CVM Algorithm

Cardinality Estimation for Segmentation

The Count-Distinct Problem

CVM (Cardinality Variance Model) addresses the count-distinct problem: efficiently estimating the number of unique elements in a data stream without storing every element.

Challenge: Given a stream of n elements with d distinct values, estimate d using far less than O(n) memory.

Streaming Analysis

CVM analyzes data in a sliding window, continuously estimating:

  • Distinct Symbol Count: How many unique bytes/tokens appear?
  • Distribution Uniformity: Are symbols evenly distributed or skewed?
  • Entropy Estimate: Approximate Shannon entropy without full histogram
  • Pattern Complexity: Indicative of data randomness vs. structure

Low Cardinality

10-50 Distinct Symbols

High repetition → Small alphabet

⟹ Use Static compression

Dictionary methods excel with limited vocabulary

High Cardinality

200+ Distinct Symbols

High diversity → Large alphabet

⟹ Use Adaptive compression

Context modeling captures complex patterns

Probabilistic Data Structures

CVM uses space-efficient algorithms for cardinality estimation:

HyperLogLog
MinHash
Bloom Filters

These structures provide approximate counts with bounded error using logarithmic space—essential for real-time segmentation decisions.

Application in HoloCodec

CVM serves as the segmentation oracle: it continuously monitors data characteristics and triggers compression head switches when cardinality crosses predefined thresholds. This enables adaptive routing without full-pass analysis.

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