15 Search Results for "Uçar, Bora"

Volume

LIPIcs, Volume 233

20th International Symposium on Experimental Algorithms (SEA 2022)

SEA 2022, July 25-27, 2022, Heidelberg, Germany

Editors: Christian Schulz and Bora Uçar

Document
DOI: 10.4230/LIPIcs.ESA.2025.79
Semi-Streaming Algorithms for Hypergraph Matching

Authors: Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz

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

Abstract
We propose two one-pass streaming algorithms for the NP-hard hypergraph matching problem. The first algorithm stores a small subset of potential matching edges in a stack using dual variables to select edges. It has an approximation guarantee of 1/(d(1+ε)) and requires 𝒪((n/ε)log²n) bits of memory, where n is the number of vertices in the hypergraph, d is the maximum number of vertices in a hyperedge, and ε > 0 is a parameter to be chosen. The second algorithm computes, stores, and updates a single matching as the edges stream, with an approximation ratio dependent on a parameter α. Its best approximation guarantee is 1/((2d-1) + 2 √{d(d-1)}), and it requires only 𝒪(n) memory. We have implemented both algorithms and compared them with respect to solution quality, memory consumption, and running times on two diverse sets of hypergraphs with a non-streaming greedy and a naive streaming algorithm. Our results show that the streaming algorithms achieve much better solution quality than naive algorithms when facing adverse orderings. Furthermore, these algorithms reduce the memory required by a factor of 13 in the geometric mean on our test problems, and also outperform the offline Greedy algorithm in running time.
Cite as

Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz. Semi-Streaming Algorithms for Hypergraph Matching. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 79:1-79:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2025.79,
  author =	{Reinst\"{a}dtler, Henrik and Ferdous, S M and Pothen, Alex and U\c{c}ar, Bora and Schulz, Christian},
  title =	{{Semi-Streaming Algorithms for Hypergraph Matching}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{79:1--79:19},
  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.2025.79},
  URN =		{urn:nbn:de:0030-drops-245478},
  doi =		{10.4230/LIPIcs.ESA.2025.79},
  annote =	{Keywords: hypergraph, matching, semi-streaming}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.69
Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing

Authors: David Eppstein, Michael T. Goodrich, and Songyu (Alfred) Liu

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

Abstract
We provide the first approximation quality guarantees for the Cuthull-McKee heuristic for reordering symmetric matrices to have low bandwidth, and we provide an algorithm for reconstructing bounded-bandwidth graphs from distance oracles with near-linear query complexity. To prove these results we introduce a new width parameter, BFS width, and we prove polylogarithmic upper and lower bounds on the BFS width of graphs of bounded bandwidth. Unlike other width parameters, such as bandwidth, pathwidth, and treewidth, BFS width can easily be computed in polynomial time. Bounded BFS width implies bounded bandwidth, pathwidth, and treewidth, which in turn imply fixed-parameter tractable algorithms for many problems that are NP-hard for general graphs. In addition to their applications to matrix ordering, we also provide applications of BFS width to graph reconstruction, to reconstruct graphs from distance queries, and graph drawing, to construct arc diagrams of small height.
Cite as

David Eppstein, Michael T. Goodrich, and Songyu (Alfred) Liu. Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 69:1-69:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{eppstein_et_al:LIPIcs.ESA.2025.69,
  author =	{Eppstein, David and Goodrich, Michael T. and Liu, Songyu (Alfred)},
  title =	{{Bandwidth vs BFS Width in Matrix Reordering, Graph Reconstruction, and Graph Drawing}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{69:1--69:17},
  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.2025.69},
  URN =		{urn:nbn:de:0030-drops-245373},
  doi =		{10.4230/LIPIcs.ESA.2025.69},
  annote =	{Keywords: Graph algorithms, graph theory, graph width, bandwidth, treewidth}
}
Artifact
Software
DOI: 10.4230/artifacts.24674
HeiHGM/Streaming

Authors: Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, and Christian Schulz

Abstract
Cite as

Henrik Reinstädtler, S M Ferdous, Alex Pothen, Bora Uçar, Christian Schulz. HeiHGM/Streaming (Software). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@misc{dagstuhl-artifact-24674,
   title = {{HeiHGM/Streaming}}, 
   author = {Reinst\"{a}dtler, Henrik and Ferdous, S M and Pothen, Alex and U\c{c}ar, Bora and Schulz, Christian},
   note = {Software, DFG-SCHU 2567/8-1, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:4e4522550296fb38202457ce7371bf7034ae45d9;origin=https://github.com/HeiHGM/Streaming;visit=swh:1:snp:981431da5340cbbf116e22fe0896634c2d164c50;anchor=swh:1:rev:acc7c88e5544a70f356db838f4027629ae8ffb4b}{\texttt{swh:1:dir:4e4522550296fb38202457ce7371bf7034ae45d9}} (visited on 2025-10-01)},
   url = {https://github.com/HeiHGM/Streaming},
   doi = {10.4230/artifacts.24674},
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.20
Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components

Authors: Sriram Bhyravarapu, Pritesh Kumar, Madhumita Kundu, Shivesh K. Roy, Sahiba, and Saket Saurabh

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Motivated by the growing interest in graph clustering and the framework proposed during the Dagstuhl Seminar 23331, we consider a natural specialization of this general approach (as also suggested during the seminar). The seminar introduced a broad perspective on clustering, where the goal is to partition a graph into connected components (or "clusters") that satisfy simple structural integrity constraints - not necessarily limited to cliques. In our work, we focus on the case where each cluster is required to have bounded vertex cover number. Specifically, a connected component C satisfies this condition if there exists a set S ⊆ V(C) with |S| ≤ d such that C - S is an independent set. We study this within the framework of the {Vertex Deletion to d-Vertex Cover Components} ({Vertex Deletion to d-VCC}) problem: given a graph G and an integer k, the task is to determine whether there exists a vertex set S ⊆ V(G) of size at most k such that every connected component of G - S has vertex cover number at most d. We also examine the edge-deletion variant, {Edge Deletion to d-Vertex Cover Components} ({Edge Deletion to d-VCC}), where the goal is to delete at most k edges so that each connected component of the resulting graph has vertex cover number at most d. We obtain following results. 1) {Vertex Deletion to d-VCC} admits a kernel with {𝒪}(d⁶k³) vertices and {𝒪}(d⁹k⁴) edges. 2) {Edge Deletion to d-VCC}, admits a kernel with {𝒪}(d⁴k) vertices and {𝒪}(d⁵k) edges. Both of our kernelization algorithms run in time 𝒪(1.253^d ⋅ (kd)^{𝒪(1)} ⋅ n log n). It is important to note that, unless the Exponential Time Hypothesis (ETH) fails, the dependence on d cannot be improved to 2^{o(d)}, as the case k = 0 reduces to solving the classical Vertex Cover problem, which is known to require 2^{Ω(d)} time under ETH. A key ingredient in our kernelization algorithms is a structural result about the hereditary graph class 𝒢_d, consisting of graphs in which every connected component has vertex cover number at most d. We show that 𝒢_d admits a finite obstruction set (with respect to the induced subgraph relation) of size 2^{𝒪(d²)}, where each obstruction graph has at most 3d + 2 vertices. This combinatorial result may be of independent interest.
Cite as

Sriram Bhyravarapu, Pritesh Kumar, Madhumita Kundu, Shivesh K. Roy, Sahiba, and Saket Saurabh. Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bhyravarapu_et_al:LIPIcs.MFCS.2025.20,
  author =	{Bhyravarapu, Sriram and Kumar, Pritesh and Kundu, Madhumita and Roy, Shivesh K. and Sahiba and Saurabh, Saket},
  title =	{{Kernelization in Almost Linear Time for Clustering into Bounded Vertex Cover Components}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.20},
  URN =		{urn:nbn:de:0030-drops-241276},
  doi =		{10.4230/LIPIcs.MFCS.2025.20},
  annote =	{Keywords: Parameterized complexity, Polynomial Kernels, Vertex Cover, Finite Forbidden Characterization}
}
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)

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@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.SEA.2025.25
Blocked Bloom Filters with Choices

Authors: Johanna Elena Schmitz, Jens Zentgraf, and Sven Rahmann

Published in: LIPIcs, Volume 338, 23rd International Symposium on Experimental Algorithms (SEA 2025)

Abstract
Probabilistic filters are approximate set membership data structures that represent a set of keys in small space, and answer set membership queries without false negative answers, but with a certain allowed false positive probability. Such filters are widely used in database systems, networks, storage systems and in biological sequence analysis because of their fast query times and low space requirements. Starting with Bloom filters in the 1970s, many filter data structures have been developed, each with its own advantages and disadvantages, e.g., Blocked Bloom filters, Cuckoo filters, XOR filters, Ribbon filters, and more. We introduce Blocked Bloom filters with choices that work similarly to Blocked Bloom filters, except that for each key there are two (or more) alternative choices of blocks where the key’s information may be stored. When inserting a key, we select the block using a cost function which takes into account the current load and the additional number of bits to be set in the candidate blocks. The result is a filter that partially inherits the advantages of a Blocked Bloom filter, such as the ability to insert keys rapidly online or the ability to slightly overload the filter with only a small penalty to the false positive rate. At the same time, it avoids the major disadvantage of a Blocked Bloom filter, namely the larger space consumption. Our new data structure uses less space at the same false positive rate, or has a lower false positive rate at the same space consumption as a Blocked Bloom filter. We discuss the methodology, cost functions for block selection, engineered implementation, a detailed performance evaluation and use cases in bioinformatics of Blocked Bloom filters with choices, showing that they can be of practical value. The implementation of the evaluated filters and the workflows used are provided via Gitlab at https://gitlab.com/rahmannlab/blowchoc-filters.
Cite as

Johanna Elena Schmitz, Jens Zentgraf, and Sven Rahmann. Blocked Bloom Filters with Choices. In 23rd International Symposium on Experimental Algorithms (SEA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 338, pp. 25:1-25:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schmitz_et_al:LIPIcs.SEA.2025.25,
  author =	{Schmitz, Johanna Elena and Zentgraf, Jens and Rahmann, Sven},
  title =	{{Blocked Bloom Filters with Choices}},
  booktitle =	{23rd International Symposium on Experimental Algorithms (SEA 2025)},
  pages =	{25:1--25:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-375-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{338},
  editor =	{Mutzel, Petra and Prezza, Nicola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2025.25},
  URN =		{urn:nbn:de:0030-drops-232631},
  doi =		{10.4230/LIPIcs.SEA.2025.25},
  annote =	{Keywords: Probabilistic filter, Bloom filter, power of two choices}
}
Artifact
Software
DOI: 10.4230/artifacts.22501
HeiOrient

Authors: Henrik Reinstädtler, Christian Schulz, and Bora Uçar

Abstract
Cite as

Henrik Reinstädtler, Christian Schulz, Bora Uçar. HeiOrient (Software, Source Code). Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@misc{dagstuhl-artifact-22501,
   title = {{HeiOrient}}, 
   author = {Reinst\"{a}dtler, Henrik and Schulz, Christian and U\c{c}ar, Bora},
   note = {Software, DFG-SCHU 2567/3-1, swhId: \href{https://archive.softwareheritage.org/swh:1:dir:be7317d125554a54dfd1c9d17521c500c4e1ebc3;origin=https://github.com/HeiOrient/HeiOrient;visit=swh:1:snp:ad428689c405e27808a6eac12433782b1de2166e;anchor=swh:1:rev:830c983f61d5199a6b6b0daab77fddf55d158cfd}{\texttt{swh:1:dir:be7317d125554a54dfd1c9d17521c500c4e1ebc3}} (visited on 2024-11-28)},
   url = {https://github.com/HeiOrient/HeiOrient},
   doi = {10.4230/artifacts.22501},
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.97
Engineering Edge Orientation Algorithms

Authors: Henrik Reinstädtler, Christian Schulz, and Bora Uçar

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
Given an undirected graph G, the edge orientation problem asks for assigning a direction to each edge to convert G into a directed graph. The aim is to minimize the maximum out-degree of a vertex in the resulting directed graph. This problem, which is solvable in polynomial time, arises in many applications. An ongoing challenge in edge orientation algorithms is their scalability, particularly in handling large-scale networks with millions or billions of edges efficiently. We propose a novel algorithmic framework based on finding and manipulating simple paths to face this challenge. Our framework is based on an existing algorithm and allows many algorithmic choices. By carefully exploring these choices and engineering the underlying algorithms, we obtain an implementation which is more efficient and scalable than the current state-of-the-art. Our experiments demonstrate significant performance improvements compared to state-of-the-art solvers. On average our algorithm is 6.59 times faster when compared to the state-of-the-art.
Cite as

Henrik Reinstädtler, Christian Schulz, and Bora Uçar. Engineering Edge Orientation Algorithms. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 97:1-97:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{reinstadtler_et_al:LIPIcs.ESA.2024.97,
  author =	{Reinst\"{a}dtler, Henrik and Schulz, Christian and U\c{c}ar, Bora},
  title =	{{Engineering Edge Orientation Algorithms}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{97:1--97:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.97},
  URN =		{urn:nbn:de:0030-drops-211682},
  doi =		{10.4230/LIPIcs.ESA.2024.97},
  annote =	{Keywords: edge orientation, pseudoarboricity, graph algorithms}
}
Document
DOI: 10.4230/DagRep.13.8.1
Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)

Authors: George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23331 "Recent Trends in Graph Decomposition", which took place from 13. August to 18. August, 2023. The seminar brought together 33 experts from academia and industry to discuss graph decomposition, a pivotal technique for handling massive graphs in applications such as social networks and scientific simulations. The seminar addressed the challenges posed by contemporary hardware designs, the potential of deep neural networks and reinforcement learning in developing heuristics, the unique optimization requirements of large sparse data, and the need for scalable algorithms suitable for emerging architectures. Through presentations, discussions, and collaborative sessions, the event fostered an exchange of innovative ideas, leading to the creation of community notes highlighting key open problems in the field.
Cite as

George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman. Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331). In Dagstuhl Reports, Volume 13, Issue 8, pp. 1-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{karypis_et_al:DagRep.13.8.1,
  author =	{Karypis, George and Schulz, Christian and Strash, Darren and Ajwani, Deepak and Bisseling, Rob H. and Casel, Katrin and \c{C}ataly\"{u}rek, \"{U}mit V. and Chevalier, C\'{e}dric and Chudigiewitsch, Florian and Faraj, Marcelo Fonseca and Fellows, Michael and Gottesb\"{u}ren, Lars and Heuer, Tobias and Kaya, Kamer and Lacki, Jakub and Langguth, Johannes and Li, Xiaoye Sherry and Mayer, Ruben and Meintrup, Johannes and Mizutani, Yosuke and Pellegrini, Fran\c{c}ois and Petrini, Fabrizio and Rosamond, Frances and Safro, Ilya and Schlag, Sebastian and Sharma, Roohani and Sullivan, Blair D. and U\c{c}ar, Bora and Yzelman, Albert-Jan},
  title =	{{Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)}},
  pages =	{1--45},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Karypis, George and Schulz, Christian and Strash, Darren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.1},
  URN =		{urn:nbn:de:0030-drops-198114},
  doi =		{10.4230/DagRep.13.8.1},
  annote =	{Keywords: combinatorial optimization, experimental algorithmics, parallel algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.87
Engineering Fast Algorithms for the Bottleneck Matching Problem

Authors: Ioannis Panagiotas, Grégoire Pichon, Somesh Singh, and Bora Uçar

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

Abstract
We investigate the maximum bottleneck matching problem in bipartite graphs. Given a bipartite graph with nonnegative edge weights, the problem is to find a maximum cardinality matching in which the minimum weight of an edge is the maximum. To the best of our knowledge, there are two widely used solvers for this problem based on two different approaches. There exists a third known approach in the literature, which seems inferior to those two which is presumably why there is no implementation of it. We take this third approach, make theoretical observations to improve its behavior, and implement the improved method. Experiments with the existing two solvers show that their run time can be too high to be useful in many interesting cases. Furthermore, their performance is not predictable, and slight perturbations of the input graph lead to considerable changes in the run time. On the other hand, the proposed solver’s performance is much more stable; it is almost always faster than or comparable to the two existing solvers, and its run time always remains low.
Cite as

Ioannis Panagiotas, Grégoire Pichon, Somesh Singh, and Bora Uçar. Engineering Fast Algorithms for the Bottleneck Matching Problem. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 87:1-87:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{panagiotas_et_al:LIPIcs.ESA.2023.87,
  author =	{Panagiotas, Ioannis and Pichon, Gr\'{e}goire and Singh, Somesh and U\c{c}ar, Bora},
  title =	{{Engineering Fast Algorithms for the Bottleneck Matching Problem}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{87:1--87:15},
  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.2023.87},
  URN =		{urn:nbn:de:0030-drops-187406},
  doi =		{10.4230/LIPIcs.ESA.2023.87},
  annote =	{Keywords: bipartite graphs, assignment problem, matching}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.SEA.2022
LIPIcs, Volume 233, SEA 2022, Complete Volume

Authors: Christian Schulz and Bora Uçar

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
LIPIcs, Volume 233, SEA 2022, Complete Volume
Cite as

20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 1-434, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@Proceedings{schulz_et_al:LIPIcs.SEA.2022,
  title =	{{LIPIcs, Volume 233, SEA 2022, Complete Volume}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{1--434},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022},
  URN =		{urn:nbn:de:0030-drops-165331},
  doi =		{10.4230/LIPIcs.SEA.2022},
  annote =	{Keywords: LIPIcs, Volume 233, SEA 2022, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.SEA.2022.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Christian Schulz and Bora Uçar

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

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

20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 0:i-0:xii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{schulz_et_al:LIPIcs.SEA.2022.0,
  author =	{Schulz, Christian and U\c{c}ar, Bora},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{0:i--0:xii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.0},
  URN =		{urn:nbn:de:0030-drops-165342},
  doi =		{10.4230/LIPIcs.SEA.2022.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.76
Engineering Fast Almost Optimal Algorithms for Bipartite Graph Matching

Authors: Ioannis Panagiotas and Bora Uçar

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We consider the maximum cardinality matching problem in bipartite graphs. There are a number of exact, deterministic algorithms for this purpose, whose complexities are high in practice. There are randomized approaches for special classes of bipartite graphs. Random 2-out bipartite graphs, where each vertex chooses two neighbors at random from the other side, form one class for which there is an O(m+nlog n)-time Monte Carlo algorithm. Regular bipartite graphs, where all vertices have the same degree, form another class for which there is an expected O(m + nlog n)-time Las Vegas algorithm. We investigate these two algorithms and turn them into practical heuristics with randomization. Experimental results show that the heuristics are fast and obtain near optimal matchings. They are also more robust than the state of the art heuristics used in the cardinality matching algorithms, and are generally more useful as initialization routines.
Cite as

Ioannis Panagiotas and Bora Uçar. Engineering Fast Almost Optimal Algorithms for Bipartite Graph Matching. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 76:1-76:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{panagiotas_et_al:LIPIcs.ESA.2020.76,
  author =	{Panagiotas, Ioannis and U\c{c}ar, Bora},
  title =	{{Engineering Fast Almost Optimal Algorithms for Bipartite Graph Matching}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{76:1--76:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.76},
  URN =		{urn:nbn:de:0030-drops-129424},
  doi =		{10.4230/LIPIcs.ESA.2020.76},
  annote =	{Keywords: bipartite graphs, matching, randomized algorithm}
}
Document
DOI: 10.4230/DagSemProc.09061.8
Combinatorial problems in solving linear systems

Authors: Iain S. Duff and Bora Ucar

Published in: Dagstuhl Seminar Proceedings, Volume 9061, Combinatorial Scientific Computing (2009)

Abstract
Numerical linear algebra and combinatorial optimization are vast subjects; as is their interaction. In virtually all cases there should be a notion of sparsity for a combinatorial problem to arise. Sparse matrices, therefore, form the basis of the interaction of these two seemingly disparate subjects. As the core of many of today's numerical linear algebra computations consists of sparse linear system solutions, we will cover combinatorial problems, notions, and algorithms relating to those computations. This talk is thus concerned with direct and iterative methods for sparse linear systems and their intercation with combinatorial optimization. On the direct methods side, we discuss matrix ordering; bipartite matching and matrix scaling for better pivoting; task assignment and scheduling for parallel multifrontal solvers. On the iterative method side, we discuss preconditioning techniques including incomplete factor preconditioners (notion of level of fill-in), support graph preconditioners (graph embedding concepts), and algebraic multigrids (independent sets in undirected graphs). In a separate part of the talk, we discuss methods that aim to exploit sparsity during linear system solution. These methods include block diagonalization of the matrix; efficient triangular system solutions for right-hand side vectors of single nonzero entries. Towards the end, we mention, quite briefly as they are topics of other invited talks, some other areas whose interactions with combinatorial optimization are of great benefit to numerical linear algebra. These include graph and hypergraph partitioning for load balancing problems, and colouring problems in numerical optimization. On closing, we compile and list a set of open problems.
Cite as

Iain S. Duff and Bora Ucar. Combinatorial problems in solving linear systems. In Combinatorial Scientific Computing. Dagstuhl Seminar Proceedings, Volume 9061, pp. 1-37, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{duff_et_al:DagSemProc.09061.8,
  author =	{Duff, Iain S. and Ucar, Bora},
  title =	{{Combinatorial problems in solving linear systems}},
  booktitle =	{Combinatorial Scientific Computing},
  pages =	{1--37},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9061},
  editor =	{Uwe Naumann and Olaf Schenk and Horst D. Simon and Sivan Toledo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09061.8},
  URN =		{urn:nbn:de:0030-drops-20779},
  doi =		{10.4230/DagSemProc.09061.8},
  annote =	{Keywords: Combinatorial scientific computing, graph theory, combinatorial optimization, sparse matrices, linear system solution}
}
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