We present two algorithms for the approximate nearest neighbor problem in high-dimensional spaces. For data sets of size n living in R d , the algorithms require space that is only polynomial in n and d, while achieving query times that are sub-linear in n and polynomial in d. We also show applications to other high-dimensional geometric problems, such as the approximate minimum spanning tree. The article is based on the material from the authors' STOC'98 and FOCS'01 papers. It unifies, generalizes and simplifies the results from those papers.

/pdf/approximate-nearest-neighbors-towards-removing-the-curse-of-27lmlz5prr.pdf

Approximate nearest neighbors: towards removing the curse of dimensionality

This paper addresses two unresolved issues about Web caching. The first issue is whether Web requests from a fixed user community are distributed according to Zipf's (1929) law. The second issue relates to a number of studies on the characteristics of Web proxy traces, which have shown that the hit-ratios and temporal locality of the traces exhibit certain asymptotic properties that are uniform across the different sets of the traces. In particular, the question is whether these properties are inherent to Web accesses or whether they are simply an artifact of the traces. An answer to these unresolved issues will facilitate both Web cache resource planning and cache hierarchy design. We show that the answers to the two questions are related. We first investigate the page request distribution seen by Web proxy caches using traces from a variety of sources. We find that the distribution does not follow Zipf's law precisely, but instead follows a Zipf-like distribution with the exponent varying from trace to trace. Furthermore, we find that there is only (i) a weak correlation between the access frequency of a Web page and its size and (ii) a weak correlation between access frequency and its rate of change. We then consider a simple model where the Web accesses are independent and the reference probability of the documents follows a Zipf-like distribution. We find that the model yields asymptotic behaviour that are consistent with the experimental observations, suggesting that the various observed properties of hit-ratios and temporal locality are indeed inherent to Web accesses observed by proxies. Finally, we revisit Web cache replacement algorithms and show that the algorithm that is suggested by this simple model performs best on real trace data. The results indicate that while page requests do indeed reveal short-term correlations and other structures, a simple model for an independent request stream following a Zipf-like distribution is sufficient to capture certain asymptotic properties observed at Web proxies.

/pdf/web-caching-and-zipf-like-distributions-evidence-and-xw99yfl0w6.pdf

Web caching and Zipf-like distributions: evidence and implications

The study of the web as a graph is not only fascinating in its own right, but also yields valuable insight into web algorithms for crawling, searching and community discovery, and the sociological phenomena which characterize its evolution. We report on experiments on local and global properties of the web graph using two Altavista crawls each with over 200 million pages and 1.5 billion links. Our study indicates that the macroscopic structure of the web is considerably more intricate than suggested by earlier experiments on a smaller scale.

/pdf/graph-structure-in-the-web-9h7qd5q9nt.pdf

Graph structure in the Web

The notion of self-similarity has been shown to apply to wide-area and local-area network traffic. We show evidence that the subset of network traffic that is due to World Wide Web (WWW) transfers can show characteristics that are consistent with self-similarity, and we present a hypothesized explanation for that self-similarity. Using a set of traces of actual user executions of NCSA Mosaic, we examine the dependence structure of WWW traffic. First, we show evidence that WWW traffic exhibits behavior that is consistent with self-similar traffic models. Then we show that the self-similarity in such traffic can be explained based on the underlying distributions of WWW document sizes, the effects of caching and user preference in file transfer, the effect of user "think time", and the superimposition of many such transfers in a local-area network. To do this, we rely on empirically measured distributions both from client traces and from data independently collected at WWW servers.

/pdf/self-similarity-in-world-wide-web-traffic-evidence-and-5boev1op7z.pdf

Self-similarity in World Wide Web traffic: evidence and possible causes

(MATH) A locality sensitive hashing scheme is a distribution on a family $\F$ of hash functions operating on a collection of objects, such that for two objects x,y, PrheF[h(x) = h(y)] = sim(x,y), where sim(x,y) e [0,1] is some similarity function defined on the collection of objects. Such a scheme leads to a compact representation of objects so that similarity of objects can be estimated from their compact sketches, and also leads to efficient algorithms for approximate nearest neighbor search and clustering. Min-wise independent permutations provide an elegant construction of such a locality sensitive hashing scheme for a collection of subsets with the set similarity measure sim(A,B) = \frac{|A ∩ B|}{|A ∪ B|}.(MATH) We show that rounding algorithms for LPs and SDPs used in the context of approximation algorithms can be viewed as locality sensitive hashing schemes for several interesting collections of objects. Based on this insight, we construct new locality sensitive hashing schemes for:A collection of vectors with the distance between → \over u and → \over v measured by O(→ \over u, → \over v)/π, where O(→ \over u, → \over v) is the angle between → \over u) and → \over v). This yields a sketching scheme for estimating the cosine similarity measure between two vectors, as well as a simple alternative to minwise independent permutations for estimating set similarity.A collection of distributions on n points in a metric space, with distance between distributions measured by the Earth Mover Distance (EMD), (a popular distance measure in graphics and vision). Our hash functions map distributions to points in the metric space such that, for distributions P and Q, EMD(P,Q) ≤ Ehe\F [d(h(P),h(Q))] ≤ O(log n log log n). EMD(P, Q).

/pdf/similarity-estimation-techniques-from-rounding-algorithms-1i3hjl99zj.pdf

Similarity estimation techniques from rounding algorithms

We have developed an efficient way to determine the syntactic similarity of files and have applied it to every document on the World Wide Web. Using this mechanism, we built a clustering of all the documents that are syntactically similar. Possible applications include a "Lost and Found" service, filtering the results of Web searches, updating widely distributed web-pages, and identifying violations of intellectual property rights.

/pdf/syntactic-clustering-of-the-web-3xo1rf1ocr.pdf

Syntactic clustering of the Web

We describe the design and performance of a caching relay for the World Wide Web. We model the distribution of requests for pages from the web and see how this distribution affects the performance of a cache. We use the data gathered from the relay to make some general characterizations about the web.

A caching relay for the World Wide Web

A computer-implemented method determines the resemblance of data objects such as Web pages. Each data object is partitioned into a sequence of tokens. The tokens are grouped into overlapping sets of the tokens to form shingles. Each shingle is represented by a unique identification element encoded as a fingerprint. A minimum element from each of the images of the set of fingerprints associated with a document under each of a plurality of pseudo random permutations of the set of all fingerprints are selected to generate a sketch of each data object. The sketches characterize the resemblance of the data objects. The sketches can be further partitioned into a plurality of groups. Each group is fingerprinted to form a feature. Data objects that share more than a certain numbers of features are estimated to be nearly identical.

Method for clustering closely resembling data objects

The MilliCent Protocol for Inexpensive Electronic Commerce

An electronic commerce system and method enforces a license agreement for content on an open network (140) by restricting the number of consumers (131) that can concurrently access the content. A consumer (131) initially acquires vendor scrip, either from a broker or the vendor (121) itself. The consumer (131) presents the vendor scrip to the vendor (121) along with a request to access the content. In response, the vendor (121) gathers information about the consumer (131) to determine whether the consumer (131) belongs to the class allowed to access the content. The information may be gathered from the scrip or from other sources. If the consumer (131) belongs to the class, then the vendor (121) determines if a license to access the content is available. Generally, a license is available if the number of other consumers (131) having licenses to access the content is less than the maximum specified in the license agreement. If no licenses are available, the vendor (121) provides the consumer (131) with an estimate of when a license will be available. If a license is available, the vendor (121) directs the consumer (131) to obtain license scrip which allows the consumer (131) to access the content. The license scrip expires after a relatively brief period of time. When the consumer (131) uses the license scrip to access the content, the vendor (121) provides the consumer (131) with new license scrip having a later expiration time.

Steven C. Glassman

Papers

Syntactic clustering of the Web

A caching relay for the World Wide Web

Method for clustering closely resembling data objects

The MilliCent Protocol for Inexpensive Electronic Commerce

Method and system for enforcing licenses on an open network