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Documents authored by Uçar, Bora

Found 2 Possible Name Variants:

Ucar, Bora

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}
}

Uçar, Bora

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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