Graph reordering is a powerful technique to increase the locality of the representations of graphs, which can be helpful in several applications. We study how the technique can be used to improve compression of graphs and inverted indexes. We extend the recent theoretical model of (KDD 2009) for graph compression, and show how it can be employed for compression-friendly reordering of social networks and web graphs and for assigning document identifiers in inverted indexes. We design and implement a novel theoretically sound reordering algorithm that is based on recursive graph bisection. Our experiments show a significant improvement of the compression rate of graph and indexes over existing heuristics. The new method is relatively simple and allows efficient parallel and distributed implementations, which is demonstrated on graphs with billions of vertices and hundreds of billions of edges.
Several papers study how to assign document identifiers in a document collection for better compression of an inverted index. A popular idea is to perform a clustering on the collection and assign close identifiers to similar documents. @cite_5 propose a reassignment heuristic motivated by the maximum travelling salesman problem (TSP). The heuristic computes a pairwise similarity between every pairs of documents (proportional to the number of shared terms), and then finds the longest path traversing the documents in the graph. An alternative algorithm calculating cosine similarities between documents is suggested by Blandford and Blelloch @cite_15 . Both methods are computationally expensive and are limited to fairly small datasets. The similarity-based approach is later improved by Blanco and Barreiro @cite_13 and by @cite_2 , who make it scalable by reducing the size of the similarity graph, respectively through dimensionality reduction and locality sensitive hashing.
@cite_5 @cite_15 @cite_13 @cite_2
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Web search engines depend on the full-text inverted index data structure. Because the query processing performance is so dependent on the size of the inverted index, a plethora of research has focused on fast end effective techniques for compressing this structure. Recently, several authors have proposed techniques for improving index compression by optimizing the assignment of document identifiers to the documents in the collection, leading to significant reduction in overall index size. In this paper, we propose improved techniques for document identifier assignment. Previous work includes simple and fast heuristics such as sorting by URL, as well as more involved approaches based on the Traveling Salesman Problem or on graph partitioning. These techniques achieve good compression but do not scale to larger document collections. We propose a new framework based on performing a Traveling Salesman computation on a reduced sparse graph obtained through Locality Sensitive Hashing. This technique achieves improved compression while scaling to tens of millions of documents. Based on this framework, we describe a number of new algorithms, and perform a detailed evaluation on three large data sets showing improvements in index size. Most modern retrieval systems use compressed Inverted Files (IF) for indexing. Recent works demonstrated that it is possible to reduce IF sizes by reassigning the document identifiers of the original collection, as it lowers the average distance between documents related to a single term. Variable-bit encoding schemes can exploit the average gap reduction and decrease the total amount of bits per document pointer. However, approximations developed so far requires great amounts of time or use an uncontrolled memory size. This paper presents an efficient solution to the reassignment problem consisting in reducing the input data dimensionality using a SVD transformation. We tested this approximation with the Greedy-NN TSP algorithm and one more efficient variant based on dividing the original problem in sub-problems. We present experimental tests and performance results in two TREC collections, obtaining good compression ratios with low running times. We also show experimental results about the tradeoff between dimensionality reduction and compression, and time performance. A key problem in document classification and clustering is learning the similarity between documents. Traditional approaches include estimating similarity between feature vectors of documents where the vectors are computed using TF-IDF in the bag-of-words model. However, these approaches do not work well when either similar documents do not use the same vocabulary or the feature vectors are not estimated correctly. In this paper, we represent documents and keywords using multiple layers of connected graphs. We pose the problem of simultaneously learning similarity between documents and keyword weights as an edge-weight regularization problem over the different layers of graphs. Unlike most feature weight learning algorithms, we propose an unsupervised algorithm in the proposed framework to simultaneously optimize similarity and the keyword weights. We extrinsically evaluate the performance of the proposed similarity measure on two different tasks, clustering and classification. The proposed similarity measure outperforms the similarity measure proposed by (, 2010), a state-of-the-art classification algorithm (Zhou and Burges, 2007) and three different baselines on a variety of standard, large data sets. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50).