Q, Theta-Optimal Histogram Bucket Construction Algorithm
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Solution Overview
Problem
Existing database management systems face inefficiencies in constructing q,θ-optimal histograms for cardinality estimation, particularly due to the computational complexity and time required for determining q,θ-acceptable histogram buckets, which affects query optimization and performance.
Innovation Solution
The development of a novel space- and time-efficient algorithm for constructing maximal q,θ-optimal histogram buckets, incorporating improved decision procedures like ISACCEPTABLEBUCKETMVS and ISACCEPTABLEBUCKETDYNAMIC, which reduce the runtime complexity by bounding the search space and integrating testing with incremental bucket construction, allowing for faster and more efficient histogram construction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional histogram construction methods are used to ensure q,θ-optimality, then cardinality estimation accuracy is improved, but construction time and computational complexity increase significantly
Solution Approach 1:
The algorithm segments the histogram construction process into distinct phases: generating candidate buckets, testing their q,θ-acceptability, and selectively adding them to the histogram. This segmentation allows for efficient processing by handling only promising candidates rather than exhaustively evaluating all possible buckets, thereby reducing construction time while maintaining accuracy guarantees.
Solution Approach 2:
The algorithm performs preliminary actions by pre-generating candidate buckets and pre-evaluating their potential acceptability before final inclusion in the histogram. The ISACCEPTABLEBUCKETMVS and ISACCEPTABLEBUCKETDYNAMIC procedures conduct preliminary tests to bound the search space, ensuring that only buckets meeting q,θ-criteria are constructed, thus avoiding wasted computational effort on invalid candidates.
2Reliability
If exhaustive search methods are used to find optimal histogram buckets, then estimation error bounds are guaranteed, but memory consumption and computational resources increase
Solution Approach 1:
The algorithm changes key parameters of the search process by introducing dynamic thresholds and bounds (q and θ parameters) that control the acceptability of histogram buckets. The ISACCEPTABLEBUCKETMVS procedure uses the θ parameter to bound the search space, while ISACCEPTABLEBUCKETDYNAMIC adjusts parameters dynamically during construction. This allows the system to guarantee error bounds through parameterized criteria rather than exhaustive search, reducing computational complexity while maintaining reliability.
3Measurement precision
If traditional bucket testing procedures are used, then q,θ-acceptability is verified, but runtime complexity increases due to unbounded search space
Solution Approach 1:
The algorithm introduces dynamic behavior into the bucket testing procedure through the ISACCEPTABLEBUCKETDYNAMIC procedure, which adjusts testing criteria and search bounds dynamically based on the current state of histogram construction. This dynamic approach allows the algorithm to verify q,θ-acceptability efficiently by adapting the search space bounds during construction, rather than using static exhaustive search, thereby improving construction speed while maintaining verification accuracy.
Solution Approach 2:
The algorithm introduces intermediary procedures (ISACCEPTABLEBUCKETMVS and ISACCEPTABLEBUCKETDYNAMIC) that act as mediators between the raw bucket data and the final histogram construction. These intermediary procedures implement the q,θ-acceptability testing with bounded search spaces, serving as a filter that verifies bucket quality without requiring exhaustive evaluation of all possible buckets, thus balancing verification rigor with construction efficiency.
Data Source
AI summary
A method and system to determine a q, θ-optimal histogram comprising a plurality of buckets over a data distribution where for any cardinality estimate made using the histogram the cardinality estimate is constrained to obey an acceptability criteria parameterized by q and θ that bounds a ratio error between the cardinality estimate and a true value of the cardinality, q being a factor by which the estimate deviates, at most, from a true value of the cardinality and θ being a threshold value which the cardinality does not exceed, wherein a maximum number of possible query intervals generated in determining the acceptability of the q, θ-optimal histogram is less than quadratic in the number of values.