We address the problem of replicating a Voronoi diagram @math of a planar point set @math by making proximity queries, which are of three possible (in decreasing order of information content): 1. the exact location of the nearest site(s) in @math ; 2. the distance to and label(s) of the nearest site(s) in @math ; 3. a unique label for every nearest site in @math . We provide algorithms showing how queries of Type 1 and Type 2 allow an exact cloning of @math with @math queries and @math processing time. We also prove that queries of Type 3 can never exactly clone @math , but we show that with @math queries we can construct an @math -approximate cloning of @math . In addition to showing the limits of nearest-neighbor database security, our methods also provide one of the first natural algorithmic applications of retroactive data structures.
There has been less prior related work that takes the black hat'' perspective of this paper, which asks the question of how quickly a data set can be discovered from seemingly minimalistic responses to queries on that object. For example, Goodrich @cite_8 studies the problem of discovering a DNA string from genomic comparison queries and Nohl and Evans @cite_38 study quantitative measures on the global system information that is leaked from learning the contents of multiple RFID tags that are generated by that system.
@cite_38 @cite_8
2154357802 2052331661 2028431844 1502916507
In this paper, we study the degree to which a genomic string, @math ,leaks details about itself any time it engages in comparison protocolswith a genomic querier, Bob, even if those protocols arecryptographically guaranteed to produce no additional information otherthan the scores that assess the degree to which @math matches stringsoffered by Bob. We show that such scenarios allow Bob to play variantsof the game of Mastermind with @math so as to learn the complete identityof @math . We show that there are a number of efficient implementationsfor Bob to employ in these Mastermind attacks, depending on knowledgehe has about the structure of @math , which show how quickly he candetermine @math . Indeed, we show that Bob can discover @math using anumber of rounds of test comparisons that is much smaller than thelength of @math , under various assumptions regarding the types of scoresthat are returned by the cryptographic protocols and whether he can useknowledge about the distribution that @math comes from, e.g., usingpublic knowledge about the properties of human DNA. We also providethe results of an experimental study we performed on a database ofmitochondrial DNA, showing the vulnerability of existing real-world DNAdata to the Mastermind attack. In recent years, the technological advances in mapping genes have made it increasingly easy to store and use a wide variety of biological data. Such data are usually in the form of very long strings for which it is difficult to determine the most relevant features for a classification task. For example, a typical DNA string may be millions of characters long, and there may be thousands of such strings in a database. In many cases, the classification behavior of the data may be hidden in the compositional behavior of certain segments of the string which cannot be easily determined apriori. Another problem which complicates the classification task is that in some cases the classification behavior is reflected in global behavior of the string, whereas in others it is reflected in local patterns. Given the enormous variation in the behavior of the strings over different data sets, it is useful to develop an approach which is sensitive to both the global and local behavior of the strings for the purpose of classification. For this purpose, we will exploit the multi-resolution property of wavelet decomposition in order to create a scheme which can mine classification characteristics at different levels of granularity. The resulting scheme turns out to be very effective in practice on a wide range of problems. Identifying approximately identical strings is key for many data cleaning and data integration processes, including similarity join and record matching. The accuracy of such tasks crucially depends on appropriate choices of string similarity measures and thresholds for the particular dataset. Manual selection of similarity measures and thresholds is infeasible. Other approaches rely on the existence of adequate historic ground-truth or massive manual effort. To address this problem, we propose an Active Learning algorithm which selects a best performing similarity measure in a given set while optimizing a decision threshold. Active Learning minimizes the number of user queries needed to arrive at an appropriate classifier. Queries require only the label match no match, which end users can easily provide in their domain. Evaluation on well-known string matching benchmark data sets shows that our approach achieves highly accurate results with a small amount of manual labeling required. 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).