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Simple Linear Comparison of Strings in V -order

Alatabbi A., Daykin J. W., Rahman M. S., Smyth W. F.

Fundamenta Informaticae

2015

Vol. 139, nr 2

115--126

In this paper we focus on a total (but non-lexicographic) ordering of strings called V - order. We devise a new linear-time algorithm for computing the V -comparison of two finite strings. In comparison with the previous algorithm in the literature, our algorithm is both conceptually simpler, based on recording letter positions in increasing order, and more straightforward to implement, requiring only linked lists.

Combinatorics of Unique Maximal Factorization Families (UMFFs)

Daykin D.E., Daykin J.W., Smyth W.F. (Bill)

Fundamenta Informaticae

2009

Vol. 97, nr 3

295-309

Suppose a set W of strings contains exactly one rotation (cyclic shift) of every primitive string on some alphabet Σ. Then W is a circ-UMFF if and only if every word in Σ+ has a unique maximal factorization over W. The classic circ-UMFF is the set of Lyndon words based on lexicographic ordering (1958). Duval (1983) designed a linear sequential Lyndon factorization algorithm; a corresponding PRAMparallel algorithmwas described by J. Daykin, Iliopoulos and Smyth (1994). Daykin and Daykin defined new circ-UMFFs based on various methods for totally ordering sets of strings (2003), and further described the structure of all circ-UMFFs (2008). Here we prove new combinatorial results for circ-UMFFs, and in particular for the case of Lyndon words. We introduce Acrobat and Flight Deck circ-UMFFs, and describe some of our results in terms of dictionaries. Applications of circ-UMFFs pertain to structured methods for concatenating and factoring strings over ordered alphabets, and those of Lyndon words are wide ranging and multidisciplinary.