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$V$-order is a global order on strings related to Unique MaximalFactorization Families (UMFFs), which are themselves generalizations of Lyndonwords. $V$-order has recently been proposed as an alternative tolexicographical order in the computation of suffix arrays and in thesuffix-sorting induced by the Burrows-Wheeler transform. Efficient $V$-orderingof strings thus becomes a matter of considerable interest. In this paper wepresent new and surprising results on $V$-order in strings, then go on toexplore the algorithmic consequences.

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