Approximate Query Answering Overview

AVGF[i:j] represents the average frequency of values from index i to j.

SSE[i:j] is computed as the sum of the squares of frequencies minus the product of the number of elements and the square of their average.

The objective is to minimize the sum of squared errors, SSE, while efficiently partitioning the data into k groups.

<p>Mapping a histogram back to an approximate relation allows for efficient query processing on the data.</p> Signup and view all the answers

<p>Continuous value mapping spreads counts evenly across bucket values, while uniform spread mapping considers the number of distinct values in each bucket.</p> Signup and view all the answers

<p>SSEP(i,k) computes the minimum sum of squared errors for partitioning the first i elements into k buckets.</p> Signup and view all the answers

<p>The primary goal of equi-depth histograms is to achieve an equal number of rows per bucket.</p> Signup and view all the answers

<p>Equi-depth histograms can be quickly constructed by sampling data and taking equally spaced splits in the sample.</p> Signup and view all the answers

<p>One-pass algorithms are utilized to maintain the counts in 1-D histograms during row insertions and deletions.</p> Signup and view all the answers

<p>Compressed histograms create singleton buckets for the largest values, providing exact information on those values.</p> Signup and view all the answers

<p>V-optimal histograms minimize the average selectivity estimation error by reducing frequency variance within buckets.</p> Signup and view all the answers

<p>The dynamic programming algorithm for V-optimal histograms has a complexity of O(B*N^2).</p> Signup and view all the answers

<p>Maintenance can involve merging adjacent buckets with small counts and splitting large buckets using sample medians.</p> Signup and view all the answers

<p>Sampling data allows for faster construction of histograms while maintaining nearly equal buckets.</p> Signup and view all the answers

<p>Reservoir sampling is a randomized algorithm used to select a random sample of $k$ items from a list of $n$ items where $n$ is unknown. It is useful because it allows for efficient sampling from large or streaming datasets without needing to load the entire dataset into memory.</p> Signup and view all the answers

<p>Equi-depth histograms divide the range of attribute values into buckets that contain an equal number of data points. They are significant because they help to maintain a balanced representation of the data distribution, facilitating accurate query estimations.</p> Signup and view all the answers

<p>Challenges include deciding the optimal number of buckets, determining the appropriate boundaries for each bucket, and ensuring that partitioning does not lead to significant data loss or misrepresentation.</p> Signup and view all the answers

<p>Multi-dimensional synopses provide summarized representations of data across multiple attributes, allowing for better selectivity estimates during query optimization. They enable more effective filtering and retrieval strategies in complex queries involving multiple attributes.</p> Signup and view all the answers

<p>V-optimal histograms minimize the variance of the error in data representation, leading to more accurate aggregate queries. They differ from other types, such as equi-depth histograms, by focusing on variance reduction rather than maintaining equal data counts across buckets.</p> Signup and view all the answers

<p>Sampling methods allow databases to analyze a small, representative subset of the data instead of the entire dataset, reducing computation time and resource usage. This efficiency enables quicker query responses, especially in large datasets.</p> Signup and view all the answers

<p>Wavelets offer a compact representation of data while preserving hierarchies and relationships across scales. They allow for efficient storage and manipulation of multi-resolution data, which is beneficial for real-time analytics.</p> Signup and view all the answers

<p>Data distribution analysis helps in understanding the frequency and spread of attribute values, which informs how likely certain query conditions will be satisfied. This understanding allows optimizers to estimate selectivity more accurately, leading to improved query plans.</p> Signup and view all the answers