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Documents authored by Strash, Darren

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.
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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.2023.61
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)

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@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}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2022.26
The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set

Authors: Ernestine Großmann, Tobias Heuer, Christian Schulz, and Darren Strash

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
The Parameterized Algorithms and Computational Experiments challenge (PACE) 2022 was devoted to engineer algorithms solving the NP-hard Directed Feedback Vertex Set (DFVS) problem. The DFVS problem is to find a minimum subset X ⊆ V in a given directed graph G = (V,E) such that, when all vertices of X and their adjacent edges are deleted from G, the remainder is acyclic. Overall, the challenge had 90 participants from 26 teams, 12 countries, and 3 continents that submitted their implementations to this year’s competition. In this report, we briefly describe the setup of the challenge, the selection of benchmark instances, as well as the ranking of the participating teams. We also briefly outline the approaches used in the submitted solvers.
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Ernestine Großmann, Tobias Heuer, Christian Schulz, and Darren Strash. The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gromann_et_al:LIPIcs.IPEC.2022.26,
  author =	{Gro{\ss}mann, Ernestine and Heuer, Tobias and Schulz, Christian and Strash, Darren},
  title =	{{The PACE 2022 Parameterized Algorithms and Computational Experiments Challenge: Directed Feedback Vertex Set}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.26},
  URN =		{urn:nbn:de:0030-drops-173826},
  doi =		{10.4230/LIPIcs.IPEC.2022.26},
  annote =	{Keywords: Feedback Vertex Set, Algorithm Engineering, FPT, Kernelization, Heuristics}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.59
Finding All Global Minimum Cuts in Practice

Authors: Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash

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

Abstract
We present a practically efficient algorithm that finds all global minimum cuts in huge undirected graphs. Our algorithm uses a multitude of kernelization rules to reduce the graph to a small equivalent instance and then finds all minimum cuts using an optimized version of the algorithm of Nagamochi, Nakao and Ibaraki. In shared memory we are able to find all minimum cuts of graphs with up to billions of edges and millions of minimum cuts in a few minutes. We also give a new linear time algorithm to find the most balanced minimum cuts given as input the representation of all minimum cuts.
Cite as

Monika Henzinger, Alexander Noe, Christian Schulz, and Darren Strash. Finding All Global Minimum Cuts in Practice. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 59:1-59:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2020.59,
  author =	{Henzinger, Monika and Noe, Alexander and Schulz, Christian and Strash, Darren},
  title =	{{Finding All Global Minimum Cuts in Practice}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{59:1--59:20},
  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.2020.59},
  URN =		{urn:nbn:de:0030-drops-129255},
  doi =		{10.4230/LIPIcs.ESA.2020.59},
  annote =	{Keywords: Minimum Cut, Graph Algorithm, Algorithm Engineering, Cut Enumeration, Balanced Cut, Global Minimum Cut, Large-scale Graph Analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.80
Simultaneous Representation of Proper and Unit Interval Graphs

Authors: Ignaz Rutter, Darren Strash, Peter Stumpf, and Michael Vollmer

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
In a confluence of combinatorics and geometry, simultaneous representations provide a way to realize combinatorial objects that share common structure. A standard case in the study of simultaneous representations is the sunflower case where all objects share the same common structure. While the recognition problem for general simultaneous interval graphs - the simultaneous version of arguably one of the most well-studied graph classes - is NP-complete, the complexity of the sunflower case for three or more simultaneous interval graphs is currently open. In this work we settle this question for proper interval graphs. We give an algorithm to recognize simultaneous proper interval graphs in linear time in the sunflower case where we allow any number of simultaneous graphs. Simultaneous unit interval graphs are much more "rigid" and therefore have less freedom in their representation. We show they can be recognized in time O(|V|*|E|) for any number of simultaneous graphs in the sunflower case where G=(V,E) is the union of the simultaneous graphs. We further show that both recognition problems are in general NP-complete if the number of simultaneous graphs is not fixed. The restriction to the sunflower case is in this sense necessary.
Cite as

Ignaz Rutter, Darren Strash, Peter Stumpf, and Michael Vollmer. Simultaneous Representation of Proper and Unit Interval Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 80:1-80:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{rutter_et_al:LIPIcs.ESA.2019.80,
  author =	{Rutter, Ignaz and Strash, Darren and Stumpf, Peter and Vollmer, Michael},
  title =	{{Simultaneous Representation of Proper and Unit Interval Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{80:1--80:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.80},
  URN =		{urn:nbn:de:0030-drops-112013},
  doi =		{10.4230/LIPIcs.ESA.2019.80},
  annote =	{Keywords: Intersection Graphs, Recognition Algorithm, Proper/Unit Interval Graphs, Simultaneous Representations}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2018.6
On Romeo and Juliet Problems: Minimizing Distance-to-Sight

Authors: Hee-Kap Ahn, Eunjin Oh, Lena Schlipf, Fabian Stehn, and Darren Strash

Published in: LIPIcs, Volume 101, 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)

Abstract
We introduce a variant of the watchman route problem, which we call the quickest pair-visibility problem. Given two persons standing at points s and t in a simple polygon P with no holes, we want to minimize the distance these persons travel in order to see each other in P. We solve two variants of this problem, one minimizing the longer distance the two persons travel (min-max) and one minimizing the total travel distance (min-sum), optimally in linear time. We also consider a query version of this problem for the min-max variant. We can preprocess a simple n-gon in linear time so that the minimum of the longer distance the two persons travel can be computed in O(log^2 n) time for any two query positions where the two persons lie.
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Hee-Kap Ahn, Eunjin Oh, Lena Schlipf, Fabian Stehn, and Darren Strash. On Romeo and Juliet Problems: Minimizing Distance-to-Sight. In 16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 101, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ahn_et_al:LIPIcs.SWAT.2018.6,
  author =	{Ahn, Hee-Kap and Oh, Eunjin and Schlipf, Lena and Stehn, Fabian and Strash, Darren},
  title =	{{On Romeo and Juliet Problems: Minimizing Distance-to-Sight}},
  booktitle =	{16th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2018)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-068-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{101},
  editor =	{Eppstein, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2018.6},
  URN =		{urn:nbn:de:0030-drops-88322},
  doi =		{10.4230/LIPIcs.SWAT.2018.6},
  annote =	{Keywords: Visibility polygon, shortest-path, watchman problems}
}
Document
DOI: 10.4230/DagSemProc.10441.2
Listing all maximal cliques in sparse graphs in near-optimal time

Authors: David Eppstein, Maarten Löffler, and Darren Strash

Published in: Dagstuhl Seminar Proceedings, Volume 10441, Exact Complexity of NP-hard Problems (2011)

Abstract
The degeneracy of an $n$-vertex graph $G$ is the smallest number $d$ such that every subgraph of $G$ contains a vertex of degree at most $d$. We show that there exists a nearly-optimal fixed-parameter tractable algorithm for enumerating all maximal cliques, parametrized by degeneracy. To achieve this result, we modify the classic Bron--Kerbosch algorithm and show that it runs in time $O(dn3^{d/3})$. We also provide matching upper and lower bounds showing that the largest possible number of maximal cliques in an $n$-vertex graph with degeneracy $d$ (when $d$ is a multiple of 3 and $nge d+3$) is $(n-d)3^{d/3}$. Therefore, our algorithm matches the $Theta(d(n-d)3^{d/3})$ worst-case output size of the problem whenever $n-d=Omega(n)$.
Cite as

David Eppstein, Maarten Löffler, and Darren Strash. Listing all maximal cliques in sparse graphs in near-optimal time. In Exact Complexity of NP-hard Problems. Dagstuhl Seminar Proceedings, Volume 10441, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{eppstein_et_al:DagSemProc.10441.2,
  author =	{Eppstein, David and L\"{o}ffler, Maarten and Strash, Darren},
  title =	{{Listing all maximal cliques in sparse graphs in near-optimal time}},
  booktitle =	{Exact Complexity of NP-hard Problems},
  pages =	{1--14},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2011},
  volume =	{10441},
  editor =	{Thore Husfeldt and Dieter Kratsch and Ramamohan Paturi and Gregory B. Sorkin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10441.2},
  URN =		{urn:nbn:de:0030-drops-29356},
  doi =		{10.4230/DagSemProc.10441.2},
  annote =	{Keywords: Clique, backtracking, degeneracy, worst-case optimality}
}
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