Optimal Aggregation Algorithms for Middleware

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Optimal Aggregation Algorithms for Middleware (2001)

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by Ronald Fagin , Amnon Lotem , Moni Naor

Venue:	IN PODS
Citations:	715 - 4 self

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@INPROCEEDINGS{Fagin01optimalaggregation,
    author = {Ronald Fagin and Amnon Lotem and Moni Naor},
    title = {Optimal Aggregation Algorithms for Middleware},
    booktitle = {IN PODS},
    year = {2001},
    pages = {102--113},
    publisher = {}
}

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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, or combining 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. We distinguish

Keyphrases

optimal aggregation algorithm aggregation function overall grade top object individual grade high-probability worst-case sense monotone aggregation function shape grade color grade simple algorithm constant-size buffer large buffer sorted list naive algorithm precise sense early stopping high probability top answer approximate version threshold algorithm database size grows

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