arXiv subjects

Jannik Olbrich

Publications and source records attributed to Jannik Olbrich.

5 recordsLinked to original sources

arXiv2026

Finding Minimum Matching Cuts in $H$-free Graphs

A matching cut is a matching that is also an edge cut. In the problem Minimum Matching Cut, we ask for a matching cut with the minimum number of edges in the matching. We investigate the differences in complexity between Minimum Matching Cut, its counterpart Maximum Matching Cut, and the decision problem Matching Cut. Our polynomial-time algorithms for $P_8$-free, $S_{1,1,3}$-free and $(P_6 + P_4)$-free graphs extend the cases where Minimum Matching Cut and Maximum Matching Cut are known to differ in complexity. In addition, they solve open cases for the well-studied problem Matching Cut. The NP-hardness proof for $3P_3$-free graphs implies that Minimum Matching Cut and Matching Cut, which is polynomial-time solvable even for $sP_3$-free graphs, for any $s \geq 1$, differ in complexity on certain graph classes. Further, we give complexity dichotomies for both general and bipartite graphs of bounded radius and diameter.

math.CO↗

arXiv2025

The TAG array of a multiple sequence alignment

Modern genomic analyses increasingly rely on pangenomes, that is, representations of the genome of entire populations. The simplest representation of a pangenome is a set of individual genome sequences. Compared to e.g. sequence graphs, this has the advantage that efficient exact search via indexes based on the Burrows-Wheeler Transform (BWT) is possible, that no chimeric sequences are created, and that the results are not influenced by heuristics. However, such an index may report a match in thousands of positions even if these all correspond to the same locus, making downstream analysis unnecessarily expensive. For sufficiently similar sequences (e.g. human chromosomes), a multiple sequence alignment (MSA) can be computed. Since an MSA tends to group similar strings in the same columns, it is likely that a string occurring thousands of times in the pangenome can be described by very few columns in the MSA. We describe a method to tag entries in the BWT with the corresponding column in the MSA and develop an index that can map matches in the BWT to columns in the MSA in time proportional to the output. As a by-product, we can efficiently project a match to a designated reference genome, a capability that current pangenome aligners based on the BWT lack.

q-bio.GN↗

arXiv2025

Fast and memory-efficient BWT construction of repetitive texts using Lyndon grammars

The Burrows-Wheeler Transform (BWT) serves as the basis for many important sequence indexes. On very large datasets (e.g. genomic databases), classical BWT construction algorithms are often infeasible because they usually need to have the entire dataset in main memory. Fortunately, such large datasets are often highly repetitive. It can thus be beneficial to compute the BWT from a compressed representation. We propose an algorithm for computing the BWT via the Lyndon straight-line program, a grammar based on the standard factorization of Lyndon words. Our algorithm can also be used to compute the extended BWT (eBWT) of a multiset of sequences. We empirically evaluate our implementation and find that we can compute the BWT and eBWT of very large datasets faster and/or with less memory than competing methods.

cs.DS↗

arXiv2024

Hardness Results on Characteristics for Elastic-Degenerated Strings

Generalizations of plain strings have been proposed as a compact way to represent a collection of nearly identical sequences or to express uncertainty at specific text positions by enumerating all possibilities. While a plain string stores a character at each of its positions, generalizations consider a set of characters (indeterminate strings), a set of strings of equal length (generalized degenerate strings, or shortly GD strings), or a set of strings of arbitrary lengths (elastic-degenerate strings, or shortly ED strings). These generalizations are of importance to compactly represent such type of data, and find applications in bioinformatics for representing and maintaining a set of genetic sequences of the same taxonomy or a multiple sequence alignment. To be of use, attention has been drawn to answering various query types such as pattern matching or measuring similarity of ED strings by generalizing techniques known to plain strings. However, for some types of queries, it has been shown that a generalization of a polynomial-time solvable query on classic strings becomes NP-hard on ED strings, e.g. [Russo et al.,2022]. In that light, we wonder about other types of queries, which are of particular interest to bioinformatics: the search for the longest repeating factor, unique substrings, absent words, anti-powers, and longest previous factors. While we obtain a polynomial time algorithm for the first problem on ED strings, we show that all others are NP-hard to compute, some of them even under the restriction that the input can be modelled as an indeterminate or GD string.

cs.DS↗

arXiv2022

On the Optimisation of the GSACA Suffix Array Construction Algorithm

The suffix array is arguably one of the most important data structures in sequence analysis and consequently there is a multitude of suffix sorting algorithms. However, to this date the GSACA algorithm introduced in 2015 is the only known non-recursive linear-time suffix array construction algorithm (SACA). Despite its interesting theoretical properties, there has been little effort in improving the algorithm's subpar real-world performance. There is a super-linear algorithm DSH which relies on the same sorting principle and is faster than DivSufSort, the fastest SACA for over a decade. This paper is concerned with analysing the sorting principle used in GSACA and DSH and exploiting its properties in order to give an optimised linear-time algorithm. Our resulting algorithm is not only significantly faster than GSACA but also outperforms DivSufSort and DSH.

cs.DS↗