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**Published in:** LIPIcs, Volume 242, 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)

We define two new computational problems in the domain of perfect genome rearrangements, and propose three algorithms to solve them. The rearrangement scenarios modeled by the problems consider Reversal and Block Interchange operations, and a PQ-tree is utilized to guide the allowed operations and to compute their weights. In the first problem, Constrained TreeToString Divergence (CTTSD), we define the basic structure-informed rearrangement based divergence measure. Here, we assume that the gene order members of the gene cluster from which the PQ-tree is constructed are permutations. The PQ-tree representing the gene cluster is ordered such that the series of gene IDs spelled by its leaves is equivalent to the reference gene order. Then, a structure-informed gene rearrangement measure is computed between the ordered PQ-tree and the target gene order. The second problem, TreeToString Divergence (TTSD), generalizes CTTSD, where the gene order members are not necessarily permutations and the structure-informed rearrangement based divergence measure is extended to also consider up to d_S and d_T gene insertion and deletion operations, respectively, when modelling the PQ-tree informed divergence process from the reference order to the target order.
The first algorithm solves CTTSD in O(n γ² ⋅ (m_p ⋅ 1.381^γ + m_q)) time and O(n²) space, where γ is the maximum number of children of a node, n is the length of the string and the number of leaves in the tree, and m_p and m_q are the number of P-nodes and Q-nodes in the tree, respectively. If one of the penalties of CTTSD is 0, then the algorithm runs in O(n m γ²) time and O(n²) space. The second algorithm solves TTSD in O(n² γ² {d_T}² {d_S}² m² (m_p ⋅ 5^γ γ + m_q)) time and O(d_T d_S m (m n + 5^γ)) space, where γ is the maximum number of children of a node, n is the length of the string, m is the number of leaves in the tree, m_p and m_q are the number of P-nodes and Q-nodes in the tree, respectively, and allowing d_T deletions from the tree and d_S deletions from the string. The third algorithm is intended to reduce the space complexity of the second algorithm. It solves a variant of the problem (where one of the penalties of TTSD is 0) in O(n γ² {d_T}² {d_S}² m² (m_p ⋅ 4^γ γ²n(d_T+d_S+m+n) + m_q)) time and O(γ² n m² d_T d_S (d_T+d_S+m+n)) space.
The algorithm is implemented as a software tool, denoted MEM-Rearrange, and applied to the comparative and evolutionary analysis of 59 chromosomal gene clusters extracted from a dataset of 1,487 prokaryotic genomes.

Eden Ozery, Meirav Zehavi, and Michal Ziv-Ukelson. New Algorithms for Structure Informed Genome Rearrangement. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 11:1-11:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ozery_et_al:LIPIcs.WABI.2022.11, author = {Ozery, Eden and Zehavi, Meirav and Ziv-Ukelson, Michal}, title = {{New Algorithms for Structure Informed Genome Rearrangement}}, booktitle = {22nd International Workshop on Algorithms in Bioinformatics (WABI 2022)}, pages = {11:1--11:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-243-3}, ISSN = {1868-8969}, year = {2022}, volume = {242}, editor = {Boucher, Christina and Rahmann, Sven}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2022.11}, URN = {urn:nbn:de:0030-drops-170454}, doi = {10.4230/LIPIcs.WABI.2022.11}, annote = {Keywords: PQ-tree, Gene Cluster, Breakpoint Distance} }

Document

**Published in:** LIPIcs, Volume 172, 20th International Workshop on Algorithms in Bioinformatics (WABI 2020)

We define a new problem in comparative genomics, denoted PQ-Tree Search, that takes as input a PQ-tree T representing the known gene orders of a gene cluster of interest, a gene-to-gene substitution scoring function h, integer parameters d_T and d_S, and a new genome S. The objective is to identify in S approximate new instances of the gene cluster that could vary from the known gene orders by genome rearrangements that are constrained by T, by gene substitutions that are governed by h, and by gene deletions and insertions that are bounded from above by d_T and d_S, respectively. We prove that the PQ-Tree Search problem is NP-hard and propose a parameterized algorithm that solves the optimization variant of PQ-Tree Search in O^*(2^{γ}) time, where γ is the maximum degree of a node in T and O^* is used to hide factors polynomial in the input size.
The algorithm is implemented as a search tool, denoted PQFinder, and applied to search for instances of chromosomal gene clusters in plasmids, within a dataset of 1,487 prokaryotic genomes. We report on 29 chromosomal gene clusters that are rearranged in plasmids, where the rearrangements are guided by the corresponding PQ-tree. One of these results, coding for a heavy metal efflux pump, is further analysed to exemplify how PQFinder can be harnessed to reveal interesting new structural variants of known gene clusters.

Galia R. Zimerman, Dina Svetlitsky, Meirav Zehavi, and Michal Ziv-Ukelson. Approximate Search for Known Gene Clusters in New Genomes Using PQ-Trees. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{zimerman_et_al:LIPIcs.WABI.2020.1, author = {Zimerman, Galia R. and Svetlitsky, Dina and Zehavi, Meirav and Ziv-Ukelson, Michal}, title = {{Approximate Search for Known Gene Clusters in New Genomes Using PQ-Trees}}, booktitle = {20th International Workshop on Algorithms in Bioinformatics (WABI 2020)}, pages = {1:1--1:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-161-0}, ISSN = {1868-8969}, year = {2020}, volume = {172}, editor = {Kingsford, Carl and Pisanti, Nadia}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2020.1}, URN = {urn:nbn:de:0030-drops-127906}, doi = {10.4230/LIPIcs.WABI.2020.1}, annote = {Keywords: PQ-Tree, Gene Cluster, Efflux Pump} }

Document

**Published in:** LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)

An important goal in microbial computational genomics is to identify crucial events in the evolution of a gene that severely alter the duplication, loss and mobilization patterns of the gene within the genomes in which it disseminates. In this paper, we formalize this microbiological goal as a new pattern-matching problem in the domain of Gene tree and Species tree reconciliation, denoted "Reconciliation-Scenario Altering Mutation (RSAM) Discovery". We propose an O(m * n * k) time algorithm to solve this new problem, where m and n are the number of vertices of the input Gene tree and Species tree, respectively, and k is a user-specified parameter that bounds from above the number of optimal solutions of interest. The algorithm first constructs a hypergraph representing the k highest scoring reconciliation scenarios between the given Gene tree and Species tree, and then interrogates this hypergraph for subtrees matching a pre-specified RSAM Pattern. Our algorithm is optimal in the sense that the number of hypernodes in the hypergraph can be lower bounded by Omega(m * n * k). We implement the new algorithm as a tool, denoted RSAM-finder, and demonstrate its application to the identification of RSAMs in toxins and drug resistance elements across a dataset spanning hundreds of species.

Roni Zoller, Meirav Zehavi, and Michal Ziv-Ukelson. A New Paradigm for Identifying Reconciliation-Scenario Altering Mutations Conferring Environmental Adaptation. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 9:1-9:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{zoller_et_al:LIPIcs.WABI.2019.9, author = {Zoller, Roni and Zehavi, Meirav and Ziv-Ukelson, Michal}, title = {{A New Paradigm for Identifying Reconciliation-Scenario Altering Mutations Conferring Environmental Adaptation}}, booktitle = {19th International Workshop on Algorithms in Bioinformatics (WABI 2019)}, pages = {9:1--9:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-123-8}, ISSN = {1868-8969}, year = {2019}, volume = {143}, editor = {Huber, Katharina T. and Gusfield, Dan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.9}, URN = {urn:nbn:de:0030-drops-110398}, doi = {10.4230/LIPIcs.WABI.2019.9}, annote = {Keywords: Gene tree, Species tree, Reconciliation} }

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Invited Talk

**Published in:** LIPIcs, Volume 128, 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)

A major concern worldwide is the acquisition of antibiotic resistance by pathogenic bacteria. Genomic elements carrying resistance and virulence function can be acquired through horizontal gene transfer, yielding a broad spread of evolutionary successful elements, both within and in between species, with devastating effect. Recent advances in pyrosequencing techniques, combined with global efforts to study microbial adaptation to a wide range of ecological niches (and in particular to life in host tissues that we perceive as pathogenesis), yield huge and rapidly-growing databases of microbial genomes.
This big new data statistically empowers genomic-context based approaches to functional analysis: the idea is that groups of genes that are clustered locally together across many genomes usually express protein products that interact in the same biological pathway, and thus the function of a new, uncharacterized gene can be deciphered based on the previously characterized genes that are co-localized with it in the same gene cluster. Identifying and interpreting microbial gene context in huge genomic data requires efficient string-based data mining algorithms. Additionally, new computational challenges are raised by the need to study the grammar and evolutionary spreading patterns of microbial gene context.
In this talk, we will review some classical combinatorial pattern matching and data mining problems, previously inspired by this application domain. We will re-examine the biological assumptions behind the previously proposed models in light of some new biological observations. We will consider the computational challenges arising in accomodating the new biological observations, and in exploiting them to scale up the algorithmic solutions to the huge new data. Our goal is to inspire interesting new problems that harness Stringology to the study of microbial adaptation and to the fight against microbiological threats ...

Michal Ziv-Ukelson. Stringology Combats Microbiological Threats (Invited Talk). In 30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 128, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{zivukelson:LIPIcs.CPM.2019.3, author = {Ziv-Ukelson, Michal}, title = {{Stringology Combats Microbiological Threats}}, booktitle = {30th Annual Symposium on Combinatorial Pattern Matching (CPM 2019)}, pages = {3:1--3:1}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-103-0}, ISSN = {1868-8969}, year = {2019}, volume = {128}, editor = {Pisanti, Nadia and P. Pissis, Solon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2019.3}, URN = {urn:nbn:de:0030-drops-104748}, doi = {10.4230/LIPIcs.CPM.2019.3}, annote = {Keywords: comparative genomics, syntenic blocks, gene clusters, reconciliation of gene and species trees} }

Document

**Published in:** LIPIcs, Volume 54, 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)

The all scores matrix of a grid graph is a matrix containing the optimal scores of paths from every vertex on the first row of the graph to every vertex on the last row. This matrix is commonly used to solve diverse string comparison problems. All scores matrices have the Monge property, and this was exploited by previous works that used all scores matrices for solving various problems. In this paper, we study an extension of grid graphs that contain an additional set of edges, called bridges. Our main result is to show several properties of the all scores matrices of such graphs. We also give an O(r(nm + n2)) time algorithm for constructing the all scores matrix of an m × n grid graph with r bridges.

Amir Carmel, Dekel Tsur, and Michal Ziv-Ukelson. On Almost Monge All Scores Matrices. In 27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 54, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{carmel_et_al:LIPIcs.CPM.2016.17, author = {Carmel, Amir and Tsur, Dekel and Ziv-Ukelson, Michal}, title = {{On Almost Monge All Scores Matrices}}, booktitle = {27th Annual Symposium on Combinatorial Pattern Matching (CPM 2016)}, pages = {17:1--17:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-012-5}, ISSN = {1868-8969}, year = {2016}, volume = {54}, editor = {Grossi, Roberto and Lewenstein, Moshe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2016.17}, URN = {urn:nbn:de:0030-drops-60770}, doi = {10.4230/LIPIcs.CPM.2016.17}, annote = {Keywords: Sequence alignment, longest common subsequences, DIST matrices, Monge matrices, all path score computations.} }

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