2020
Comparing Degenerate Strings
Publication
Publication
Fundamenta Informaticae , Volume 175  Issue 14 p. 41 58
Uncertain sequences are compact representations of sets of similar strings. They highlight common segments by collapsing them, and explicitly represent varying segments by listing all possible options. A generalized degenerate string (GD string) is a type of uncertain sequence. Formally, a GD string S is a sequence of n sets of strings of total size N, where the ith set contains strings of the same length ki but this length can vary between different sets. We denote by W the sum of these lengths k0, k1,... , kn1. Our main result is an (N + M)time algorithm for deciding whether two GD strings of total sizes N and M, respectively, over an integer alphabet, have a nonempty intersection. This result is based on a combinatorial result of independent interest: although the intersection of two GD strings can be exponential in the total size of the two strings, it can be represented in linear space. We then apply our string comparison tool to devise a simple algorithm for computing all palindromes in S in (min{W, n2}N)time. We complement this upper bound by showing a similar conditional lower bound for computing maximal palindromes in S. We also show that a result, which is essentially the same as our string comparison lineartime algorithm, can be obtained by employing an automatabased approach.
Additional Metadata  

degenerate strings, elasticdegenerate strings, generalized degenerate strings, palindromes, string comparison  
doi.org/10.3233/FI20201947  
Fundamenta Informaticae  
Alzamel, M, Ayad, L.A.K, Bernardini, G, Grossi, R, Iliopoulos, C.S, Pisanti, N, … Rosone, G. (2020). Comparing Degenerate Strings. Fundamenta Informaticae, 175(14), 41–58. doi:10.3233/FI20201947
