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Large-scale graph processing using Apache Giraph
This book takes its reader on a journey through Apache Giraph, a popular distributed graph processing platform designed to bring the power of big data processing to graph data. Designed as a step-by-step self-study guide for everyone interested in large-scale graph processing, it describes the fundamental abstractions of the system, its programming models and various techniques for using the system to process graph data at scale, including the implementation of several popular and advanced graph analytics algorithms. The book is organized as follows: Chapter 1 starts by providing a general background of the big data phenomenon and a general introduction to the Apache Giraph system, its abstraction, programming model and design architecture. Next, chapter 2 focuses on Giraph as a platform and how to use it. Based on a sample job, even more advanced topics like monitoring the Giraph application lifecycle and different methods for monitoring Giraph jobs are explained. Chapter 3 then provides an introduction to Giraph programming, introduces the basic Giraph graph model and explains how to write Giraph programs. In turn, Chapter 4 discusses in detail the implementation of some popular graph algorithms including PageRank, connected components, shortest paths and triangle closing. Chapter 5 focuses on advanced Giraph programming, discussing common Giraph algorithmic optimizations, tunable Giraph configurations that determine the system?s utilization of the underlying resources, and how to write a custom graph input and output format. Lastly, chapter 6 highlights two systems that have been introduced to tackle the challenge of large scale graph processing, GraphX and GraphLab, and explains the main commonalities and differences between these systems and Apache Giraph. This book serves as an essential reference guide for students, researchers and practitioners in the domain of large scale graph processing. It offers step-by-step guidance, with several code examples and the complete source code available in the related github repository. Students will find a comprehensive introduction to and hands-on practice with tackling large scale graph processing problems using the Apache Giraph system, while researchers will discover thorough coverage of the emerging and ongoing advancements in big graph processing systems.
Book
LIMITS OF LOCAL ALGORITHMS OVER SPARSE RANDOM GRAPHS
Local algorithms on graphs are algorithms that run in parallel on the nodes of a graph to compute some global structural feature of the graph. Such algorithms use only local information available at nodes to determine local aspects of the global structure, while also potentially using some randomness. Recent research has shown that such algorithms show significant promise in computing structures like large independent sets in graphs locally. Indeed the promise led to a conjecture by Hatami, Lovász and Szegedy [Geom. Funct. Anal. 24 (2014) 269–296] that local algorithms defined specifically as so-called i.i.d. factors may be able to find approximately largest independent sets in random d-regular graphs. In this paper, we refute this conjecture and show that every independent set produced by local algorithms is multiplicative factor 1/2+1/(2√2) smaller than the largest, asymptotically as d → ∞. Our result is based on an important clustering phenomena predicted first in the literature on spin glasses, and recently proved rigorously for a variety of constraint satisfaction problems on random graphs. Such properties suggest that the geometry of the solution space can be quite intricate. The specific clustering property that we prove and apply in this paper shows that typically every two large independent sets in a random graph either have a significant intersection, or have a very small intersection. As a result, large independent sets are clustered according to the proximity to each other. While the clustering property was postulated earlier as an obstruction for the success of local algorithms, our result is the first one where the clustering property is used to formally prove limits on local algorithms.
Journal Article
Incremental k-core decomposition: algorithms and evaluation
A k-core of a graph is a maximal connected subgraph in which every vertex is connected to at least k vertices in the subgraph. k-core decomposition is often used in large-scale network analysis, such as community detection, protein function prediction, visualization, and solving NP-hard problems on real networks efficiently, like maximal clique finding. In many real-world applications, networks change over time. As a result, it is essential to develop efficient incremental algorithms for dynamic graph data. In this paper, we propose a suite of incremental k-core decomposition algorithms for dynamic graph data. These algorithms locate a small subgraph that is guaranteed to contain the list of vertices whose maximum k-core values have changed and efficiently process this subgraph to update the k-core decomposition. We present incremental algorithms for both insertion and deletion operations, and propose auxiliary vertex state maintenance techniques that can further accelerate these operations. Our results show a significant reduction in runtime compared to non-incremental alternatives. We illustrate the efficiency of our algorithms on different types of real and synthetic graphs, at varying scales. For a graph of 16 million vertices, we observe relative throughputs reaching a million times, relative to the non-incremental algorithms.
Journal Article
How many matchings cover the nodes of a graph?
Given an undirected graph, are there
k
matchings whose union covers all of its nodes, that is, a
matching-k-cover
? When
k
=
1
, the problem is equivalent to the existence of a perfect matching for which Tutte’s celebrated matching theorem (J. Lon. Math. Soc., 1947) provides a ‘good’ characterization. We prove here, when
k
is greater than one, a ‘good’ characterization
à la Kőnig
:
for
k
≥
2
,
there exist
k
matchings covering every node if and only if for every stable set
S
,
we have
|
S
|
≤
k
·
|
N
(
S
)
|
. Moreover, somewhat surprisingly, we use only techniques from bipartite matching in the proof, through a simple, polynomial algorithm. A different approach to matching-k-covers has been previously suggested by Wang et al. (Math. Prog., 2014), relying on general matching and using matroid union for matching-matroids, or the Edmonds-Gallai structure theorem. Our approach provides a simpler polynomial algorithm together with an elegant certificate of non-existence when appropriate. Further results, generalizations and interconnections between several problems are then deduced as consequences of the new minimax theorem, with surprisingly simple proofs (again using only the level of difficulty of bipartite matchings). One of the equivalent formulations leads to a solution of weighted minimization for non-negative edge-weights, while the edge-cardinality maximization of matching-2-covers turns out to be already NP-hard. We have arrived at this problem as the line graph special case of a model arising for manufacturing integrated circuits with the technology called ‘Directed Self Assembly’.
Journal Article
Shadow algorithms data miner
\"Digital shadow generation continues to be an important aspect of visualization and visual effects in film, games, simulations, and scientific applications. This resource offers a thorough picture of the motivations, complexities, and categorized algorithms available to generate digital shadows. From general fundamentals to specific applications, it addresses \"out of core\" shadow algorithms and how to manage huge data sets from a shadow perspective. The book also examines the use of shadow algorithms in industrial applications, in terms of what algorithms are used and what software is applicable.\"-- Provided by publisher.
Book
Special Issue on “Graph Algorithms and Applications”
The mixture of data in real life exhibits structure or connection property in nature. Typical data include biological data, communication network data, image data, etc. Graphs provide a natural way to represent and analyze these types of data and their relationships. For instance, more recently, graphs have found new applications in solving problems for emerging research fields such as social network analysis, design of robust computer network topologies, frequency allocation in wireless networks, and bioinformatics. Unfortunately, the related algorithms usually suffer from high computational complexity, since some of these problems are NP-hard. Therefore, in recent years, many graph models and optimization algorithms have been proposed to achieve a better balance between efficacy and efficiency. The aim of this Special Issue is to provide an opportunity for researchers and engineers from both academia and the industry to publish their latest and original results on graph models, algorithms, and applications to problems in the real world, with a focus on optimization and computational complexity.
Journal Article
Graph partitioning and graph clustering : 10th DIMACS Implementation Challenge Workshop, February 13-14, 2012, Georgia Institute of Technology, Atlanta, GA
Graph partitioning and graph clustering are ubiquitous subtasks in many applications where graphs play an important role. Generally speaking, both techniques aim at the identification of vertex subsets with many internal and few external edges. To name only a few, problems addressed by graph partitioning and graph clustering algorithms are: li>What are the communities within an (online) social network?How do I speed up a numerical simulation by mapping it efficiently onto a parallel computer?How must components be organised on a computer chip such that they can communicate efficiently with each other?What are the segments of a digital image?Which functions are certain genes (most likely) responsible for?The 10th DIMACS Implementation Challenge Workshop was devoted to determining realistic performance of algorithms where worst case analysis is overly pessimistic and probabilistic models are too unrealistic. Articles in the volume describe and analyse various experimental data with the goal of getting insight into realistic algorithm performance in situations where analysis fails. This book is published in cooperation with the Center for Discrete Mathematics and Theoretical Computer Science.
eBook
Exact values for three domination-like problems in circular and infinite grid graphs of small height
In this paper we study three domination-like problems, namely identifying codes, locating-dominating codes, and locating-total-dominating codes. We are interested in finding the minimum cardinality of such codes in circular and infinite grid graphs of given height. We provide an alternate proof for already known results, as well as new results. These were obtained by a computer search based on a generic framework, that we developed earlier, for the search of a minimum labeling satisfying a pseudo-d-local property in rotagraphs.
Journal Article