Sudo-Lyndon

Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed

CreaTology: Patterns in Digital Creative Arts

This special session presents research work on patterns in interdisciplinary areas, such as social network analyses, creative deception, and musicology with stringology. The work presented here is encouraging and opens up opportunities for potential further research and development

Evaluation of a Permutation-Based Evolutionary Framework for Lyndon Factorizations

String factorization is an important tool for partitioning data for parallel processing and other algorithmic techniques often found in the context of big data applications such as bioinformatics or compression. Duval’s well-known algorithm uniquely factors a string over an ordered alphabet into Lyndon words, i.e., patterned strings which arestrictly smaller than all of their cyclic rotations. While Duval’s algorithm produces a pre-determined factorization, modern applications motivate the demand for factorizations with specific properties, e.g., those that minimize the number of factors or consist of factors with similar lengths. In this paper, we consider the problem of finding an alphabet ordering that yields a Lyndon factorization with such properties. We introduce a flexible evolutionary framework and evaluate it on biological sequence data. For the minimization case, we also propose a new problem-specific heuristic, Flexi-Duval, and a problem-specific mutation operator for Lyndon factorization. Our results show that our framework is competitive with Flexi-Duval for minimization and yields high quality and robust solutions for balancing where no problem-specific algorithm is available

On the Size of Lempel-Ziv and Lyndon Factorizations

Peer reviewe

Longest Lyndon Substring After Edit

The longest Lyndon substring of a string T is the longest substring of T which is a Lyndon word. LLS(T) denotes the length of the longest Lyndon substring of a string T. In this paper, we consider computing LLS(T\u27) where T\u27 is an edited string formed from T. After O(n) time and space preprocessing, our algorithm returns LLS(T\u27) in O(log n) time for any single character edit. We also consider a version of the problem with block edits, i.e., a substring of T is replaced by a given string of length l. After O(n) time and space preprocessing, our algorithm returns LLS(T\u27) in O(l log sigma + log n) time for any block edit where sigma is the number of distinct characters in T. We can modify our algorithm so as to output all the longest Lyndon substrings of T\u27 for both problems