Enhanced string factoring from alphabet orderings

Abstract

In this note we consider the concept of alphabet ordering in the context of string factoring. We propose a greedy-type algorithm which produces Lyndon factorizations with small numbers of factors along with a modification for large numbers of factors. For the technique we introduce the Exponent Parikh vector.Applications and research directions derived from circ-UMFFs are discussed.

Practical evaluation of Lyndon factors via alphabet reordering

“…In Section 3, we present two variants of a (very) simple heuristic for reordering the alphabet based on the most frequent symbols of the input string. In Section 4, we compare our heuristic with results by Clare and Daykin [4] and we show that, although simpler, ours produces results close to those presented by Clare and Daykin's method in most cases (even though not satisfactorily, as we discuss next). Unfortunately, we were not able to execute methods based on evolutionary search techniques presented in [5,11] due their high running time complexity.…”

“…This problem has been recently investigated in [4,5,11] with greedy and evolutionary algorithms (on short sequences in the range of thousands of symbols). In the next section we present a straightforward heuristic for reordering the alphabet based on frequencies of symbols in s, which produce similar results to those by Clare and Daykin's method [4].…”

“…Recent approaches (e.g. [4,5,11]) have investigated how to modify (increase or reduce) the number of Lyndon factors via reordering the symbols in the alphabet (considering a new alphabetic order for string comparisons). Very recently, Gibney and Thankachan [8] showed that the problem of finding an alphabet ordering to either minimize or maximize the number of factors is NP-complete.…”

Evolutionary search techniques for the Lyndon factorization of biosequences

“…• The output of the greedy alphabet ordering algorithm [7] may be a useful starting point from which to create one or more of the populations at the start of the search, even though this could be a local optimum. • Investigate further mutation and crossover operators for this permutation-based problem (such as the best-order crossover and other permutation crossover operators [2,3]).…”

“…In recent research, Clare and Daykin [7] proposed a greedy alphabet ordering algorithm for enhancing a Lyndon factorization. They mainly considered minimizing the number of factors while observing that the algorithm could be modified to maximize.…”