Variance of the Internal Profile in Suffix Trees

TL;DR

This paper provides a detailed asymptotic analysis of the variance of the internal profile in suffix trees built from nonuniform random binary strings, addressing a longstanding open problem in the field.

Contribution

It introduces new analytical techniques combining combinatorics, singularity analysis, and Mellin transforms to analyze the variance of suffix tree profiles.

Findings

Identifies three regimes of asymptotic variance growth.

Provides precise asymptotic formulas for variance in nonuniform cases.

Addresses a longstanding open problem in suffix tree analysis.

Abstract

The precise analysis of the variance of the profile of a suffix tree has been a longstanding open problem. We analyze three regimes of the asymptotic growth of the variance of the profile of a suffix tree built from a randomly generated binary string, in the nonuniform case. We utilize combinatorics on words, singularity analysis, and the Mellin transform.