Abstract: Assume that each object in a database has m grades, or scores, one for each of m attributes. For example, an object can have a color grade, that tells how red it is, and a shape grade, that tells how round it is. For each attribute, there is a sorted list, which lists each object and its grade under that attribute, sorted by grade (highest grade first). There is some monotone aggregation function, orcombining rule, such as min or average, that combines the individual grades to obtain an overall grade. To determine the top k objects (that have the best overall grades), the naive algorithm must access every object in the database, to find its grade under each attribute. Fagin has given an algorithm (“Fagin’s Algorithm”, or FA) that is much more efficient. For some monotone aggregation functions, FA is optimal with high probability in the worst case. We analyze an elegant and remarkably simple algorithm (“the threshold algorithm”, or TA) that is optimal in a much stronger sense than FA. We show that TA is essentially optimal, not just for some monotone aggregation functions, but for all of them, and not just in a high-probability worst-case sense, but over every database. Unlike FA, which requires large buffers (whose size may grow unboundedly as the database size grows), TA requires only a small, constant-size buffer. TA allows early stopping, which yields, in a precise sense, an approximate version of the top k answers.

Current-day crawlers retrieve content only from the publicly indexable Web, i.e., the set of web pages reachable purely by following hypertext links, ignoring search forms and pages that require authorization or prior registration.

There are essential differences between multimedia databases (which may contain complicated objects, such as images), and traditional databases. These differences lead to interesting new issues, and in particular cause us to consider new types of queries. For example, in a multimedia database it is reasonable and natural to ask for images that are somehow "similar to" some fixed image. Furthermore, there are different ways of obtaining and accessing information in a multimedia database than information in a traditional database. For example, in a multimedia database, it might be reasonable to have a query that asks for, say, the top 10 images that are similar to a fixed image. This is in contrast to a relational database, where the answer to a query is simply a set. (Of course, in a relational database, the result to a query may be sorted in some way for convenience in presentation, such as sorting department members by salary, but logically speaking, the result is still simply a set, ...

Assume that each object in a database has m grades, or scores, one for each of m attributes.

One of the important issues in data mining is the interestingness problem. This problem is described as finding the interesting patterns from a large number of discovered patterns. Typically, in a data mining application, it is all too easy to discover a huge number of patterns. Most of these patterns are actually useless or uninteresting to the user. But due to the huge number of patterns, it is difficult for a user to comprehend all the patterns and to identify those interesting to him/her. To prevent the user from being overwhelmed by the large number of patterns, techniques are needed to analyze and to rank the patterns according to their interestingness. This paper proposes such a technique. It performs post-analysis of the discovered patterns to help the user identify those interesting ones. The technique is based on fuzzy matching of the discovered patterns with a set of user-specified patterns. The degrees of match are then used to rank the discovered patterns according to vari...

Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Summary discovery is one of the major components of knowledge discovery in databases, which provides the user with comprehensive information for grasping the essence from a large amount of information in a database. In this paper, we propose an interactive top-down summary discovery process which utilizes fuzzy ISA hierarchies as domain knowledge. We define a generalized tuple as a representational form of a database summary including fuzzy concepts. By virtue of fuzzy ISA hierarchies where fuzzy ISA relationships common in actual domains are naturally expressed, the discovery process comes up with more accurate database summaries. We also present an informativeness measure for distinguishing generalized tuples that delivers much information to users, based on Shannon's information theory. Keywords--- data mining, summary discovery, fuzzy set application I. Introduction A S the rapid growth of database volumes has deepened the gap between data generation and data understanding, kn...

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The Method of Imprecision, or M o I, is a formal method for incorporating imprecise information into a design process. This methodology has been exercised on a problem in preliminary vehicle structure design in collaboration with VW Wolfsburg. Results show that the method is useful in trading off multiple conflicting attributes, including styling preferences and engineering requirements. Keywords: Industrial Applications of DTM; Vehicle Structure Design; Design Methods and Models; Design Representations; Computational Methods of Design; Fuzzy Sets INTRODUCTION Preliminary design is inherently imprecise (Becker, 1973; Blockley, 1980; Gavin, 1994; Yao and Furuta, 1986), and many preliminary design decisions are made informally. Preliminary design has enormous economic importance, as much of the cost of a design is determined by these (often informal) preliminary decisions (Whitney, 1988). A further complication is the difficulty of communicating imprecise information between different...

A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization.