76d3403d0a
- Start with 4-char IDs for small databases (0-500 issues) - Scale to 5-char at 500-1500 issues, 6-char at 1500+ - Configurable via max_collision_prob, min/max_hash_length - Birthday paradox math ensures collision probability stays under threshold - Comprehensive tests and documentation - Collision calculator tool for analysis Also filed bd-aa744b to remove sequential ID code path.
121 lines
3.1 KiB
Go
121 lines
3.1 KiB
Go
package main
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import (
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"fmt"
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"math"
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)
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// Birthday paradox: P(collision) ≈ 1 - e^(-n²/2N)
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// where n = number of items, N = total possible values
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func collisionProbability(numIssues int, idLength int) float64 {
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base := 36.0 // lowercase alphanumeric
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totalPossibilities := math.Pow(base, float64(idLength))
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exponent := -float64(numIssues*numIssues) / (2.0 * totalPossibilities)
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return 1.0 - math.Exp(exponent)
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}
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// Find the expected number of collisions
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func expectedCollisions(numIssues int, idLength int) float64 {
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// Expected number of pairs that collide
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totalPairs := float64(numIssues * (numIssues - 1) / 2)
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return totalPairs * (1.0 / math.Pow(36, float64(idLength)))
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}
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// Find optimal ID length for a given database size and max collision probability
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func optimalIdLength(numIssues int, maxCollisionProb float64) int {
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for length := 3; length <= 12; length++ {
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prob := collisionProbability(numIssues, length)
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if prob <= maxCollisionProb {
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return length
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}
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}
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return 12 // fallback
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}
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func main() {
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fmt.Println("=== Collision Probability Analysis ===")
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dbSizes := []int{50, 100, 200, 500, 1000, 2000, 5000, 10000}
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idLengths := []int{4, 5, 6, 7, 8}
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// Print table header
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fmt.Printf("%-10s", "DB Size")
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for _, length := range idLengths {
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fmt.Printf("%8d-char", length)
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}
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fmt.Println()
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fmt.Println("----------------------------------------------------------")
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// Print collision probabilities
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for _, size := range dbSizes {
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fmt.Printf("%-10d", size)
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for _, length := range idLengths {
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prob := collisionProbability(size, length)
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fmt.Printf("%11.2f%%", prob*100)
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}
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fmt.Println()
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}
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fmt.Println("\n=== Recommended ID Length by Threshold ===")
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thresholds := []float64{0.10, 0.25, 0.50}
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fmt.Printf("%-10s", "DB Size")
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for _, threshold := range thresholds {
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fmt.Printf("%10.0f%%", threshold*100)
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}
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fmt.Println()
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fmt.Println("----------------------------------")
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for _, size := range dbSizes {
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fmt.Printf("%-10d", size)
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for _, threshold := range thresholds {
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optimal := optimalIdLength(size, threshold)
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fmt.Printf("%10d", optimal)
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}
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fmt.Println()
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}
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fmt.Println("\n=== Expected Number of Collisions ===")
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fmt.Printf("%-10s", "DB Size")
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for _, length := range idLengths {
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fmt.Printf("%10d-char", length)
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}
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fmt.Println()
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fmt.Println("----------------------------------------------------------")
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for _, size := range dbSizes {
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fmt.Printf("%-10d", size)
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for _, length := range idLengths {
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expected := expectedCollisions(size, length)
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fmt.Printf("%14.2f", expected)
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}
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fmt.Println()
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}
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fmt.Println("\n=== Adaptive Scaling Strategy ===")
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fmt.Println("Threshold: 25% collision probability")
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fmt.Printf("%-15s %-12s %-20s\n", "DB Size Range", "ID Length", "Collision Prob")
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fmt.Println("-------------------------------------------------------")
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ranges := []struct {
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min, max int
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}{
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{0, 50},
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{51, 150},
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{151, 500},
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{501, 1500},
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{1501, 5000},
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{5001, 15000},
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}
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threshold := 0.25
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for _, r := range ranges {
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optimal := optimalIdLength(r.max, threshold)
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prob := collisionProbability(r.max, optimal)
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fmt.Printf("%-15s %-12d %18.2f%%\n",
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fmt.Sprintf("%d-%d", r.min, r.max),
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optimal,
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prob*100)
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}
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}
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