Veli Mäkinen

Veli Mäkinen

*This is an algorithmically generated author record based on publicly available information.

Current Organizations / Institutes

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Previous Organizations / Institutes

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Veli Mäkinen has a total of 260 co-authors. Here are the top co-authors by number of shared publications:


Latest Publications

  • Open Access

    Adaptive Encodings for Small and Fast Compressed Suffix Arrays

    by Diego Díaz-Domínguez, Veli Mäkinen

    Compressed suffix arrays index large repetitive collections and are widely used in bioinformatics, version control, and natural language processing. The \( r \) -index and its variants combine the run-length Burrows–Wheeler transform (BWT) with a sample of the suffix array to achieve space proportional to the number of equal-symbol runs. While effective for near-identical strings, their size grows quickly when edited copies are added to the collection, as the number of BWT runs is sensitive to variation. Existing approaches either apply extra compression at the cost of slower queries or prioritize speed at the expense of space, limiting practical tradeoffs at large scale. We introduce variable-length blocking (VLB), an adaptive encoding for BWT-based compressed suffix arrays. Our technique adapts the amount of indexing information to the local run structure: compressible regions retain less auxiliary data, while incompressible areas store more. Specifically, we recursively partition the BWT until each block contains at most \( w \) runs (a parameter), and organize the blocks into a tree. Accessing a position requires descending a root-to-leaf path followed by a short run scan. Compressible regions are placed near the root, while incompressible regions lie deeper and are augmented with additional indexing data to speed up access. This strategy balances space and query speed by reallocating bits saved in compressible areas to accelerate access to incompressible ones. The VLB-tree also improves memory locality by co-locating related BWT and suffix array information. Backward search relies on rank and successor queries over the BWT. We introduce a sampling technique that relaxes global correctness by guaranteeing that these queries are correct only along valid backward-search states. This restriction reduces space usage without affecting the speed or correctness of pattern matching. We further extend the concepts of the VLB-tree to encode suffix array samples and then to the subsampled \( r \) -index ( \(sr\) -index), thus producing a small fully functional compressed suffix array. Experiments show that VLB-tree variants outperform the \( r \) -index and \(sr\) -index in query time, while retaining space close to that of the \(sr\) -index. The move data structure, a recent encoding, is faster than the VLB-tree but uses considerably more space, yielding a clear space-time tradeoff.

  • Practical Colinear Chaining on Sequences Revisited

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen

  • Open Access

    Exploiting uniqueness: seed-chain-extend alignment on elastic founder graphs

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen

    Summary: Sequence-to-graph alignment is a central challenge of computational pangenomics. To overcome the theoretical hardness of the problem, state-of-the-art tools use seed-and-extend or seed-chain-extend heuristics to alignment. We implement a complete seed-chain-extend alignment workflow based on indexable elastic founder graphs (iEFGs) that support linear-time exact searches unlike general graphs. We show how to construct iEFGs, find high-quality seeds, chain, and extend them at the scale of a telomere-to-telomere assembled human chromosome. Availability and implementation: Our sequence-to-graph alignment tool and the scripts to replicate our experiments are available in https://github.com/algbio/SRFAligner.

  • Open Access

    Exploiting uniqueness: seed-chain-extend alignment on elastic founder graphs

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen

    Sequence-to-graph alignment is a central challenge of computational pangenomics. To overcome the theoretical hardness of the problem, state-of-the-art tools use seed-and-extend or seed-chain-extend heuristics to alignment, therefore reducing the computational resources required for the task. However, two main problems still remain: on the one hand, the daunting amount of sequencing data requires us to trade alignment accuracy with computational resources; on the other hand, current graph representations of pangenomes introduce an excessive amount of spurious recombinations. In this paper, we implement a complete seed-chain-extend alignment workflow based on indexable elastic founder graphs (iEFGs), a class of graphs built from aligned sequences and supporting fast pattern matching while reducing the number of artificial recombinations. We show how to construct iEFGs from the variations to a linear reference, find high-quality seeds, and extend them using GraphAligner , at the scale of a telomere-to-telomere assembled human chromosome. The main ingredient of our workflow is the use and the efficient computation of semi-repeat-free seeds (srf), a novel class of iEFG-based seeds introduced in this work. The amount of srf seeds is two orders of magnitude less than that of minimizers at the human chromosome level while maintaining comparable speed. Thanks to the uniqueness properties of iEFGs, we show that srf-based seeds suffice to maintain high accuracy while leveraging the speed of our tool. To further stress our point, we also implement chaining of seeds on the elastic degenerate string relaxation of the iEFG and show that only chained seeds suffice to achieve high accuracy alignments. Our sequence-to-graph alignment tool and the scripts to replicate our experiments are available in https://github.com/algbio/SRFAligner .


  • Open Access

    Finding maximal exact matches in graphs

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen

    Background: We study the problem of finding maximal exact matches (MEMs) between a query stringQand a labeled graphG. MEMs are an important class of seeds, often used in seed-chain-extend type of practical alignment methods because of their strong connections to classical metrics. A principled way to speed up chaining is to limit the number of MEMs by considering only MEMs of length at least $$\kappa$$κ ( $$\kappa$$κ -MEMs). However, on arbitrary input graphs, the problem of finding MEMs cannot be solved in truly sub-quadratic time under SETH (Equi et al., TALG 2023) even on acyclic graphs.Results: In this paper we show an $$O(n\cdot L \cdot d^{L-1} + m + M_{\kappa ,L})$$O(n·L·dL-1+m+Mκ,L) -time algorithm finding all $$\kappa$$κ -MEMs betweenQandGspanning exactlyLnodes inG, wherenis the total length of node labels,dis the maximum degree of a node inG, $$m = |Q|$$m=|Q| , and $$M_{\kappa ,L}$$Mκ,L is the number of output MEMs. We use this algorithm to develop a $$\kappa$$κ -MEM finding solution on indexable Elastic Founder Graphs (Equi et al., Algorithmica 2022) running in time $$O(nH^2 + m + M_\kappa )$$O(nH2+m+Mκ) , whereHis the maximum number of nodes in a block, and $$M_\kappa$$Mκ is the total number of $$\kappa$$κ -MEMs. Our results generalize to the analysis of multiple query strings (MEMs betweenGand any of the strings). Additionally, we provide some experimental results showing that the number of graph MEMs is an order of magnitude smaller than the number of string MEMs of the corresponding concatenated collection.Conclusions: We show that seed-chain-extend type of alignment methods can be implemented on top of indexable Elastic Founder Graphs by providing an efficient way to produce the seeds between a set of queries and the graph. The code is available inhttps://github.com/algbio/efg-mems.


  • Open Access

    Tackling reference bias in genotyping by using founder sequences with PanVC 3

    by Tuukka Norri, Veli Mäkinen

    Overcoming reference bias and calling insertions and deletions are major challenges in genotyping. We present PanVC 3, a set of software that can be utilized as part of various variant calling workflows. We show that, by incorporating known genetic variants to a set of founder sequences to which reads are aligned, reference bias is reduced and precision of calling insertions and deletions is improved. PanVC 3 and its source code are freely available at https://github.com/tsnorri/panvc3 and at https://anaconda.org/tsnorri/panvc3 under the MIT licence. The experiment scripts are available at https://github.com/algbio/panvc3-experiments.

  • Chaining of Maximal Exact Matches in Graphs

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen


  • Open Access

    Chaining for accurate alignment of erroneous long reads to acyclic variation graphs

    by Jun Ma, Manuel Cáceres, Leena Salmela, Veli Mäkinen, Alexandru I Tomescu

    Aligning reads to a variation graph is a standard task in pangenomics, with downstream applications such as improving variant calling. While the vg toolkit [Garrison et al. (Variation graph toolkit improves read mapping by representing genetic variation in the reference. Nat Biotechnol 2018;36:875–9)] is a popular aligner of short reads, GraphAligner [Rautiainen and Marschall (GraphAligner: rapid and versatile sequence-to-graph alignment. Genome Biol 2020;21:253–28)] is the state-of-the-art aligner of erroneous long reads. GraphAligner works by finding candidate read occurrences based on individually extending the best seeds of the read in the variation graph. However, a more principled approach recognized in the community is to co-linearly chain multiple seeds. We present a new algorithm to co-linearly chain a set of seeds in a string labeled acyclic graph, together with the first efficient implementation of such a co-linear chaining algorithm into a new aligner of erroneous long reads to acyclic variation graphs, GraphChainer. We run experiments aligning real and simulated PacBio CLR reads with average error rates 15% and 5%. Compared to GraphAligner, GraphChainer aligns 12–17% more reads, and 21–28% more total read length, on real PacBio CLR reads from human chromosomes 1, 22, and the whole human pangenome. On both simulated and real data, GraphChainer aligns between 95% and 99% of all reads, and of total read length. We also show that minigraph [Li et al. (The design and construction of reference pangenome graphs with minigraph. Genome Biol 2020;21:265–19.)] and minichain [Chandra and Jain (Sequence to graph alignment using gap-sensitive co-linear chaining. In: Proceedings of the 27th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2023). Springer, 2023, 58–73.)] obtain an accuracy of <60% on this setting. GraphChainer is freely available at https://github.com/algbio/GraphChainer. The datasets and evaluation pipeline can be reached from the previous address.


  • Open Access

    Chaining of Maximal Exact Matches in Graphs

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen

    We show how to chain maximal exact matches (MEMs) between a query string $Q$ and a labeled directed acyclic graph (DAG) $G=(V,E)$ to solve the longest common subsequence (LCS) problem between $Q$ and $G$. We obtain our result via a new symmetric formulation of chaining in DAGs that we solve in $O(m+n+k^2|V| + |E| + kN\log N)$ time, where $m=|Q|$, $n$ is the total length of node labels, $k$ is the minimum number of paths covering the nodes of $G$ and $N$ is the number of MEMs between $Q$ and node labels, which we show encode full MEMs.


  • Open Access

    Finding Maximal Exact Matches in Graphs

    by Nicola Rizzo, Manuel Cáceres, Veli Mäkinen

    We study the problem of finding maximal exact matches (MEMs) between a query string $Q$ and a labeled graph $G$. MEMs are an important class of seeds, often used in seed-chain-extend type of practical alignment methods because of their strong connections to classical metrics. A principled way to speed up chaining is to limit the number of MEMs by considering only MEMs of length at least $κ$ ($κ$-MEMs). However, on arbitrary input graphs, the problem of finding MEMs cannot be solved in truly sub-quadratic time under SETH (Equi et al., ICALP 2019) even on acyclic graphs. In this paper we show an $O(n\cdot L \cdot d^{L-1} + m + M_{κ,L})$-time algorithm finding all $κ$-MEMs between $Q$ and $G$ spanning exactly $L$ nodes in $G$, where $n$ is the total length of node labels, $d$ is the maximum degree of a node in $G$, $m = |Q|$, and $M_{κ,L}$ is the number of output MEMs. We use this algorithm to develop a $κ$-MEM finding solution on indexable Elastic Founder Graphs (Equi et al., Algorithmica 2022) running in time $O(nH^2 + m + M_κ)$, where $H$ is the maximum number of nodes in a block, and $M_κ$ is the total number of $κ$-MEMs. Our results generalize to the analysis of multiple query strings (MEMs between $G$ and any of the strings). Additionally, we provide some preliminary experimental results showing that the number of graph MEMs is an order of magnitude smaller than the number of string MEMs of the corresponding concatenated collection.