform better and certainly large differences may be observed in hardware resources utilization. Finally, we outline the most important trends in the sequencing field, and try to predict their impact on the computational models in the future. (C) 2016 Elsevier B.V. All rights reserved.
This paper presents new results and graph algorithms for the automatic:testing of protocols using ''unique input/output'' (UIO) sequences. UIO sequences can be efficiently employed in checking conforma...
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This paper presents new results and graph algorithms for the automatic:testing of protocols using ''unique input/output'' (UIO) sequences. UIO sequences can be efficiently employed in checking conformance of protocols to their specifications by using transition testing. The optimization of the test sequence is based on finding the rural Chinese postman tour of the state transition diagram of a finite state machine (FSM). The process of conformance test generation using a touring algorithm is valid provided that certain connectivity properties of the graph are present. This implies that a weakly connected graph must be constructed. It is possible that this connectivity condition may not be met when multiple UIO sequences are used even if the reset capability and/or the self-loop properties are present. The ''weakly connected graph problem'' consists of finding an edge-induced subgraph of the FSM which is still weakly connected when multiple UIO sequences are used. The ''multiple UIO tour minimization problem'' addresses the assignment of edges to UIO sequences for minimizing the degree of the directed UIO graph. This process may not also minimize the length of the tour. The above two problems, left open in previous papers, are solved in this paper. It is proved that by appropriately changing the original assignment graph and using network flow techniques with a new UIO generation process referred to as chaining, efficient solutions can be provided. The theoretical approaches behind the solution to these problems are fully characterized.
We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram fra...
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We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram framework of Braverman and Ostrovsky (FOCS 2007) to almost-smooth functions, which includes all subadditive functions. Specifically, we show that if a subadditive function can be (1 + epsilon)-approximated in the insertion-only streaming model, then it can be (2 + epsilon)-approximated also in the sliding-window model with space complexity larger by factor O(epsilon(-1) log omega), where w is the window size. We demonstrate how our framework yields new approximation algorithms with relatively little effort for a variety of problems that do not admit the smooth-histogram technique. For example, in the frequency-vector model, a symmetric norm is subadditive and thus we obtain a sliding-window (2 + epsilon)-approximation algorithm for it. Another example is for streaming matrices, where we derive a new sliding-window (root 2 + epsilon)-approximation algorithm for Schatten 4-norm. We then consider graph streams and show that many graph problems are subadditive, including maximum submodular matching, minimum vertex-cover, and maximum k-cover, thereby deriving sliding-window O(1)-approximation algorithms for them almost for free (using known insertion-only algorithms). Finally, we design for every d is an element of (1, 2] an artificial function, based on the maximum-matching size, whose almost-smoothness parameter is exactly d.
SuiteSparse:graphBLAS is a full implementation of the graphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. W...
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ISBN:
(纸本)9781538659892
SuiteSparse:graphBLAS is a full implementation of the graphBLAS standard, which defines a set of sparse matrix operations on an extended algebra of semirings using an almost unlimited variety of operators and types. When applied to sparse adjacency matrices, these algebraic operations are equivalent to computations on graphs. graphBLAS provides a powerful and expressive framework for creating graph algorithms based on the elegant mathematics of sparse matrix operations on a semiring. To illustrate graphBLAS, two graph algorithms are constructed in graphBLAS and compared with efficient implementations without graphBLAS: triangle counting and constructing the k-truss of a graph.
Parallel algorithms for computing the minimum spanning tree of a weighted undirected graph, and the bridges and articulation points of an undirected graphs on a fixed-size linear array of processors are presented. For...
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Parallel algorithms for computing the minimum spanning tree of a weighted undirected graph, and the bridges and articulation points of an undirected graphs on a fixed-size linear array of processors are presented. For a graph of n vertices, the algorithms operate on a linear array of p processors and require O(n2/p) time for all p, 1 ≤ p ≤ n. In particular, using n processors the algorithms require O(n) time which is optimal on this model. The paper describes two approaches to limit the communication requirements for solving the problems. The first is a divide-and-conquer strategy applied to Sollin"s algorithm for finding the minimum spanning tree of a graph. The second uses a novel data-reduction technique that constructs an auxiliary graph with no more than 2n − 2 edges, whose bridges and articulation points are the bridges and articulation points of the original graph.
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