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

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.