arXiv subjects

Andrej Baláž

Publications and source records attributed to Andrej Baláž.

4 recordsLinked to original sources

arXiv2026

Towards Optimal Prefix-Free Graph Construction: NP-Hardness and Structural Insights

Prefix-free parsing provides an efficient way to construct compressed representations of large and repetitive pangenomes and naturally induces a graph representation known as a prefix-free graph. In this work, we initiate a theoretical study of the problem of constructing prefix-free graphs of minimum size, where the size accounts for both the total length of distinct segment labels and the paths representing the input sequences. We show that selecting an optimal set of trigger words is NP-hard, already when triggers consist of single characters. Using a synchronized-code reduction, we extend this hardness result to every fixed trigger length and further show that the problem remains NP-hard over an alphabet of size three. We then establish a structural connection between prefix-free graphs and de Bruijn graphs. In particular, we show that every compacted de Bruijn graph can be realized as a prefix-free graph and derive a hierarchy relating the sizes of minimum pangenomic graphs, minimum prefix-free graphs, compacted de Bruijn graphs, and de Bruijn graphs. Finally, we give an exact fixed-parameter algorithm running in $O(2^q n)$ time, where $q$ is the number of distinct candidate trigger words and $n$ is the total pangenome length. Our results characterize both the computational limitations and the structural properties of optimizing prefix-free graph representations and provide a theoretical foundation for the design of compact graph representations of repetitive pangenomic data.

cs.CC↗

arXiv2023

Prefix-free graphs and suffix array construction in sublinear space

A recent paradigm shift in bioinformatics from a single reference genome to a pangenome brought with it several graph structures. These graph structures must implement operations, such as efficient construction from multiple genomes and read mapping. Read mapping is a well-studied problem in sequential data, and, together with data structures such as suffix array and Burrows-Wheeler transform, allows for efficient computation. Attempts to achieve comparatively high performance on graphs bring many complications since the common data structures on strings are not easily obtainable for graphs. In this work, we introduce prefix-free graphs, a novel pangenomic data structure; we show how to construct them and how to use them to obtain well-known data structures from stringology in sublinear space, allowing for many efficient operations on pangenomes.

cs.DS↗

arXiv2022

MARIA: Multiple-alignment $r$-index with aggregation

There now exist compact indexes that can efficiently list all the occurrences of a pattern in a dataset consisting of thousands of genomes, or even all the occurrences of all the pattern's maximal exact matches (MEMs) with respect to the dataset. Unless we are lucky and the pattern is specific to only a few genomes, however, we could be swamped by hundreds of matches -- or even hundreds per MEM -- only to discover that most or all of the matches are to substrings that occupy the same few columns in a multiple alignment. To address this issue, in this paper we present a simple and compact data index MARIA that stores a multiple alignment such that, given the position of one match of a pattern (or a MEM or other substring of a pattern) and its length, we can quickly list all the distinct columns of the multiple alignment where matches start.

cs.DS↗

arXiv2022

Prefix-free parsing for building large tunnelled Wheeler graphs

We propose a new technique for creating a space-efficient index for large repetitive text collections, such as pangenomic databases containing sequences of many individuals from the same species. We combine two recent techniques from this area: Wheeler graphs (Gagie et al., 2017) and prefix-free parsing (PFP, Boucher et al., 2019). Wheeler graphs (WGs) are a general framework encompassing several indexes based on the Burrows-Wheeler transform (BWT), such as the FM-index. Wheeler graphs admit a succinct representation which can be further compacted by employing the idea of tunnelling, which exploits redundancies in the form of parallel, equally-labelled paths called blocks that can be merged into a single path. The problem of finding the optimal set of blocks for tunnelling, i.e. the one that minimizes the size of the resulting WG, is known to be NP-complete and remains the most computationally challenging part of the tunnelling process. To find an adequate set of blocks in less time, we propose a new method based on the prefix-free parsing (PFP). The idea of PFP is to divide the input text into phrases of roughly equal sizes that overlap by a fixed number of characters. The original text is represented by a sequence of phrase ranks (the parse) and a list of all used phrases (the dictionary). In repetitive texts, the PFP of the text is generally much shorter than the original. To speed up the block selection for tunnelling, we apply the PFP to obtain the parse and the dictionary of the text, tunnel the WG of the parse using existing heuristics and subsequently use this tunnelled parse to construct a compact WG of the original text. Compared with constructing a WG from the original text without PFP, our method is much faster and uses less memory on collections of pangenomic sequences. Therefore, our method enables the use of WGs as a pangenomic reference for real-world datasets.

cs.DS↗