3 Search Results for "Hevia, Anthony"

Document
DOI: 10.4230/LIPIcs.ESA.2025.43
Edge Clique Partition and Cover Beyond Independence

Authors: Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Covering and partitioning the edges of a graph into cliques are classical problems at the intersection of combinatorial optimization and graph theory, having been studied through a range of algorithmic and complexity-theoretic lenses. Despite the well-known fixed-parameter tractability of these problems when parameterized by the total number of cliques, such a parameterization often fails to be meaningful for sparse graphs. In many real-world instances, on the other hand, the minimum number of cliques in an edge cover or partition can be very close to the size of a maximum independent set α(G). Motivated by this observation, we investigate above-α parameterizations of the edge clique cover and partition problems. Concretely, we introduce and study Edge Clique Cover Above Independent Set (ECC/α) and Edge Clique Partition Above Independent Set (ECP/α), where the goal is to cover or partition all edges of a graph using at most α(G) + k cliques, and k is the parameter. Our main results reveal a distinct complexity landscape for the two variants. We show that ECP/α is fixed-parameter tractable, whereas ECC/α is NP-complete for all k ≥ 2, yet can be solved in polynomial time for k ∈ {0,1}. These findings highlight intriguing differences between the two problems when viewed through the lens of parameterization above a natural lower bound. Finally, we demonstrate that ECC/α becomes fixed-parameter tractable when parameterized by k + ω(G), where ω(G) is the size of a maximum clique of the graph G. This result is particularly relevant for sparse graphs, in which ω is typically small. For H-minor free graphs, we design a subexponential algorithm of running time f(H)^√k ⋅ n^𝒪(1).
Cite as

Fedor V. Fomin, Petr A. Golovach, Danil Sagunov, and Kirill Simonov. Edge Clique Partition and Cover Beyond Independence. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{fomin_et_al:LIPIcs.ESA.2025.43,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Sagunov, Danil and Simonov, Kirill},
  title =	{{Edge Clique Partition and Cover Beyond Independence}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.43},
  URN =		{urn:nbn:de:0030-drops-245113},
  doi =		{10.4230/LIPIcs.ESA.2025.43},
  annote =	{Keywords: edge clique partition, edge clique cover, independence number, parameterized complexity, above guarantee}
}
Document
DOI: 10.4230/LIPIcs.WABI.2025.17
An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT

Authors: Ahsan Sanaullah, Degui Zhi, and Shaojie Zhang

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

Abstract
String matching problems in bioinformatics are typically for finding exact substring matches between a query and a reference text. Previous formulations often focus on maximum exact matches (MEMs). However, multiple occurrences of substrings of the query in the text that are long enough but not maximal may not be captured by MEMs. Such long matches can be informative, especially when the text is a collection of similar sequences such as genomes. In this paper, we describe a new type of match between a pattern and a text that aren't necessarily maximal in the query, but still contain useful matching information: locally maximal exact matches (LEMs). There are usually a large amount of LEMs, so we only consider those above some length threshold ℒ. These are referred to as long LEMs. The purpose of long LEMs is to capture substring matches between a query and a text that are not necessarily maximal in the pattern but still long enough to be important. Therefore efficient long LEMs finding algorithms are desired for these datasets. However, these datasets are too large to query on traditional string indexes. Fortunately, these datasets are very repetitive. Recently, compressed string indexes that take advantage of the redundancy in the data but retain efficient querying capability have been proposed as a solution. We therefore give an efficient algorithm for computing all the long LEMs of a query and a text in a BWT runs compressed string index. We describe an O(m+occ) expected time algorithm that relies on an O(r) words space string index for outputting all long LEMs of a pattern with respect to a text given the matching statistics of the pattern with respect to the text. Here m is the length of the query, occ is the number of long LEMs outputted, and r is the number of runs in the BWT of the text. The O(r) space string index we describe relies on an adaptation of the move data structure by Nishimoto and Tabei. We are able to support LCP[i] queries in constant time given SA[i]. In other words, we answer PLCP[i] queries in constant time. These PLCP queries enable the efficient long LEM query. Long LEMs may provide useful similarity information between a pattern and a text that MEMs may ignore. This information is particularly useful in pangenome and biobank scale haplotype panel contexts.
Cite as

Ahsan Sanaullah, Degui Zhi, and Shaojie Zhang. An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT. In 25th International Conference on Algorithms for Bioinformatics (WABI 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 344, pp. 17:1-17:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

Copy BibTex To Clipboard

@InProceedings{sanaullah_et_al:LIPIcs.WABI.2025.17,
  author =	{Sanaullah, Ahsan and Zhi, Degui and Zhang, Shaojie},
  title =	{{An Efficient Data Structure and Algorithm for Long-Match Query in Run-Length Compressed BWT}},
  booktitle =	{25th International Conference on Algorithms for Bioinformatics (WABI 2025)},
  pages =	{17:1--17:25},
  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.2025.17},
  URN =		{urn:nbn:de:0030-drops-239433},
  doi =		{10.4230/LIPIcs.WABI.2025.17},
  annote =	{Keywords: BWT, LEM, Long LEM, MEM, Run Length Compressed BWT, Move Data Structure, Pangenome}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.61
Solving Edge Clique Cover Exactly via Synergistic Data Reduction

Authors: Anthony Hevia, Benjamin Kallus, Summer McClintic, Samantha Reisner, Darren Strash, and Johnathan Wilson

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
The edge clique cover (ECC) problem - where the goal is to find a minimum cardinality set of cliques that cover all the edges of a graph - is a classic NP-hard problem that has received much attention from both the theoretical and experimental algorithms communities. While small sparse graphs can be solved exactly via the branch-and-reduce algorithm of Gramm et al. [JEA 2009], larger instances can currently only be solved inexactly using heuristics with unknown overall solution quality. We revisit computing minimum ECCs exactly in practice by combining data reduction for both the ECC and vertex clique cover (VCC) problems. We do so by modifying the polynomial-time reduction of Kou et al. [Commun. ACM 1978] to transform a reduced ECC instance to a VCC instance; alternatively, we show it is possible to "lift" some VCC reductions to the ECC problem. Our experiments show that combining data reduction for both problems (which we call synergistic data reduction) enables finding exact minimum ECCs orders of magnitude faster than the technique of Gramm et al., and allows solving large sparse graphs on up to millions of vertices and edges that have never before been solved. With these new exact solutions, we evaluate the quality of recent heuristic algorithms on large instances for the first time. The most recent of these, EO-ECC by Abdullah et al. [ICCS 2022], solves 8 of the 27 instances for which we have exact solutions. It is our hope that our strategy rallies researchers to seek improved algorithms for the ECC problem.
Cite as

Anthony Hevia, Benjamin Kallus, Summer McClintic, Samantha Reisner, Darren Strash, and Johnathan Wilson. Solving Edge Clique Cover Exactly via Synergistic Data Reduction. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 61:1-61:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{hevia_et_al:LIPIcs.ESA.2023.61,
  author =	{Hevia, Anthony and Kallus, Benjamin and McClintic, Summer and Reisner, Samantha and Strash, Darren and Wilson, Johnathan},
  title =	{{Solving Edge Clique Cover Exactly via Synergistic Data Reduction}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{61:1--61:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.61},
  URN =		{urn:nbn:de:0030-drops-187148},
  doi =		{10.4230/LIPIcs.ESA.2023.61},
  annote =	{Keywords: Edge clique cover, Vertex clique cover, Data reduction, Degeneracy}
}
  • Refine by Type
  • 3 Document/PDF
  • 2 Document/HTML

  • Refine by Publication Year
  • 2 2025
  • 1 2023

  • Refine by Author
  • 1 Fomin, Fedor V.
  • 1 Golovach, Petr A.
  • 1 Hevia, Anthony
  • 1 Kallus, Benjamin
  • 1 McClintic, Summer
  • Show More...

  • Refine by Series/Journal
  • 3 LIPIcs

  • Refine by Classification
  • 1 Mathematics of computing → Combinatorial algorithms
  • 1 Mathematics of computing → Graph algorithms
  • 1 Theory of computation → Data compression
  • 1 Theory of computation → Fixed parameter tractability
  • 1 Theory of computation → Graph algorithms analysis
  • Show More...

  • Refine by Keyword
  • 1 BWT
  • 1 Data reduction
  • 1 Degeneracy
  • 1 Edge clique cover
  • 1 LEM
  • Show More...

Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact