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1. The effect of genome graph expressiveness on the discrepancy between genome graph distance and string set distance

   Qiu, Yutong; Kingsford, Carl (January 2022, ISCB ISMB 2022)

   Motivation: Intra-sample heterogeneity describes the phenomenon where a genomic sample contains a diverse set of genomic sequences. In practice, the true string sets in a sample are often unknown due to limitations in sequencing technology. In order to compare heterogeneous samples, genome graphs can be used to represent such sets of strings. However, a genome graph is generally able to represent a string set universe that contains multiple sets of strings in addition to the true string set. This difference between genome graphs and string sets is not well characterized. As a result, a distance metric between genome graphs may not match the distance between true string sets. Results: We extend a genome graph distance metric, Graph Traversal Edit Distance (GTED) proposed by Ebrahimpour Boroojeny et al., to FGTED to model the distance between heterogeneous string sets and show that GTED and FGTED always underestimate the Earth Mover’s Edit Distance (EMED) between string sets. We introduce the notion of string set universe diameter of a genome graph. Using the diameter, we are able to upper-bound the deviation of FGTED from EMED and to improve FGTED so that it reduces the average error in empirically estimating the similarity between true string sets. On simulated T-cell receptor sequences and actual Hepatitis B virus genomes, we show that the diameter-corrected FGTED reduces the average deviation of the estimated distance from the true string set distances by more than 250%. Availability and implementation: Data and source code for reproducing the experiments are available at: https:// github.com/Kingsford-Group/gtedemedtest/. 

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2. A New String Edit Distance and Applications

   https://doi.org/10.3390/a15070242  

   Petty, Taylor; Hannig, Jan; Huszar, Tunde I.; Iyer, Hari (July 2022, Algorithms)

   String edit distances have been used for decades in applications ranging from spelling correction and web search suggestions to DNA analysis. Most string edit distances are variations of the Levenshtein distance and consider only single-character edits. In forensic applications polymorphic genetic markers such as short tandem repeats (STRs) are used. At these repetitive motifs the DNA copying errors consist of more than just single base differences. More often the phenomenon of “stutter” is observed, where the number of repeated units differs (by whole units) from the template. To adapt the Levenshtein distance to be suitable for forensic applications where DNA sequence similarity is of interest, a generalized string edit distance is defined that accommodates the addition or deletion of whole motifs in addition to single-nucleotide edits. A dynamic programming implementation is developed for computing this distance between sequences. The novelty of this algorithm is in handling the complex interactions that arise between multiple- and single-character edits. Forensic examples illustrate the purpose and use of the Restricted Forensic Levenshtein (RFL) distance measure, but applications extend to sequence alignment and string similarity in other biological areas, as well as dynamic programming algorithms more broadly. 

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3. Efficient Parallel Output-Sensitive Edit Distance

   https://doi.org/10.4230/LIPIcs.ESA.2023.40  

   Ding, Xiangyun; Dong, Xiaojun; Gu, Yan; Liu, Youzhe; Sun, Yihan (September 2023, 31st Annual European Symposium on Algorithms (ESA 2023))

   Gørtz, Inge Li; Farach-Colton, Martin; Puglisi, Simon J.; Herman, Grzegorz (Ed.)

   In this paper, we study efficient parallel edit distance algorithms, both in theory and in practice. Given two strings A[1..n] and B[1..m], and a set of operations allowed to edit the strings, the edit distance between A and B is the minimum number of operations required to transform A into B. In this paper, we use edit distance to refer to the Levenshtein distance, which allows for unit-cost single-character edits (insertions, deletions, substitutions). Sequentially, a standard Dynamic Programming (DP) algorithm solves edit distance with Θ(nm) cost. In many real-world applications, the strings to be compared are similar to each other and have small edit distances. To achieve highly practical implementations, we focus on output-sensitive parallel edit-distance algorithms, i.e., to achieve asymptotically better cost bounds than the standard Θ(nm) algorithm when the edit distance is small. We study four algorithms in the paper, including three algorithms based on Breadth-First Search (BFS), and one algorithm based on Divide-and-Conquer (DaC). Our BFS-based solution is based on the Landau-Vishkin algorithm. We implement three different data structures for the longest common prefix (LCP) queries needed in the algorithm: the classic solution using parallel suffix array, and two hash-based solutions proposed in this paper. Our DaC-based solution is inspired by the output-insensitive solution proposed by Apostolico et al., and we propose a non-trivial adaption to make it output-sensitive. All of the algorithms studied in this paper have good theoretical guarantees, and they achieve different tradeoffs between work (total number of operations), span (longest dependence chain in the computation), and space. We test and compare our algorithms on both synthetic data and real-world data, including DNA sequences, Wikipedia texts, GitHub repositories, etc. Our BFS-based algorithms outperform the existing parallel edit-distance implementation in ParlayLib in all test cases. On cases with fewer than 10⁵ edits, our algorithm can process input sequences of size 10⁹ in about ten seconds, while ParlayLib can only process sequences of sizes up to 10⁶ in the same amount of time. By comparing our algorithms, we also provide a better understanding of the choice of algorithms for different input patterns. We believe that our paper is the first systematic study in the theory and practice of parallel edit distance. 

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4. On the Complexity of Sequence to Graph Alignment

   https://doi.org/10.1007/978-3-030-17083-7  

   Jain, Chirag; Zhang, Haowen; Gao, Yu; Aluru, Srinivas (April 2019, Lecture Notes in Computer Science)

   Availability of extensive genetics data across multiple individuals and populations is driving the growing importance of graph based reference representations. Aligning sequences to graphs is a fundamental operation on several types of sequence graphs (variation graphs, assembly graphs, pan-genomes, etc.) and their biological applications. Though research on sequence to graph alignments is nascent, it can draw from related work on pattern matching in hypertext. In this paper, we study sequence to graph alignment problems under Hamming and edit distance models, and linear and affine gap penalty functions, for multiple variants of the problem that allow changes in query alone, graph alone, or in both. We prove that when changes are permitted in graphs either standalone or in conjunction with changes in the query, the sequence to graph alignment problem is NP -complete under both Hamming and edit distance models for alphabets of size ≥2 . For the case where only changes to the sequence are permitted, we present an O(|V|+m|E|) time algorithm, where m denotes the query size, and V and E denote the vertex and edge sets of the graph, respectively. Our result is generalizable to both linear and affine gap penalty functions, and improves upon the run-time complexity of existing algorithms. 

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5. Near-linear time insertion-deletion codes and (1+ ε)-approximating edit distance via indexing

   https://doi.org/10.1145/3313276.3316371  

   Haeupler, Bernhard; Rubinstein, Aviad; Shahrasbi, Amirbehshad (April 2019, ACM Symposium on Theory of Computing)

   We introduce fast-decodable indexing schemes for edit distance which can be used to speed up edit distance computations to near-linear time if one of the strings is indexed by an indexing string I. In particular, for every length n and every ε >0, one can in near linear time construct a string I ∈ Σ′n with |Σ′| = Oε(1), such that, indexing any string S ∈ Σn, symbol-by-symbol, with I results in a string S′ ∈ Σ″n where Σ″ = Σ × Σ′ for which edit distance computations are easy, i.e., one can compute a (1+ε)-approximation of the edit distance between S′ and any other string in O(n (log n)) time. Our indexing schemes can be used to improve the decoding complexity of state-of-the-art error correcting codes for insertions and deletions. In particular, they lead to near-linear time decoding algorithms for the insertion-deletion codes of [Haeupler, Shahrasbi; STOC ‘17] and faster decoding algorithms for list-decodable insertion-deletion codes of [Haeupler, Shahrasbi, Sudan; ICALP ‘18]. Interestingly, the latter codes are a crucial ingredient in the construction of fast-decodable indexing schemes. 

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