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34
GraphChi: Largescale Graph Computation On just a PC
 In Proceedings of the 10th USENIX conference on Operating Systems Design and Implementation, OSDI’12
, 2012
"... Current systems for graph computation require a distributed computing cluster to handle very large realworld problems, such as analysis on social networks or the web graph. While distributed computational resources have become more accessible, developing distributed graph algorithms still remains c ..."
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Cited by 17 (2 self)
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Current systems for graph computation require a distributed computing cluster to handle very large realworld problems, such as analysis on social networks or the web graph. While distributed computational resources have become more accessible, developing distributed graph algorithms still remains challenging, especially to nonexperts. In this work, we present GraphChi, a diskbased system for computing efficiently on graphs with billions of edges. By using a wellknown method to break large graphs into small parts, and a novel parallel sliding windows method, GraphChi is able to execute several advanced data mining, graph mining, and machine learning algorithms on very large graphs, using just a single consumerlevel computer. We further extend GraphChi to support graphs that evolve over time, and demonstrate that, on a single computer, GraphChi can process over one hundred thousand graph updates per second, while simultaneously performing computation. We show, through experiments and theoretical analysis, that GraphChi performs well on both SSDs and rotational hard drives. By repeating experiments reported for existing distributed systems, we show that, with only fraction of the resources, GraphChi can solve the same problems in very reasonable time. Our work makes largescale graph computation available to anyone with a modern PC. 1
PowerGraph: Distributed GraphParallel Computation on Natural Graphs
"... Largescale graphstructured computation is central to tasks ranging from targeted advertising to natural language processing and has led to the development of several graphparallel abstractions including Pregel and GraphLab. However, the natural graphs commonly found in the realworld have highly ..."
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Cited by 17 (2 self)
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Largescale graphstructured computation is central to tasks ranging from targeted advertising to natural language processing and has led to the development of several graphparallel abstractions including Pregel and GraphLab. However, the natural graphs commonly found in the realworld have highly skewed powerlaw degree distributions, which challenge the assumptions made by these abstractions, limiting performance and scalability. In this paper, we characterize the challenges of computation on natural graphs in the context of existing graphparallel abstractions. We then introduce the PowerGraph abstraction which exploits the internal structure of graph programs to address these challenges. Leveraging the PowerGraph abstraction we introduce a new approach to distributed graph placement and representation that exploits the structure of powerlaw graphs. We provide a detailed analysis and experimental evaluation comparing PowerGraph to two popular graphparallel systems. Finally, we describe three different implementation strategies for PowerGraph and discuss their relative merits with empirical evaluations on largescale realworld problems demonstrating order of magnitude gains. 1
Compact RichFunctional Binary Relation Representations
"... Abstract. Binary relations are an important abstraction arising in a number of data representation problems. Each existing data structure specializes in the few basic operations required by one single application, and takes only limited advantage of the inherent redundancy of binary relations. We sh ..."
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Cited by 12 (7 self)
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Abstract. Binary relations are an important abstraction arising in a number of data representation problems. Each existing data structure specializes in the few basic operations required by one single application, and takes only limited advantage of the inherent redundancy of binary relations. We show how to support more general operations efficiently, while taking better advantage of some forms of redundancy in practical instances. As a basis for a more general discussion on binary relation data structures, we list the operations of potential interest for practical applications, and give reductions between operations. We identify a set of operations that yield the support of all others. As a first contribution to the discussion, we present two data structures for binary relations, each of which achieves a distinct tradeoff between the space used to store and index the relation, the set of operations supported in sublinear time, and the time in which those operations are supported. The experimental performance of our data structures shows that they not only offer good time complexities to carry out many operations, but also take advantage of regularities that arise in practical instances in order to reduce space usage. 1
Extended Compact Web Graph Representations
"... Abstract. Many relevant Web mining tasks translate into classical algorithms on the Web graph. Compact Web graph representations allow running these tasks on larger graphs within main memory. These representations at least provide fast navigation (to the neighbors of a node), yet more sophisticated ..."
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Cited by 9 (6 self)
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Abstract. Many relevant Web mining tasks translate into classical algorithms on the Web graph. Compact Web graph representations allow running these tasks on larger graphs within main memory. These representations at least provide fast navigation (to the neighbors of a node), yet more sophisticated operations are desirable for several Web analyses. We present a compact Web graph representation that, in addition, supports reverse navigation (to the nodes pointing to the given one). The standard approach to achieve this is to represent the graph and its transpose, which basically doubles the space requirement. Our structure, instead, represents the adjacency list using a compact sequence representation that allows finding the positions where a given node v is mentioned, and answers reverse navigation using that primitive. This is combined with a previous proposal based on grammar compression of the adjacency list. The combination yields interesting algorithmic problems. As a result, we achieve the smallest graph representation reported in the
bbit minwise hashing
 In WWW. 671–680
, 2010
"... This paper establishes the theoretical framework of bbit minwise hashing. The original minwise hashing method has become a standard technique for estimating set similarity (e.g., resemblance) with applications in information retrieval, data management, computational advertising, etc. By only storin ..."
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Cited by 8 (1 self)
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This paper establishes the theoretical framework of bbit minwise hashing. The original minwise hashing method has become a standard technique for estimating set similarity (e.g., resemblance) with applications in information retrieval, data management, computational advertising, etc. By only storing b bits of each hashed value (e.g., b =1or 2), we gain substantial advantages in terms of storage space. We prove the basic theoretical results and provide an unbiased estimator of the resemblance for any b. We demonstrate that, even in the least favorable scenario, using b =1 may reduce the storage space at least by a factor of 21.3 (or 10.7) compared to b =64(or b =32), if one is interested in resemblance ≥ 0.5.
Neighbor Query Friendly Compression of Social Networks ∗
"... Compressing social networks can substantially facilitate mining and advanced analysis of large social networks. Preferably, social networks should be compressed in a way that they still can be queried efficiently without decompression. Arguably, neighbor queries, which search for all neighbors of a ..."
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Cited by 8 (1 self)
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Compressing social networks can substantially facilitate mining and advanced analysis of large social networks. Preferably, social networks should be compressed in a way that they still can be queried efficiently without decompression. Arguably, neighbor queries, which search for all neighbors of a query vertex, are the most essential operations on social networks. Can we compress social networks effectively in a neighbor query friendly manner, that is, neighbor queries still can be answered in sublinear time using the compression? In this paper, we develop an effective social network compression approach achieved by a novel Eulerian data structure using multiposition linearizations of directed graphs. Our method comes with a nontrivial theoretical bound on the compression rate. To the best of our
GBASE: A Scalable and General Graph Management System
"... Graphs appear in numerous applications including cybersecurity, the Internet, social networks, protein networks, recommendation systems, and many more. Graphs with millions or even billions of nodes and edges are commonplace. How to store such large graphs efficiently? What are the core operations ..."
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Cited by 7 (4 self)
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Graphs appear in numerous applications including cybersecurity, the Internet, social networks, protein networks, recommendation systems, and many more. Graphs with millions or even billions of nodes and edges are commonplace. How to store such large graphs efficiently? What are the core operations/queries on those graph? How to answer the graph queries quickly? We propose GBASE, a scalable and general graph management and mining system. The key novelties lie in 1) our storage and compression scheme for a parallel setting and 2) the carefully chosen graph operations and their efficient implementation. We designed and implemented an instance of GBASE using MAPREDUCE/HADOOP. GBASE provides a parallel indexing mechanism for graph mining operations that both saves storage space, as well as accelerates queries. We ran numerous experiments on real graphs, spanning billions of nodes and edges, and we show that our proposed GBASE is indeed fast, scalable and nimble, with significant savings in space and time.
Beyond ‘Caveman Communities’: Hubs and Spokes for Graph Compression and Mining
"... Abstract—Given a real world graph, how should we layout its edges? How can we compress it? These questions are closely related, and the typical approach so far is to find cliquelike communities, like the ‘cavemen graph’, and compress them. We show that the blockdiagonal mental image of the ‘cavemen ..."
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Cited by 6 (4 self)
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Abstract—Given a real world graph, how should we layout its edges? How can we compress it? These questions are closely related, and the typical approach so far is to find cliquelike communities, like the ‘cavemen graph’, and compress them. We show that the blockdiagonal mental image of the ‘cavemen graph ’ is the wrong paradigm, in full agreement with earlier results that real world graphs have no good cuts. Instead, we propose to envision graphs as a collection of hubs connecting spokes, with superhubs connecting the hubs, and so on, recursively. Based on the idea, we propose the SLASHBURN method (burn the hubs, and slash the remaining graph into smaller connected components). Our view point has several advantages: (a) it avoids the ‘no good cuts ’ problem, (b) it gives better compression, and (c) it leads to faster execution times for matrixvector operations, which are the backbone of most graph processing tools. Experimental results show that our SLASHBURN method consistently outperforms other methods on all datasets, giving good compression and faster running time.
CMUML10100 Fast Nearestneighbor Search in Diskresident Graphs
, 2010
"... Link prediction, personalized graph search, fraud detection, and many such graph mining problems revolve around the computation of the most “similar ” k nodes to a given query node. One widely used class of similarity measures is based on random walks on graphs, e.g., personalized pagerank, hitting ..."
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Cited by 6 (1 self)
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Link prediction, personalized graph search, fraud detection, and many such graph mining problems revolve around the computation of the most “similar ” k nodes to a given query node. One widely used class of similarity measures is based on random walks on graphs, e.g., personalized pagerank, hitting and commute times, and simrank. There are two fundamental problems associated with these measures. First, existing online algorithms typically examine the local neighborhood of the query node which can become significantly slower whenever highdegree nodes are encountered (a common phenomenon in realworld graphs). We prove that turning high degree nodes into sinks results in only a small approximation error, while greatly improving running times. The second problem is that of computing similarities at query time when the graph is too large to be memoryresident. The obvious solution is to split the graph into clusters of nodes and store each cluster on a disk page; ideally random walks will rarely cross cluster boundaries and cause pagefaults. Our contributions here are twofold: (a) we present an efficient deterministic algorithm to find the k closest neighbors (in terms of personalized pagerank) of any query node in such a clustered graph, and (b) we develop a clustering algorithm (RWDISK) that uses only sequential sweeps over data files. Empirical results on several large publicly available graphs like DBLP, Citeseer and LiveJournal ( ∼ 90 M edges) demonstrate that turning high degree nodes into sinks not only improves running time of RWDISK by a factor of 3 but also boosts link prediction accuracy by a factor of 4 on average. We also show that RWDISK returns more desirable (high conductance and small size) clusters than the popular clustering algorithm METIS, while requiring much less memory. Finally our deterministic algorithm for computing nearest neighbors incurs far fewer pagefaults (factor of 5) than actually simulating random walks
On Compressing the Textual Web
"... Nowadays we know how to effectively compress most basic components of any modern search engine, such as, the graphs arising from the Web structure and/or its usage, the posting lists, and the dictionary of terms. But we are not aware of any study which has deeply addressed the issue of compressing t ..."
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Cited by 4 (1 self)
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Nowadays we know how to effectively compress most basic components of any modern search engine, such as, the graphs arising from the Web structure and/or its usage, the posting lists, and the dictionary of terms. But we are not aware of any study which has deeply addressed the issue of compressing the raw Web pages. Many Web applications use simple compression algorithms — e.g. gzip, or wordbased MovetoFront or Huffman coders — and conclude that, even compressed, raw data take more space than Inverted Lists. In this paper we investigate two typical scenarios of use of data compression for large Web collections. In the first scenario, the compressed pages are stored on disk and we only need to support the fast scanning of large parts of the compressed collection (such as for mapreduce paradigms). In the second scenario, we consider the fast access to individual pages of the compressed collection that is distributed among the RAMs of many PCs (such as for search engines and miners). For the first scenario, we provide a thorough experimental comparison among stateoftheart compressors thus indicating pros and cons of the available solutions. For the second scenario, we compare compressedstorage solutions with the new technology of compressed selfindexes [45]. Our results show that Web pages are more compressible than expected and, consequently, that some common beliefs in this area should be reconsidered. Our results are novel for the large spectrum of tested approaches and the size of datasets, and provide a threefold contribution: a nontrivial baseline for designing new compressedstorage solutions, a guide for software developers faced with Webpage storage, and a natural complement to the recent figures on InvertedListcompression achieved by [57, 58].