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DOI: 10.4230/LIPIcs.GD.2025.21

On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers

Authors: Parinya Chalermsook, Ly Orgo, and Minoo Zarsav

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract

This paper considers the Zarankiewicz problem in bipartite graphs with low-dimensional geometric representation (i.e., low Ferrers dimension). Let Z(n;k) be the maximum number of edges in a bipartite graph with n nodes and is free of a k-by-k biclique. Note that Z(n;k) ∈ Ω(nk) for all "natural" graph classes. Our first result reveals a separation between bipartite graphs of Ferrers dimension three and four: while we show that Z(n;k) ≤ 9n(k-1) for graphs of Ferrers dimension three, Z(n;k) ∈ Ω(n k ⋅ (log n)/(log log n)) for Ferrers dimension four graphs (Chan & Har-Peled, 2023) (Chazelle, 1990). To complement this, we derive a tight upper bound of 2n(k-1) for chordal bipartite graphs and 54n(k-1) for grid intersection graphs (GIG), a prominent graph class residing in four Ferrers dimensions and capturing planar bipartite graphs as well as bipartite intersection graphs of rectangles. Previously, the best-known bound for GIG was Z(n;k) ∈ O(2^{O(k)} n), implied by the results of Fox & Pach (2006) and Mustafa & Pach (2016). Our results advance and offer new insights into the interplay between Ferrers dimensions and extremal combinatorics.

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Parinya Chalermsook, Ly Orgo, and Minoo Zarsav. On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 21:1-21:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chalermsook_et_al:LIPIcs.GD.2025.21,
  author =	{Chalermsook, Parinya and Orgo, Ly and Zarsav, Minoo},
  title =	{{On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{21:1--21:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.21},
  URN =		{urn:nbn:de:0030-drops-250074},
  doi =		{10.4230/LIPIcs.GD.2025.21},
  annote =	{Keywords: Bipartite graph classes, extremal graph theory, geometric intersection graphs, Zarankiewicz problem, bicliques}
}

Document

DOI: 10.4230/LIPIcs.WABI.2025.11

Mutational Signature Refitting on Sparse Pan-Cancer Data

Authors: Gal Gilad, Teresa M. Przytycka, and Roded Sharan

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

Abstract

Mutational processes shape cancer genomes, leaving characteristic marks that are termed signatures. The level of activity of each such process, or its signature exposure, provides important information on the disease, improving patient stratification and the prediction of drug response. Thus, there is growing interest in developing refitting methods that decipher those exposures. Previous work in this domain was unsupervised in nature, employing algebraic decomposition and probabilistic inference methods. Here we provide a supervised approach to the problem of signature refitting and show its superiority over current methods. Our method, SuRe, leverages a neural network model to capture correlations between signature exposures in real data. We show that SuRe outperforms previous methods on sparse mutation data from tumor type specific data sets, as well as pan-cancer data sets, with an increasing advantage as the data become sparser. We further demonstrate its utility in clinical settings.

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Gal Gilad, Teresa M. Przytycka, and Roded Sharan. Mutational Signature Refitting on Sparse Pan-Cancer Data. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 11:1-11:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{gilad_et_al:LIPIcs.WABI.2025.11,
  author =	{Gilad, Gal and Przytycka, Teresa M. and Sharan, Roded},
  title =	{{Mutational Signature Refitting on Sparse Pan-Cancer Data}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{11:1--11:23},
  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.2025.11},
  URN =		{urn:nbn:de:0030-drops-239374},
  doi =		{10.4230/LIPIcs.WABI.2025.11},
  annote =	{Keywords: mutational signatures, signature refitting, cancer genomics, genomic data analysis, somatic mutations}
}

Document

DOI: 10.4230/LIPIcs.WABI.2025.9

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.

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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

DOI: 10.4230/LIPIcs.WABI.2025.5

Improved Algorithms for Bi-Partition Function Computation

Authors: John D. Bridgers, Jan Hoinka, S. Cenk Sahinalp, Salem Malikic, Teresa M. Przytycka, and Funda Ergun

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

Abstract

The evolutionary history of a tumor, inferred from single-cell sequencing data, is typically represented as a tree in which each subtree corresponds to a clade of cells seeded by a specific set of mutations. Traditional methods typically identify a single most likely tree for downstream analyses, such as detecting driver mutations, studying mutation co-occurrence patterns and identifying common evolutionary trajectories. However, the reliability of such inferred trees, particularly their topology, clade composition, and mutational placements, often remains uncertain. To quantify this uncertainty, the concept of a Bi-partition Function was recently introduced, providing a probabilistic measure of how reliably a mutation seeds a given clade of cells. The single available algorithm for estimating the Bi-partition Function relies on simplifying assumptions and uses sampling for limited exploration of the tree-space. In this paper, we introduce the first exact algorithm for computing the Bi-partition Function. Our algorithm scales linearly with the number of mutations but exhibits super-exponential complexity with respect to the number of cells. Despite this complexity, it establishes crucial ground truth values, essential for accurately benchmarking and validating approximate methods. Additionally, we present a GPU-accelerated version of the available sampling-based algorithm, significantly boosting the computational performance through large-scale parallelization, enabling more accurate Bi-partition Function estimates via deeper exploration of the tree spaces. We compare our methods on synthetic datasets, demonstrating that especially when the number of mutations sufficiently exceed the number of cells, our GPU-accelerated sampling algorithm closely approximates the exact ground truth values.

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John D. Bridgers, Jan Hoinka, S. Cenk Sahinalp, Salem Malikic, Teresa M. Przytycka, and Funda Ergun. Improved Algorithms for Bi-Partition Function Computation. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bridgers_et_al:LIPIcs.WABI.2025.5,
  author =	{Bridgers, John D. and Hoinka, Jan and Sahinalp, S. Cenk and Malikic, Salem and Przytycka, Teresa M. and Ergun, Funda},
  title =	{{Improved Algorithms for Bi-Partition Function Computation}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{5:1--5:18},
  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.2025.5},
  URN =		{urn:nbn:de:0030-drops-239318},
  doi =		{10.4230/LIPIcs.WABI.2025.5},
  annote =	{Keywords: Tumor Evolution, Bi-partition Function, Single-Cell Sequencing, Algorithms}
}

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Invited Talk

DOI: 10.4230/LIPIcs.WABI.2023.1

Algorithmic Approaches to Study Mutational Processes in Cancer (Invited Talk)

Authors: Teresa M. Przytycka

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

Abstract

Mutations are the driving force of evolution, yet they underlie many diseases and, in particular, cancer. They are thought to arise from a combination of stochastic errors in DNA processing, naturally occurring DNA damage (e.g., the spontaneous deamination of methylated CpG sites), replication errors, carcinogenic exposures or cancer related aberrations of DNA maintenance machinery. These processes often lead to distinctive patterns of mutations, called "mutational signatures". Starting with the seminal work of Alexandrov at al. [Ludmil B Alexandrov et al., 2013] several computational approaches have been developed to uncover such mutational signatures. However connecting mutational signatures to mutational processes is not always easy [Kim et al., 2021]. To gain insights into the relationships between mutational processes and computationally derived somatic mutation patterns (mutational signatures), we developed several complementary approaches that leverage different algorithmic techniques allowing us to link such patterns to their potential causes. For example, to investigate the genetic aberrations associated with mutational signatures, we took a network-based approach considering mutational signatures as phenotypes. Specifically, our analysis aims to answer the following two complementary questions: (i) what are functional pathways whose gene expression activities correlate with the strengths of mutational signatures, and (ii) are there pathways whose genetic alterations might have led to specific mutational signatures? To identify mutated pathways, we adopted an optimization method based on integer linear programming. Analyzing a breast cancer dataset, we identified pathways associated with mutational signatures on both expression and mutation levels. Our analysis captured important differences in the etiology of the APOBEC related signatures and the two clock-like signatures. In particular, it revealed that clustered and dispersed APOBEC mutations may be caused by different mutagenic processes. In addition, our analysis elucidated differences between two age related signatures - one of the signatures is correlated with the expression of cell cycle genes while the other has no such correlation but shows patterns consistent with the exposure to environmental/external processes [Kim et al., 2020]. Complementing this approach, we also developed a network-based method, named GENESIGNET that constructs an influence/information flow network connecting genes and mutational signatures [Amgalan et al., 2023]. The approach leverages sparse partial correlation among other statistical techniques to uncover dominant influence relations between the activities of network nodes. Applying GENESIGNET to cancer data sets, we uncovered important relations between mutational signatures and several cellular processes that can shed light on cancer-related processes. In particular, GENESIGNET exposed a link between the SBS8 signature of unknown etiology and the Nucleotide Excision Repair (NER) pathway. Linking mutational signatures to molecular features can help understand the etiology and develop personalized cancer therapy. However, due to the complex and dynamic nature of tumor evolution, untangling the cause and effect relationship can be challenging and requires further integrated and comprehensive analyses.

Cite as

Teresa M. Przytycka. Algorithmic Approaches to Study Mutational Processes in Cancer (Invited Talk). In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 1:1-1:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{przytycka:LIPIcs.WABI.2023.1,
  author =	{Przytycka, Teresa M.},
  title =	{{Algorithmic Approaches to Study Mutational Processes in Cancer}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{1:1--1:2},
  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.2023.1},
  URN =		{urn:nbn:de:0030-drops-186278},
  doi =		{10.4230/LIPIcs.WABI.2023.1},
  annote =	{Keywords: Biological Networks, Cancer, Mutational Signatures, DNA Damage, DNA Repair}
}

5 Search Results for "Przytycka, Teresa M."

On Geometric Bipartite Graphs with Asymptotically Smallest Zarankiewicz Numbers

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Mutational Signature Refitting on Sparse Pan-Cancer Data

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Dolphyin: A Combinatorial Algorithm for Identifying 1-Dollo Phylogenies in Cancer

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Improved Algorithms for Bi-Partition Function Computation

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Algorithmic Approaches to Study Mutational Processes in Cancer (Invited Talk)

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