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Documents authored by El-Kebir, Mohammed


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Dolphyin

Authors: Daniel W. Feng and Mohammed El-Kebir


Abstract

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Daniel W. Feng, Mohammed El-Kebir. Dolphyin (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@misc{dagstuhl-artifact-24317,
   title = {{Dolphyin}}, 
   author = {Feng, Daniel W. and El-Kebir, Mohammed},
   note = {Software, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:61c0cd5f22da3a8e10cc6fdac70dd7d93ecb6be5;origin=https://github.com/elkebir-group/Dolphyin;visit=swh:1:snp:40995a37bef2ff3ba9886e82d6e8c8f3e0253b9a;anchor=swh:1:rev:fbf400f4100a33ee4aeb47286cefb957abd9b77d}{\texttt{swh:1:dir:61c0cd5f22da3a8e10cc6fdac70dd7d93ecb6be5}} (visited on 2025-08-15)},
   url = {https://github.com/elkebir-group/Dolphyin},
   doi = {10.4230/artifacts.24317},
}
Document
Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer

Authors: Daniel W. Feng and Mohammed El-Kebir

Published in: LIPIcs, Volume 344, 25th International Conference on Algorithms for Bioinformatics (WABI 2025)


Abstract
Several recent cancer phylogeny inference methods have used the k-Dollo evolutionary model for single-nucleotide variants. Specifically, in this problem one is given an m × n binary matrix B and seeks a rooted tree T with m leaves that correspond to the m rows of B, and each node of T is labeled by a binary state for each of the n characters subject to the restriction that each character is gained at most once (0-to-1 transition) and subsequently lost at most k times (1-to-0 transitions). The 1-Dollo variant, also known as the persistent perfect phylogeny where one is restricted to at most k = 1 losses per character, has been studied extensively, but its hardness remains an open question. Here, we prove that the 1-Dollo Linear Phylogeny (1DLP) problem, where we additionally require the resulting 1-Dollo phylogeny T to be linear, is equivalent to verifying whether the input matrix B adheres to the Consecutive Ones Property (C1P), which can be solved in polynomial time. Due to the equivalence, several known NP-hardness results for relevant variants of C1P carry over to 1DLP, including the minimization of false negatives (0-to-1 modifications to the input matrix B) or the allowance of 2 gains and 2 losses. We furthermore show how we can recursively decompose any, not necessarily linear, 1-Dollo phylogeny T into several 1-Dollo linear phylogenies, connected by matching branching points. We extend this characterization to matrices B that admit 1-Dollo phylogenies, giving necessary and sufficient conditions for the existence of a novel decomposition of B into several submatrices and corresponding branching points. This decomposition forms the basis of Dolphyin, a new exponential-time algorithm for inferring 1-Dollo phylogenies that efficiently leverages the determination of linear 1-Dollo phylogenies as a subroutine. Dolphyin can also be applied to input matrices B with false negatives. We demonstrate that Dolphyin is runtime-competitive with a previous integer linear programming based algorithm SPhyR on simulated datasets. We additionally analyze simulated datasets with false negative errors and find that in the median case, Dolphyin infers 1-Dollo phylogenies with inferred error rates at or below the ground truth rate. Finally, we apply Dolphyin to 99 acute myeloid leukemia single-cell sequencing datasets, finding that the majority of the cancers can be explained by 1-Dollo phylogenies with false negative error rates in line with the used sequencing technology. Availability. Dolphyin is available at: https://github.com/elkebir-group/Dolphyin.

Cite as

Daniel W. Feng and Mohammed El-Kebir. Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 9:1-9:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)


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@InProceedings{feng_et_al:LIPIcs.WABI.2025.9,
  author =	{Feng, Daniel W. and El-Kebir, Mohammed},
  title =	{{Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{9:1--9:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-386-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{344},
  editor =	{Brejov\'{a}, Bro\v{n}a and Patro, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2025.9},
  URN =		{urn:nbn:de:0030-drops-239356},
  doi =		{10.4230/LIPIcs.WABI.2025.9},
  annote =	{Keywords: Intra-tumor heterogeneity, persistent perfect phylogeny, consecutive ones property, combinatorics}
}
Document
Sapling: Inferring and Summarizing Tumor Phylogenies from Bulk Data Using Backbone Trees

Authors: Yuanyuan Qi and Mohammed El-Kebir

Published in: LIPIcs, Volume 312, 24th International Workshop on Algorithms in Bioinformatics (WABI 2024)


Abstract
Cancer phylogenies are key to understanding tumor evolution. There exist many important downstream analyses that take as input a single or a small number of trees. However, due to uncertainty, one typically infers many, equally-plausible phylogenies from bulk DNA sequencing data of tumors. We introduce Sapling, a heuristic method to solve the Backbone Tree Inference from Reads problem, which seeks a small set of backbone trees on a smaller subset of mutations that collectively summarize the entire solution space. Sapling also includes a greedy algorithm to solve the Backbone Tree Expansion from Reads problem, which aims to expand an inferred backbone tree into a full tree. We prove that both problems are NP-hard. On simulated and real data, we demonstrate that Sapling is capable of inferring high-quality backbone trees that adequately summarize the solution space and that can be expanded into full trees.

Cite as

Yuanyuan Qi and Mohammed El-Kebir. Sapling: Inferring and Summarizing Tumor Phylogenies from Bulk Data Using Backbone Trees. In 24th International Workshop on Algorithms in Bioinformatics (WABI 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 312, pp. 7:1-7:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{qi_et_al:LIPIcs.WABI.2024.7,
  author =	{Qi, Yuanyuan and El-Kebir, Mohammed},
  title =	{{Sapling: Inferring and Summarizing Tumor Phylogenies from Bulk Data Using Backbone Trees}},
  booktitle =	{24th International Workshop on Algorithms in Bioinformatics (WABI 2024)},
  pages =	{7:1--7:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-340-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{312},
  editor =	{Pissis, Solon P. and Sung, Wing-Kin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2024.7},
  URN =		{urn:nbn:de:0030-drops-206518},
  doi =		{10.4230/LIPIcs.WABI.2024.7},
  annote =	{Keywords: Cancer, intra-tumor heterogeneity, consensus, maximum agreement}
}
Document
Inferring Temporally Consistent Migration Histories

Authors: Mrinmoy Saha Roddur, Sagi Snir, and Mohammed El-Kebir

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)


Abstract
Not only do many biological populations undergo evolution, but population members may also migrate from one location to another. For example, tumor cells may migrate from the primary tumor and seed a new metastasis, and pathogens may migrate from one host to another. One may represent a population’s migration history by labeling the vertices of a given phylogeny T with locations such that an edge incident to vertices with distinct locations represents a migration. Additionally, in some biological populations, taxa from distinct lineages may comigrate from one location to another in a single event, a phenomenon known as a comigration. Here, we show that a previous problem statement for inferring migration histories that are parsimonious in terms of migrations and comigrations may lead to temporally inconsistent solutions. To remedy this deficiency, we introduce precise definitions of temporal consistency of comigrations in a phylogeny, leading to three successive problems. First, we formulate the Temporally Consistent Comigrations (TCC) problem to check if a set of comigrations is temporally consistent and provide a linear time algorithm for solving this problem. Second, we formulate the Parsimonious Consistent Comigration (PCC) problem, which aims to find comigrations given a location labeling of a phylogeny. We show that PCC is NP-hard. Third, we formulate the Parsimonious Consistent Comigration History (PCCH) problem, which infers the migration history given a phylogeny and locations of its extant vertices only. We show that PCCH is NP-hard as well. On the positive side, we propose integer linear programming models to solve the PCC and PCCH problems. We apply our approach to real and simulated data.

Cite as

Mrinmoy Saha Roddur, Sagi Snir, and Mohammed El-Kebir. Inferring Temporally Consistent Migration Histories. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 9:1-9:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{roddur_et_al:LIPIcs.WABI.2023.9,
  author =	{Roddur, Mrinmoy Saha and Snir, Sagi and El-Kebir, Mohammed},
  title =	{{Inferring Temporally Consistent Migration Histories}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{9:1--9:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.9},
  URN =		{urn:nbn:de:0030-drops-186357},
  doi =		{10.4230/LIPIcs.WABI.2023.9},
  annote =	{Keywords: Metastasis, Migration, Integer Linear Programming, Maximum parsimony}
}
Document
Balancing Minimum Free Energy and Codon Adaptation Index for Pareto Optimal RNA Design

Authors: Xinyu Gu, Yuanyuan Qi, and Mohammed El-Kebir

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)


Abstract
The problem of designing an RNA sequence v that encodes for a given target protein w plays an important role in messenger RNA (mRNA) vaccine design. Due to codon degeneracy, there exist exponentially many RNA sequences for a single target protein. These candidate RNA sequences may adopt different secondary structure conformations with varying minimum free energy (MFE), affecting their thermodynamic stability and consequently mRNA half-life. In addition, species-specific codon usage bias, as measured by the codon adaptation index (CAI), also plays an essential role in translation efficiency. While previous works have focused on optimizing either MFE or CAI, more recent works have shown the merits of optimizing both objectives. Importantly, there is a trade-off between MFE and CAI, i.e. optimizing one objective is at the expense of the other. Here, we formulate the Pareto Optimal RNA Design problem, seeking the set of Pareto optimal solutions for which no other solution exists that is better in terms of both MFE and CAI. We introduce DERNA (DEsign RNA), which uses the weighted sum method to enumerate the Pareto front by optimizing convex combinations of both objectives. DERNA uses dynamic programming to solve each convex combination in O(|w|³) time and O(|w|²) space. Compared to a previous approach that only optimizes MFE, we show on a benchmark dataset that DERNA obtains solutions with identical MFE but superior CAI. Additionally, we show that DERNA matches the performance in terms of solution quality of LinearDesign, a recent approach that similarly seeks to balance MFE and CAI. Finally, we demonstrate our method’s potential for mRNA vaccine design using SARS-CoV-2 spike as the target protein.

Cite as

Xinyu Gu, Yuanyuan Qi, and Mohammed El-Kebir. Balancing Minimum Free Energy and Codon Adaptation Index for Pareto Optimal RNA Design. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{gu_et_al:LIPIcs.WABI.2023.21,
  author =	{Gu, Xinyu and Qi, Yuanyuan and El-Kebir, Mohammed},
  title =	{{Balancing Minimum Free Energy and Codon Adaptation Index for Pareto Optimal RNA Design}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.21},
  URN =		{urn:nbn:de:0030-drops-186479},
  doi =		{10.4230/LIPIcs.WABI.2023.21},
  annote =	{Keywords: Multi-objective optimization, dynamic programming, RNA sequence design, reverse translation, mRNA vaccine design}
}
Document
Complete Volume
LIPIcs, Volume 201, WABI 2021, Complete Volume

Authors: Alessandra Carbone and Mohammed El-Kebir

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)


Abstract
LIPIcs, Volume 201, WABI 2021, Complete Volume

Cite as

21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 1-400, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@Proceedings{carbone_et_al:LIPIcs.WABI.2021,
  title =	{{LIPIcs, Volume 201, WABI 2021, Complete Volume}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{1--400},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021},
  URN =		{urn:nbn:de:0030-drops-143520},
  doi =		{10.4230/LIPIcs.WABI.2021},
  annote =	{Keywords: LIPIcs, Volume 201, WABI 2021, Complete Volume}
}
Document
Front Matter
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Alessandra Carbone and Mohammed El-Kebir

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)


Abstract
Front Matter, Table of Contents, Preface, Conference Organization

Cite as

21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{carbone_et_al:LIPIcs.WABI.2021.0,
  author =	{Carbone, Alessandra and El-Kebir, Mohammed},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{0:i--0:x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.0},
  URN =		{urn:nbn:de:0030-drops-143531},
  doi =		{10.4230/LIPIcs.WABI.2021.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Parsimonious Clone Tree Reconciliation in Cancer

Authors: Palash Sashittal, Simone Zaccaria, and Mohammed El-Kebir

Published in: LIPIcs, Volume 201, 21st International Workshop on Algorithms in Bioinformatics (WABI 2021)


Abstract
Every tumor is composed of heterogeneous clones, each corresponding to a distinct subpopulation of cells that accumulated different types of somatic mutations, ranging from single-nucleotide variants (SNVs) to copy-number aberrations (CNAs). As the analysis of this intra-tumor heterogeneity has important clinical applications, several computational methods have been introduced to identify clones from DNA sequencing data. However, due to technological and methodological limitations, current analyses are restricted to identifying tumor clones only based on either SNVs or CNAs, preventing a comprehensive characterization of a tumor’s clonal composition. To overcome these challenges, we formulate the identification of clones in terms of both SNVs and CNAs as a reconciliation problem while accounting for uncertainty in the input SNV and CNA proportions. We thus characterize the computational complexity of this problem and we introduce a mixed integer linear programming formulation to solve it exactly. On simulated data, we show that tumor clones can be identified reliably, especially when further taking into account the ancestral relationships that can be inferred from the input SNVs and CNAs. On 49 tumor samples from 10 prostate cancer patients, our reconciliation approach provides a higher resolution view of tumor evolution than previous studies.

Cite as

Palash Sashittal, Simone Zaccaria, and Mohammed El-Kebir. Parsimonious Clone Tree Reconciliation in Cancer. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{sashittal_et_al:LIPIcs.WABI.2021.9,
  author =	{Sashittal, Palash and Zaccaria, Simone and El-Kebir, Mohammed},
  title =	{{Parsimonious Clone Tree Reconciliation in Cancer}},
  booktitle =	{21st International Workshop on Algorithms in Bioinformatics (WABI 2021)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-200-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{201},
  editor =	{Carbone, Alessandra and El-Kebir, Mohammed},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2021.9},
  URN =		{urn:nbn:de:0030-drops-143624},
  doi =		{10.4230/LIPIcs.WABI.2021.9},
  annote =	{Keywords: Intra-tumor heterogeneity, phylogenetics, mixed integer linear programming}
}
Document
Phyolin: Identifying a Linear Perfect Phylogeny in Single-Cell DNA Sequencing Data of Tumors

Authors: Leah L. Weber and Mohammed El-Kebir

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


Abstract
Cancer arises from an evolutionary process where somatic mutations occur and eventually give rise to clonal expansions. Modeling this evolutionary process as a phylogeny is useful for treatment decision-making as well as understanding evolutionary patterns across patients and cancer types. However, cancer phylogeny inference from single-cell DNA sequencing data of tumors is challenging due to limitations with sequencing technology and the complexity of the resulting problem. Therefore, as a first step some value might be obtained from correctly classifying the evolutionary process as either linear or branched. The biological implications of these two high-level patterns are different and understanding what cancer types and which patients have each of these trajectories could provide useful insight for both clinicians and researchers. Here, we introduce the Linear Perfect Phylogeny Flipping Problem as a means of testing a null model that the tree topology is linear and show that it is NP-hard. We develop Phyolin and, through both in silico experiments and real data application, show that it is an accurate, easy to use and a reasonably fast method for classifying an evolutionary trajectory as linear or branched.

Cite as

Leah L. Weber and Mohammed El-Kebir. Phyolin: Identifying a Linear Perfect Phylogeny in Single-Cell DNA Sequencing Data of Tumors. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{weber_et_al:LIPIcs.WABI.2020.5,
  author =	{Weber, Leah L. and El-Kebir, Mohammed},
  title =	{{Phyolin: Identifying a Linear Perfect Phylogeny in Single-Cell DNA Sequencing Data of Tumors}},
  booktitle =	{20th International Workshop on Algorithms in Bioinformatics (WABI 2020)},
  pages =	{5:1--5:14},
  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.2020.5},
  URN =		{urn:nbn:de:0030-drops-127946},
  doi =		{10.4230/LIPIcs.WABI.2020.5},
  annote =	{Keywords: Constraint programming, intra-tumor heterogeneity, combinatorial optimization}
}
Document
Parsimonious Migration History Problem: Complexity and Algorithms

Authors: Mohammed El-Kebir

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)


Abstract
In many evolutionary processes we observe extant taxa in different geographical or anatomical locations. To reconstruct the migration history from a given phylogenetic tree T, one can model locations using an additional character and apply parsimony criteria to assign a location to each internal vertex of T. The migration criterion assumes that migrations are independent events. This assumption does not hold for evolutionary processes where distinct taxa from different lineages comigrate from one location to another in a single event, as is the case in metastasis and in certain infectious diseases. To account for such cases, the comigration criterion was recently introduced, and used as an optimization criterion in the Parsimonious Migration History (PMH) problem. In this work, we show that PMH is NP-hard. In addition, we show that a variant of PMH is fixed parameter tractable (FPT) in the number of locations. On simulated instances of practical size, we demonstrate that our FPT algorithm outperforms a previous integer linear program in terms of running time.

Cite as

Mohammed El-Kebir. Parsimonious Migration History Problem: Complexity and Algorithms. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 24:1-24:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{elkebir:LIPIcs.WABI.2018.24,
  author =	{El-Kebir, Mohammed},
  title =	{{Parsimonious Migration History Problem: Complexity and Algorithms}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{24:1--24:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.24},
  URN =		{urn:nbn:de:0030-drops-93263},
  doi =		{10.4230/LIPIcs.WABI.2018.24},
  annote =	{Keywords: Reconciliation, maximum parsimony, metastasis, infection, phylogenetics, phylogeography, fixed parameter tractability}
}
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