Exponential Histogram Constant-Time Insertion
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Solution Overview
Problem
Existing techniques for building exponential histograms are inefficient, as inserting a sample takes O(n) time, which can skew sample data and limit the collection of runtimes in real-time, especially when building histograms concurrently with software processes.
Innovation Solution
The proposed techniques allow for constant-time (O(1)) insertion of samples into exponential histograms using two approaches: a general approach applicable to any exponent factor and a CPU-optimized approach specific to an exponent factor of 2, leveraging hardware instructions for faster operations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If existing techniques are used to build exponential histograms, then the histogram can be constructed with detailed bins, but the time required to insert each sample increases proportionally with the number of bins
Solution Approach 1:
The patent introduces an intermediary data structure (array of bin boundaries) that mediates between the sample value and the bin selection process. By pre-computing and storing bin boundaries in an accessible structure, the system enables rapid determination of which bin a sample belongs to without linearly searching through all bins, thus resolving the contradiction between detailed histograms and fast insertion.
Solution Approach 2:
The patent applies preliminary action by pre-computing bin boundaries before the actual histogram construction and insertion process. The bin boundaries are calculated in advance based on the exponential distribution parameters, allowing the insertion phase to simply compare sample values against these pre-computed boundaries rather than performing complex calculations during insertion, thereby achieving O(1) insertion time.
2Manufacturing precision
If sample insertion takes O(n) time, then the histogram can be built with n bins, but the insertion process can skew the sample data when building concurrently with software processes
Solution Approach 1:
The pre-computed bin boundaries act as an intermediary that decouples the sample insertion process from the bin determination logic. This intermediary structure enables constant-time bin selection, ensuring that the insertion process does not introduce delays or skewness into the concurrently running software processes, thereby maintaining sample data accuracy while achieving detailed histogram construction.
Solution Approach 2:
The patent changes the parameter of insertion time complexity from O(n) to O(1) by transforming the bin selection process. Instead of iterating through bins or performing linear searches, the system uses pre-computed exponential bin boundaries with constant-time comparison, fundamentally changing the time parameter while preserving the detailed histogram structure.
3Manufacturing precision
If the number of bins is increased for better visualization, then the histogram detail improves, but the insertion time for each sample increases
Solution Approach 1:
The patent applies preliminary action by pre-computing all bin boundaries regardless of the final number of bins. This allows the system to support high-detail visualizations with many bins while maintaining constant-time insertion performance, as the pre-computed boundaries enable direct comparison-based bin selection without linear iteration, thus resolving the contradiction between visualization detail and insertion speed.
Data Source
AI summary
Computer-implemented techniques for efficiently building exponential histograms are provided. In certain embodiments, these techniques can insert a sample into an exponential histogram with n bins in constant (i.e., O(1)) time, rather than O(n) time. Accordingly, these techniques can scale well for large values of n (which allows for a high level of histogram detail/granularity) and can avoid sample skew when building an exponential histogram of software process runtimes or other software metrics.