String Comparison in $V$-Order: New Lexicographic Properties & On-line Applications

TL;DR

This paper explores the properties of $V$-order, a string ordering related to UMFFs, and investigates its algorithmic applications in suffix array computation and string sorting.

Contribution

It introduces new properties of $V$-order and examines their implications for efficient string processing algorithms.

Findings

New properties of $V$-order are established.

Implications for suffix array and string sorting algorithms are analyzed.

Potential improvements in string processing efficiency are discussed.

Abstract

$V$-order is a global order on strings related to Unique Maximal Factorization Families (UMFFs), which are themselves generalizations of Lyndon words. $V$-order has recently been proposed as an alternative to lexicographical order in the computation of suffix arrays and in the suffix-sorting induced by the Burrows-Wheeler transform. Efficient $V$-ordering of strings thus becomes a matter of considerable interest. In this paper we present new and surprising results on $V$-order in strings, then go on to explore the algorithmic consequences.