10 research outputs found
Longest Common Subsequence with Gap Constraints
We consider the longest common subsequence problem in the context of
subsequences with gap constraints. In particular, following Day et al. 2022, we
consider the setting when the distance (i. e., the gap) between two consecutive
symbols of the subsequence has to be between a lower and an upper bound (which
may depend on the position of those symbols in the subsequence or on the
symbols bordering the gap) as well as the case where the entire subsequence is
found in a bounded range (defined by a single upper bound), considered by
Kosche et al. 2022. In all these cases, we present effcient algorithms for
determining the length of the longest common constrained subsequence between
two given strings
Matching Patterns with Variables Under Simon's Congruence
We introduce and investigate a series of matching problems for patterns with
variables under Simon's congruence. Our results provide a thorough picture of
these problems' computational complexity
Combinatorial Algorithms for Subsequence Matching: A Survey
In this paper we provide an overview of a series of recent results regarding
algorithms for searching for subsequences in words or for the analysis of the
sets of subsequences occurring in a word.Comment: This is a revised version of the paper with the same title which
appeared in the Proceedings of NCMA 2022, EPTCS 367, 2022, pp. 11-27 (DOI:
10.4204/EPTCS.367.2). The revision consists in citing a series of relevant
references which were not covered in the initial version, and commenting on
how they relate to the results we survey. arXiv admin note: text overlap with
arXiv:2206.1389
The Edit Distance to k-Subsequence Universality
A word u is a subsequence of another word w if u can be obtained from w by deleting some of its letters. In the early 1970s, Imre Simon defined the relation ?_k (called now Simon-Congruence) as follows: two words having exactly the same set of subsequences of length at most k are ?_k-congruent. This relation was central in defining and analysing piecewise testable languages, but has found many applications in areas such as algorithmic learning theory, databases theory, or computational linguistics. Recently, it was shown that testing whether two words are ?_k-congruent can be done in optimal linear time. Thus, it is a natural next step to ask, for two words w and u which are not ?_k-equivalent, what is the minimal number of edit operations that we need to perform on w in order to obtain a word which is ?_k-equivalent to u.
In this paper, we consider this problem in a setting which seems interesting: when u is a k-subsequence universal word. A word u with alph(u) = ? is called k-subsequence universal if the set of subsequences of length k of u contains all possible words of length k over ?. As such, our results are a series of efficient algorithms computing the edit distance from w to the language of k-subsequence universal words
Subsequences in Bounded Ranges: Matching and Analysis Problems
In this paper, we consider a variant of the classical algorithmic problem of
checking whether a given word is a subsequence of another word . More
precisely, we consider the problem of deciding, given a number (defining a
range-bound) and two words and , whether there exists a factor
(or, in other words, a range of length ) of having as
subsequence (i.\,e., occurs as a subsequence in the bounded range
). We give matching upper and lower quadratic bounds for the time
complexity of this problem. Further, we consider a series of algorithmic
problems in this setting, in which, for given integers , and a word ,
we analyse the set -Subseq of all words of length which occur
as subsequence of some factor of length of . Among these, we consider
the -universality problem, the -equivalence problem, as well as problems
related to absent subsequences. Surprisingly, unlike the case of the classical
model of subsequences in words where such problems have efficient solutions in
general, we show that most of these problems become intractable in the new
setting when subsequences in bounded ranges are considered. Finally, we provide
an example of how some of our results can be applied to subsequence matching
problems for circular words.Comment: Extended version of a paper which will appear in the proceedings of
the 16th International Conference on Reachability Problems, RP 202
Longest common subsequence with gap constraints
We consider the longest common subsequence problem in the context of subsequences with gap constraints. In particular, following Day et al. 2022, we consider the setting when the distance (i. e., the gap) between two consecutive symbols of the subsequence has to be between a lower and an upper bound (which may depend on the position of those symbols in the subsequence or on the symbols bordering the gap) as well as the case where the entire subsequence is found in a bounded range (defined by a single upper bound), considered by Kosche et al. 2022. In all these cases, we present efficient algorithms for determining the length of the longest common constrained subsequence between two given strings.</p
LIPIcs, Volume 248, ISAAC 2022, Complete Volume
LIPIcs, Volume 248, ISAAC 2022, Complete Volum