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1. Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model

   https://doi.org/10.4230/LIPIcs.SWAT.2024.3  

   Bailey, Lora; Blake, Heather Smith; Cochran, Garner; Fox, Nathan; Levet, Michael; Mahmoud, Reem; Singgih, Inne; Stadnyk, Grace; Wiedemann, Alexander (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Bodlaender, Hans L (Ed.)

   Genome rearrangement is a common model for molecular evolution. In this paper, we consider the Pairwise Rearrangement problem, which takes as input two genomes and asks for the number of minimum-length sequences of permissible operations transforming the first genome into the second. In the Single Cut-and-Join model (Bergeron, Medvedev, & Stoye, J. Comput. Biol. 2010), Pairwise Rearrangement is #P-complete (Bailey, et. al., COCOON 2023), which implies that exact sampling is intractable. In order to cope with this intractability, we investigate the parameterized complexity of this problem. We exhibit a fixed-parameter tractable algorithm with respect to the number of components in the adjacency graph that are not cycles of length 2 or paths of length 1. As a consequence, we obtain that Pairwise Rearrangement in the Single Cut-and-Join model is fixed-parameter tractable by distance. Our results suggest that the number of nontrivial components in the adjacency graph serves as the key obstacle for efficient sampling. 

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2. Estimating repeat spectra and genome length from low-coverage genome skims with RESPECT

   https://doi.org/10.1371/journal.pcbi.1009449  

   Sarmashghi, Shahab; Balaban, Metin; Rachtman, Eleonora; Touri, Behrouz; Mirarab, Siavash; Bafna, Vineet (November 2021, PLOS Computational Biology)

   Segata, Nicola (Ed.)

   The cost of sequencing the genome is dropping at a much faster rate compared to assembling and finishing the genome. The use of lightly sampled genomes (genome-skims) could be transformative for genomic ecology, and results using k -mers have shown the advantage of this approach in identification and phylogenetic placement of eukaryotic species. Here, we revisit the basic question of estimating genomic parameters such as genome length, coverage, and repeat structure, focusing specifically on estimating the k -mer repeat spectrum. We show using a mix of theoretical and empirical analysis that there are fundamental limitations to estimating the k -mer spectra due to ill-conditioned systems, and that has implications for other genomic parameters. We get around this problem using a novel constrained optimization approach (Spline Linear Programming), where the constraints are learned empirically. On reads simulated at 1X coverage from 66 genomes, our method, REPeat SPECTra Estimation (RESPECT), had 2.2% error in length estimation compared to 27% error previously achieved. In shotgun sequenced read samples with contaminants, RESPECT length estimates had median error 4%, in contrast to other methods that had median error 80%. Together, the results suggest that low-pass genomic sequencing can yield reliable estimates of the length and repeat content of the genome. The RESPECT software will be publicly available at https://urldefense.proofpoint.com/v2/url?u=https-3A__github.com_shahab-2Dsarmashghi_RESPECT.git&d=DwIGAw&c=-35OiAkTchMrZOngvJPOeA&r=ZozViWvD1E8PorCkfwYKYQMVKFoEcqLFm4Tg49XnPcA&m=f-xS8GMHKckknkc7Xpp8FJYw_ltUwz5frOw1a5pJ81EpdTOK8xhbYmrN4ZxniM96&s=717o8hLR1JmHFpRPSWG6xdUQTikyUjicjkipjFsKG4w&e= . 

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3. Parallel Longest Common SubSequence Analysis In Chapel

   https://doi.org/10.1109/HPEC58863.2023.10363472  

   Vahidi, Soroush; Schieber, Baruch; Du, Zhihui; Bader, David A (September 2023, IEEE)

   One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of strings. In this paper, we select a typical parallel LCS algorithm and integrate it into our large-scale string analysis algorithm library to support different types of large string analysis. Specifically, we take advantage of the high-level parallel language, Chapel, to integrate Lu and Liu’s parallel LCS algorithm into Arkouda, an open-source framework. Through Arkouda, data scientists can easily handle large string analytics on the back-end high-performance computing resources from the front-end Python interface. The Chapel-enabled parallel LCS algorithm can identify the longest common subsequences of two strings, and experimental results are given to show how the number of parallel resources and the length of input strings can affect the algorithm’s performance. 

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4. Parallel Longest Common SubSequence Analysis In Chapel

   Vahidi, Soroush; Schieber, Baruch; Du, Zhihui; Bader, David (September 2023, The 27th Annual IEEE High Performance Extreme Computing Conference (HPEC))

   One of the most critical problems in the field of string algorithms is the longest common subsequence problem (LCS). The problem is NP-hard for an arbitrary number of strings but can be solved in polynomial time for a fixed number of strings. In this paper, we select a typical parallel LCS algorithm and integrate it into our large-scale string analysis algorithm library to support different types of large string analysis. Specifically, we take advantage of the high-level parallel language, Chapel, to integrate Lu and Liu’s parallel LCS algorithm into Arkouda, an open-source framework. Through Arkouda, data scientists can easily handle large string analytics on the back-end high-performance computing resources from the front-end Python interface. The Chapel-enabled parallel LCS algorithm can identify the longest common subsequences of two strings, and experimental results are given to show how the number of parallel resources and the length of input strings can affect the algorithm’s performance. 

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5. On k-Mer-Based and Maximum Likelihood Estimation Algorithms for Trace Reconstruction

   Cheng, Kuan; Grigorescu, Elena; Li, Xin; Sudan, Madhu; Zhu, Minshen (July 2024, IEEE Press)

   The goal of the trace reconstruction problem is to recover a string x E {0, 1} given many independent traces of x, where a trace is a subsequence obtained from deleting bits of x independently with some given probability. In this paper we consider two kinds of algorithms for the trace reconstruction problem. We first observe that the state-of-the-art result of Chase (STOC 2021), which is based on statistics of arbitrary length-k subsequences, can also be obtained by considering the “k-mer statistics”, i.e., statistics regarding occurrences of contiguous k-bit strings (a.k.a, k-mers) in the initial string x, for k = Mazooji and Shomorony (ISIT 2023) show that such statistics (called k-mer density map) can be estimated within accuracy from poly(n, 2k, l/e) traces. We call an algorithm to be k-mer-based if it reconstructs x given estimates of the k-mer density map. Such algorithms essentially capture all the analyses in the worst-case and smoothed-complexity models of the trace reconstruction problem we know of so far. Our first, and technically more involved, result shows that any k-mer-based algorithm for trace reconstruction must use exp n)) traces, under the assumption that the estimator requires poly(2k, 1 e) traces, thus establishing the optimality of this number of traces. Our analysis also shows that the analysis technique used by Chase is essentially tight, and hence new techniques are needed in order to improve the worst-case upper bound. Our second, simple, result considers the performance of the Maximum Likelihood Estimator (MLE), which specifically picks the source string that has the maximum likelihood to generate the samples (traces). We show that the MLE algorithm uses a nearly optimal number of traces, i.e., up to a factor of n in the number of samples needed for an optimal algorithm, and show that this factor of n loss may be necessary under general “model estimation” settings. 

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