6 Search Results for "Schmidt, Daniel R."

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.49
Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint

Authors: Max Klimm and Martin Knaack

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
This paper studies the problem of maximizing a monotone submodular function under an unknown knapsack constraint. A solution to this problem is a policy that decides which item to pack next based on the past packing history. The robustness factor of a policy is the worst case ratio of the solution obtained by following the policy and an optimal solution that knows the knapsack capacity. We develop an algorithm with a robustness factor that is decreasing in the curvature c of the submodular function. For the extreme cases c = 0 corresponding to a modular objective, it matches a previously known and best possible robustness factor of 1/2. For the other extreme case of c = 1 it yields a robustness factor of ≈ 0.35 improving over the best previously known robustness factor of ≈ 0.06.
Cite as

Max Klimm and Martin Knaack. Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 49:1-49:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{klimm_et_al:LIPIcs.APPROX/RANDOM.2022.49,
  author =	{Klimm, Max and Knaack, Martin},
  title =	{{Maximizing a Submodular Function with Bounded Curvature Under an Unknown Knapsack Constraint}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{49:1--49:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.49},
  URN =		{urn:nbn:de:0030-drops-171711},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.49},
  annote =	{Keywords: submodular function, knapsack, approximation algorithm, robust optimization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.79
Restricted Adaptivity in Stochastic Scheduling

Authors: Guillaume Sagnol and Daniel Schmidt genannt Waldschmidt

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee Ω((log m)/(log log m)). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of δ-delay and τ-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an 𝒪(log log m)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any δ-delay and τ-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy.
Cite as

Guillaume Sagnol and Daniel Schmidt genannt Waldschmidt. Restricted Adaptivity in Stochastic Scheduling. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 79:1-79:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sagnol_et_al:LIPIcs.ESA.2021.79,
  author =	{Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel},
  title =	{{Restricted Adaptivity in Stochastic Scheduling}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{79:1--79:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.79},
  URN =		{urn:nbn:de:0030-drops-146603},
  doi =		{10.4230/LIPIcs.ESA.2021.79},
  annote =	{Keywords: stochastic scheduling, makespan minimzation, approximation algorithm, fixed assignment policy, non-anticipatory policy}
}
Document
Media Exposition
DOI: 10.4230/LIPIcs.SoCG.2020.73
Space Ants: Constructing and Reconfiguring Large-Scale Structures with Finite Automata (Media Exposition)

Authors: Amira Abdel-Rahman, Aaron T. Becker, Daniel E. Biediger, Kenneth C. Cheung, Sándor P. Fekete, Neil A. Gershenfeld, Sabrina Hugo, Benjamin Jenett, Phillip Keldenich, Eike Niehs, Christian Rieck, Arne Schmidt, Christian Scheffer, and Michael Yannuzzi

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)

Abstract
In this video, we consider recognition and reconfiguration of lattice-based cellular structures by very simple robots with only basic functionality. The underlying motivation is the construction and modification of space facilities of enormous dimensions, where the combination of new materials with extremely simple robots promises structures of previously unthinkable size and flexibility. We present algorithmic methods that are able to detect and reconfigure arbitrary polyominoes, based on finite-state robots, while also preserving connectivity of a structure during reconfiguration. Specific results include methods for determining a bounding box, scaling a given arrangement, and adapting more general algorithms for transforming polyominoes.
Cite as

Amira Abdel-Rahman, Aaron T. Becker, Daniel E. Biediger, Kenneth C. Cheung, Sándor P. Fekete, Neil A. Gershenfeld, Sabrina Hugo, Benjamin Jenett, Phillip Keldenich, Eike Niehs, Christian Rieck, Arne Schmidt, Christian Scheffer, and Michael Yannuzzi. Space Ants: Constructing and Reconfiguring Large-Scale Structures with Finite Automata (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 73:1-73:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{abdelrahman_et_al:LIPIcs.SoCG.2020.73,
  author =	{Abdel-Rahman, Amira and Becker, Aaron T. and Biediger, Daniel E. and Cheung, Kenneth C. and Fekete, S\'{a}ndor P. and Gershenfeld, Neil A. and Hugo, Sabrina and Jenett, Benjamin and Keldenich, Phillip and Niehs, Eike and Rieck, Christian and Schmidt, Arne and Scheffer, Christian and Yannuzzi, Michael},
  title =	{{Space Ants: Constructing and Reconfiguring Large-Scale Structures with Finite Automata}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{73:1--73:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.73},
  URN =		{urn:nbn:de:0030-drops-122310},
  doi =		{10.4230/LIPIcs.SoCG.2020.73},
  annote =	{Keywords: Finite automata, reconfiguration, construction, scaling}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.18
On the Cost of Essentially Fair Clusterings

Authors: Ioana O. Bercea, Martin Groß, Samir Khuller, Aounon Kumar, Clemens Rösner, Daniel R. Schmidt, and Melanie Schmidt

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
Clustering is a fundamental tool in data mining and machine learning. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters - especially if the data is already biased. At NIPS 2017, Chierichetti et al. [Flavio Chierichetti et al., 2017] proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair k-center problem and a O(t)-approximation for the fair k-median problem, where t is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair k-center [Clemens Rösner and Melanie Schmidt, 2018]. We extend and improve the known results. Firstly, we give a 5-approximation for the fair k-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives k-center, k-supplier, k-median, k-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed.
Cite as

Ioana O. Bercea, Martin Groß, Samir Khuller, Aounon Kumar, Clemens Rösner, Daniel R. Schmidt, and Melanie Schmidt. On the Cost of Essentially Fair Clusterings. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{bercea_et_al:LIPIcs.APPROX-RANDOM.2019.18,
  author =	{Bercea, Ioana O. and Gro{\ss}, Martin and Khuller, Samir and Kumar, Aounon and R\"{o}sner, Clemens and Schmidt, Daniel R. and Schmidt, Melanie},
  title =	{{On the Cost of Essentially Fair Clusterings}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{18:1--18:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.18},
  URN =		{urn:nbn:de:0030-drops-112337},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.18},
  annote =	{Keywords: approximation, clustering, fairness, LP rounding}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.70
An Exact Algorithm for the Steiner Forest Problem

Authors: Daniel R. Schmidt, Bernd Zey, and François Margot

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
The Steiner forest problem asks for a minimum weight forest that spans a given number of terminal sets. The problem has famous linear programming based 2-approximations [Agrawal et al., 1995; Goemans and Williamson, 1995; Jain, 2001] whose bottleneck is the fact that the most natural formulation of the problem as an integer linear program (ILP) has an integrality gap of 2. We propose new cut-based ILP formulations for the problem along with exact branch-and-bound based algorithms. While our new formulations cannot improve the integrality gap, we can prove that one of them yields stronger linear programming bounds than the two previous strongest formulations: The directed cut formulation [Balakrishnan et al., 1989; Chopra and Rao, 1994] and the advanced flow-based formulation by Magnanti and Raghavan [Magnanti and Raghavan, 2005]. In an experimental evaluation, we show that the linear programming bounds of the new formulations are indeed strong on practical instances and that our new branch-and-bound algorithms outperform branch-and-bound algorithms based on the previous formulations. Our formulations can be seen as a cut-based analogon to [Magnanti and Raghavan, 2005], whose existence was an open problem.
Cite as

Daniel R. Schmidt, Bernd Zey, and François Margot. An Exact Algorithm for the Steiner Forest Problem. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 70:1-70:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{schmidt_et_al:LIPIcs.ESA.2018.70,
  author =	{Schmidt, Daniel R. and Zey, Bernd and Margot, Fran\c{c}ois},
  title =	{{An Exact Algorithm for the Steiner Forest Problem}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{70:1--70:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.70},
  URN =		{urn:nbn:de:0030-drops-95339},
  doi =		{10.4230/LIPIcs.ESA.2018.70},
  annote =	{Keywords: branch-and-bound algorithms, Steiner network problems}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.31
A Local-Search Algorithm for Steiner Forest

Authors: Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, and José Verschae

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by, e.g., the elegant primal-dual algorithm of Agrawal, Klein, and Ravi from 1995. We give a local-search-based constant-factor approximation for the problem. Local search brings in new techniques to an area that has for long not seen any improvements and might be a step towards a combinatorial algorithm for the more general survivable network design problem. Moreover, local search was an essential tool to tackle the dynamic MST/Steiner Tree problem, whereas dynamic Steiner Forest is still wide open. It is easy to see that any constant factor local search algorithm requires steps that add/drop many edges together. We propose natural local moves which, at each step, either (a) add a shortest path in the current graph and then drop a bunch of inessential edges, or (b) add a set of edges to the current solution. This second type of moves is motivated by the potential function we use to measure progress, combining the cost of the solution with a penalty for each connected component. Our carefully-chosen local moves and potential function work in tandem to eliminate bad local minima that arise when using more traditional local moves. Our analysis first considers the case where the local optimum is a single tree, and shows optimality w.r.t. moves that add a single edge (and drop a set of edges) is enough to bound the locality gap. For the general case, we show how to "project" the optimal solution onto the different trees of the local optimum without incurring too much cost (and this argument uses optimality w.r.t. both kinds of moves), followed by a tree-by-tree argument. We hope both the potential function, and our analysis techniques will be useful to develop and analyze local-search algorithms in other contexts.
Cite as

Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, and José Verschae. A Local-Search Algorithm for Steiner Forest. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gro_et_al:LIPIcs.ITCS.2018.31,
  author =	{Gro{\ss}, Martin and Gupta, Anupam and Kumar, Amit and Matuschke, Jannik and Schmidt, Daniel R. and Schmidt, Melanie and Verschae, Jos\'{e}},
  title =	{{A Local-Search Algorithm for Steiner Forest}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.31},
  URN =		{urn:nbn:de:0030-drops-83134},
  doi =		{10.4230/LIPIcs.ITCS.2018.31},
  annote =	{Keywords: Local Search, Steiner Forest, Approximation Algorithms, Network Design}
}
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