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Documents authored by Ergun, Funda

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.
Cite as

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}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.42
Streaming Periodicity with Mismatches

Authors: Funda Ergün, Elena Grigorescu, Erfan Sadeqi Azer, and Samson Zhou

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
We study the problem of finding all k-periods of a length-n string S, presented as a data stream. S is said to have k-period p if its prefix of length n-p differs from its suffix of length n-p in at most k locations. We give a one-pass streaming algorithm that computes the k-periods of a string S using poly(k, log n) bits of space, for k-periods of length at most n/2. We also present a two-pass streaming algorithm that computes k-periods of S using poly(k, log n) bits of space, regardless of period length. We complement these results with comparable lower bounds.
Cite as

Funda Ergün, Elena Grigorescu, Erfan Sadeqi Azer, and Samson Zhou. Streaming Periodicity with Mismatches. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 42:1-42:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ergun_et_al:LIPIcs.APPROX-RANDOM.2017.42,
  author =	{Erg\"{u}n, Funda and Grigorescu, Elena and Sadeqi Azer, Erfan and Zhou, Samson},
  title =	{{Streaming Periodicity with Mismatches}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{42:1--42:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.42},
  URN =		{urn:nbn:de:0030-drops-75911},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.42},
  annote =	{Keywords: String algorithms, Streaming algorithms, Pattern matching, Randomized algorithms, Sublinear algorithms}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.149
Palindrome Recognition In The Streaming Model

Authors: Petra Berenbrink, Funda Ergün, Frederik Mallmann-Trenn, and Erfan Sadeqi Azer

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract
A palindrome is defined as a string which reads forwards the same as backwards, like, for example, the string "racecar". In the Palindrome Problem, one tries to find all palindromes in a given string. In contrast, in the case of the Longest Palindromic Substring Problem, the goal is to find an arbitrary one of the longest palindromes in the string. In this paper we present three algorithms in the streaming model for the the above problems, where at any point in time we are only allowed to use sublinear space. We first present a one-pass randomized algorithm that solves the Palindrome Problem. It has an additive error and uses square root of n space. We also give two variants of the algorithm which solve related and practical problems. The second algorithm determines the exact locations of all longest palindromes using two passes and square root of n space. The third algorithm is a one-pass randomized algorithm, which solves the Longest Palindromic Substring Problem. It has a multiplicative error using only O(log(n)) space.
Cite as

Petra Berenbrink, Funda Ergün, Frederik Mallmann-Trenn, and Erfan Sadeqi Azer. Palindrome Recognition In The Streaming Model. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 149-161, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{berenbrink_et_al:LIPIcs.STACS.2014.149,
  author =	{Berenbrink, Petra and Erg\"{u}n, Funda and Mallmann-Trenn, Frederik and Sadeqi Azer, Erfan},
  title =	{{Palindrome Recognition In The Streaming Model}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{149--161},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.149},
  URN =		{urn:nbn:de:0030-drops-44544},
  doi =		{10.4230/LIPIcs.STACS.2014.149},
  annote =	{Keywords: Palindromes, Streaming Model, Complementary Palindrome}
}
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