11 Search Results for "Schlöter, Jens"

Document
DOI: 10.4230/LIPIcs.STACS.2026.32
Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid

Authors: Haya Diwan, Lisa Hellerstein, Nicole Megow, and Jens Schlöter

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
Research in explorable uncertainty addresses combinatorial optimization problems where there is partial information about the values of numeric input parameters, and exact values of these parameters can be determined by performing costly queries. The goal is to design an adaptive query strategy that minimizes the query cost incurred in computing an optimal solution. Solving such problems generally requires that we be able to solve the associated verification problem: given the answers to all queries in advance, find a minimum-cost set of queries that certifies an optimal solution to the combinatorial optimization problem. We present a polynomial-time algorithm for verifying a minimum-weight basis of a matroid, where each weight lies in a given uncertainty area. These areas may be finite sets, real intervals, or unions of open and closed intervals, strictly generalizing previous work by Erlebach and Hoffman which only handled the special case of open intervals. Our algorithm introduces new techniques to address the resulting challenges. Verification problems are of particular importance in the area of explorable uncertainty, as the structural insights and techniques used to solve the verification problem often heavily influence work on the corresponding online problem and its stochastic variant. In our case, we use structural results from the verification problem to give a best-possible algorithm for a promise variant of the corresponding adaptive online problem. Finally, we show that our algorithms can be applied to two learning-augmented variants of the minimum-weight basis problem under explorable uncertainty.
Cite as

Haya Diwan, Lisa Hellerstein, Nicole Megow, and Jens Schlöter. Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{diwan_et_al:LIPIcs.STACS.2026.32,
  author =	{Diwan, Haya and Hellerstein, Lisa and Megow, Nicole and Schl\"{o}ter, Jens},
  title =	{{Optimal Verification of a Minimum-Weight Basis in an Uncertainty Matroid}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.32},
  URN =		{urn:nbn:de:0030-drops-255216},
  doi =		{10.4230/LIPIcs.STACS.2026.32},
  annote =	{Keywords: Matroid verification, minimum-weight basis, query strategy, uncertainty matroid, explorable uncertainty}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.6
On the Complexity of Knapsack Under Explorable Uncertainty: Hardness and Algorithms

Authors: Jens Schlöter

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

Abstract
In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the corresponding profits. The actual item profit can be obtained via a query. The goal of the problem is to adaptively query item profits until the revealed information suffices to compute an optimal (or approximate) solution to the underlying knapsack instance. Since queries are costly, the objective is to minimize the number of queries. In the offline variant of this problem, we assume knowledge of the precise profits and the task is to compute a query set of minimum cardinality that a third party without access to the profits could use to identify an optimal (or approximate) knapsack solution. We show that this offline variant is complete for the second-level of the polynomial hierarchy, i.e., Σ₂^p-complete, and cannot be approximated within a non-trivial factor unless Σ₂^p = Δ₂^p. Motivated by these strong hardness results, we consider a "resource-augmented" variant of the problem where the requirements on the query set computed by an algorithm are less strict than the requirements on the optimal solution we compare against. More precisely, a query set computed by the algorithm must reveal sufficient information to identify an approximate knapsack solution, while the optimal query set we compare against has to reveal sufficient information to identify an optimal solution. We show that this resource-augmented setting allows interesting non-trivial algorithmic results.
Cite as

Jens Schlöter. On the Complexity of Knapsack Under Explorable Uncertainty: Hardness and Algorithms. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{schloter:LIPIcs.ESA.2025.6,
  author =	{Schl\"{o}ter, Jens},
  title =	{{On the Complexity of Knapsack Under Explorable Uncertainty: Hardness and Algorithms}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{6:1--6:15},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-244740},
  doi =		{10.4230/LIPIcs.ESA.2025.6},
  annote =	{Keywords: Explorable uncertainty, knapsack, queries, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.12
Online Knapsack Problems with Estimates

Authors: Jakub Balabán, Matthias Gehnen, Henri Lotze, Finn Seesemann, and Moritz Stocker

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

Abstract
Imagine you are a computer scientist who enjoys attending conferences or workshops within the year. Sadly, your travel budget is limited, so you must select a subset of events you can travel to. When you are aware of all possible events and their costs at the beginning of the year, you can select the subset of the possible events that maximizes your happiness and is within your budget. On the other hand, if you are blind about the options, you will likely have a hard time when trying to decide if you want to register somewhere or not, and will likely regret decisions you made in the future. These scenarios can be modeled by knapsack variants, either by an offline or an online problem. However, both scenarios are somewhat unrealistic: Usually, you will not know the exact costs of each workshop at the beginning of the year. The online version, however, is too pessimistic, as you might already know which options there are and how much they cost roughly. At some point, you have to decide whether to register for some workshop, but then you are aware of the conference fee and the flight and hotel prices. We model this problem within the setting of online knapsack problems with estimates: in the beginning, you receive a list of potential items with their estimated size as well as the accuracy of the estimates. Then, the items are revealed one by one in an online fashion with their actual size, and you need to decide whether to take one or not. In this article, we show a best-possible algorithm for each estimate accuracy δ (i.e., when each actual item size can deviate by ± δ from the announced size) for both the simple knapsack (also known as subset sum problem) and the simple knapsack with removability.
Cite as

Jakub Balabán, Matthias Gehnen, Henri Lotze, Finn Seesemann, and Moritz Stocker. Online Knapsack Problems with Estimates. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 12:1-12:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{balaban_et_al:LIPIcs.MFCS.2025.12,
  author =	{Balab\'{a}n, Jakub and Gehnen, Matthias and Lotze, Henri and Seesemann, Finn and Stocker, Moritz},
  title =	{{Online Knapsack Problems with Estimates}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{12:1--12:19},
  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.2025.12},
  URN =		{urn:nbn:de:0030-drops-241190},
  doi =		{10.4230/LIPIcs.MFCS.2025.12},
  annote =	{Keywords: Knapsack, Online Knapsack, Removability, Estimate, Prediction}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.8
Identifying Approximate Minimizers Under Stochastic Uncertainity

Authors: Hessa Al-Thani and Viswanath Nagarajan

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We study a fundamental stochastic selection problem involving n independent random variables, each of which can be queried at some cost. Given a tolerance level δ, the goal is to find a δ-approximately minimum (or maximum) value over all the random variables, at minimum expected cost. A solution to this problem is an adaptive sequence of queries, where the choice of the next query may depend on previously-observed values. Two variants arise, depending on whether the goal is to find a δ-minimum value or a δ-minimizer. When all query costs are uniform, we provide a 4-approximation algorithm for both variants. When query costs are non-uniform, we provide a 5.83-approximation algorithm for the δ-minimum value and a 7.47-approximation for the δ-minimizer. All our algorithms rely on non-adaptive policies (that perform a fixed sequence of queries), so we also upper bound the corresponding "adaptivity" gaps. Our analysis relates the stopping probabilities in the algorithm and optimal policies, where a key step is in proving and using certain stochastic dominance properties.
Cite as

Hessa Al-Thani and Viswanath Nagarajan. Identifying Approximate Minimizers Under Stochastic Uncertainity. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{althani_et_al:LIPIcs.ICALP.2025.8,
  author =	{Al-Thani, Hessa and Nagarajan, Viswanath},
  title =	{{Identifying Approximate Minimizers Under Stochastic Uncertainity}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.8},
  URN =		{urn:nbn:de:0030-drops-233854},
  doi =		{10.4230/LIPIcs.ICALP.2025.8},
  annote =	{Keywords: Approximation algorithms, stochastic optimization, selection problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.127
Cost Preserving Dependent Rounding for Allocation Problems

Authors: Lars Rohwedder, Arman Rouhani, and Leo Wennmann

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a dependent randomized rounding scheme, which rounds fractional solutions to integral solutions satisfying certain hard constraints on the output while preserving Chernoff-like concentration properties. In contrast to previous dependent rounding schemes, our algorithm guarantees that the cost of the rounded integral solution does not exceed that of the fractional solution. Our algorithm works for a class of assignment problems with restrictions similar to those of prior works. In a non-trivial combination of our general result with a classical approach from Shmoys and Tardos [Math. Programm.'93] and more recent linear programming techniques developed for the restricted assignment variant by Bansal, Sviridenko [STOC'06] and Davies, Rothvoss, Zhang [SODA'20], we derive a O(log n)-approximation algorithm for the Budgeted Santa Claus Problem. In this new variant, the goal is to allocate resources with different values to players, maximizing the minimum value a player receives, and satisfying a budget constraint on player-resource allocation costs.
Cite as

Lars Rohwedder, Arman Rouhani, and Leo Wennmann. Cost Preserving Dependent Rounding for Allocation Problems. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder_et_al:LIPIcs.ICALP.2025.127,
  author =	{Rohwedder, Lars and Rouhani, Arman and Wennmann, Leo},
  title =	{{Cost Preserving Dependent Rounding for Allocation Problems}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{127:1--127:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2025.127},
  URN =		{urn:nbn:de:0030-drops-235049},
  doi =		{10.4230/LIPIcs.ICALP.2025.127},
  annote =	{Keywords: Matching, Randomized Rounding, Santa Claus, Approximation Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.47
Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem

Authors: Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz

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

Abstract
We consider an incremental variant of the rooted prize-collecting Steiner-tree problem with a growing budget constraint. While no incremental solution exists that simultaneously approximates the optimum for all budgets, we show that a bicriterial (α,μ)-approximation is possible, i.e., a solution that with budget B+α for all B ∈ ℝ_{≥ 0} is a multiplicative μ-approximation compared to the optimum solution with budget B. For the case that the underlying graph is a tree, we present a polynomial-time density-greedy algorithm that computes a (χ,1)-approximation, where χ denotes the eccentricity of the root vertex in the underlying graph, and show that this is best possible. An adaptation of the density-greedy algorithm for general graphs is (γ,2)-competitive where γ is the maximal length of a vertex-disjoint path starting in the root. While this algorithm does not run in polynomial time, it can be adapted to a (γ,3)-competitive algorithm that runs in polynomial time. We further devise a capacity-scaling algorithm that guarantees a (3χ,8)-approximation and, more generally, a ((4𝓁 - 1)χ, (2^{𝓁 + 2})/(2^𝓁 -1))-approximation for every fixed 𝓁 ∈ ℕ.
Cite as

Yann Disser, Svenja M. Griesbach, Max Klimm, and Annette Lutz. Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{disser_et_al:LIPIcs.ESA.2024.47,
  author =	{Disser, Yann and Griesbach, Svenja M. and Klimm, Max and Lutz, Annette},
  title =	{{Bicriterial Approximation for the Incremental Prize-Collecting Steiner-Tree Problem}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{47:1--47:16},
  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.2024.47},
  URN =		{urn:nbn:de:0030-drops-211188},
  doi =		{10.4230/LIPIcs.ESA.2024.47},
  annote =	{Keywords: incremental optimization, competitive analysis, prize-collecting Steiner-tree}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.17
Competitive Query Minimization for Stable Matching with One-Sided Uncertainty

Authors: Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, and Amitabh Trehan

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are unknown. An algorithm can make queries to reveal information about the preferences of the agents in B. We examine three query models: comparison queries, interviews, and set queries. Using competitive analysis, our aim is to design algorithms that minimize the number of queries required to solve the problem of finding a stable matching or verifying that a given matching is stable (or stable and optimal for the agents of one side). We present various upper and lower bounds on the best possible competitive ratio as well as results regarding the complexity of the offline problem of determining the optimal query set given full information.
Cite as

Evripidis Bampis, Konstantinos Dogeas, Thomas Erlebach, Nicole Megow, Jens Schlöter, and Amitabh Trehan. Competitive Query Minimization for Stable Matching with One-Sided Uncertainty. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 17:1-17:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bampis_et_al:LIPIcs.APPROX/RANDOM.2024.17,
  author =	{Bampis, Evripidis and Dogeas, Konstantinos and Erlebach, Thomas and Megow, Nicole and Schl\"{o}ter, Jens and Trehan, Amitabh},
  title =	{{Competitive Query Minimization for Stable Matching with One-Sided Uncertainty}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{17:1--17:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.17},
  URN =		{urn:nbn:de:0030-drops-210100},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.17},
  annote =	{Keywords: Matching under Preferences, Stable Marriage, Query-Competitive Algorithms, Uncertainty}
}
Document
DOI: 10.4230/DagRep.13.2.1
Scheduling (Dagstuhl Seminar 23061)

Authors: Nicole Megow, Benjamin J. Moseley, David Shmoys, Ola Svensson, Sergei Vassilvitskii, and Jens Schlöter

Published in: Dagstuhl Reports, Volume 13, Issue 2 (2023)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23061 "Scheduling". The seminar focused on the emerging models for beyond-worst case algorithm design, in particular, recent approaches that incorporate learning. This includes models for the integration of learning into algorithm design that have been proposed recently and that have already demonstrated advances in the state-of-art for various scheduling applications: (i) scheduling with error-prone learned predictions, (ii) data-driven algorithm design, and (iii) stochastic and Bayesian learning in scheduling.
Cite as

Nicole Megow, Benjamin J. Moseley, David Shmoys, Ola Svensson, Sergei Vassilvitskii, and Jens Schlöter. Scheduling (Dagstuhl Seminar 23061). In Dagstuhl Reports, Volume 13, Issue 2, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@Article{megow_et_al:DagRep.13.2.1,
  author =	{Megow, Nicole and Moseley, Benjamin J. and Shmoys, David and Svensson, Ola and Vassilvitskii, Sergei and Schl\"{o}ter, Jens},
  title =	{{Scheduling (Dagstuhl Seminar 23061)}},
  pages =	{1--19},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2023},
  volume =	{13},
  number =	{2},
  editor =	{Megow, Nicole and Moseley, Benjamin J. and Shmoys, David and Svensson, Ola and Vassilvitskii, Sergei and Schl\"{o}ter, Jens},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.2.1},
  URN =		{urn:nbn:de:0030-drops-191789},
  doi =		{10.4230/DagRep.13.2.1},
  annote =	{Keywords: scheduling, mathematical optimization, approximation algorithms, learning methods, uncertainty}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.49
Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty

Authors: Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study how to utilize (possibly erroneous) predictions in a model for computing under uncertainty in which an algorithm can query unknown data. Our aim is to minimize the number of queries needed to solve the minimum spanning tree problem, a fundamental combinatorial optimization problem that has been central also to the research area of explorable uncertainty. For all integral γ ≥ 2, we present algorithms that are γ-robust and (1+1/γ)-consistent, meaning that they use at most γOPT queries if the predictions are arbitrarily wrong and at most (1+1/γ)OPT queries if the predictions are correct, where OPT is the optimal number of queries for the given instance. Moreover, we show that this trade-off is best possible. Furthermore, we argue that a suitably defined hop distance is a useful measure for the amount of prediction error and design algorithms with performance guarantees that degrade smoothly with the hop distance. We also show that the predictions are PAC-learnable in our model. Our results demonstrate that untrusted predictions can circumvent the known lower bound of 2, without any degradation of the worst-case ratio. To obtain our results, we provide new structural insights for the minimum spanning tree problem that might be useful in the context of query-based algorithms regardless of predictions. In particular, we generalize the concept of witness sets - the key to lower-bounding the optimum - by proposing novel global witness set structures and completely new ways of adaptively using those.
Cite as

Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter. Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 49:1-49:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{erlebach_et_al:LIPIcs.ESA.2022.49,
  author =	{Erlebach, Thomas and de Lima, Murilo Santos and Megow, Nicole and Schl\"{o}ter, Jens},
  title =	{{Learning-Augmented Query Policies for Minimum Spanning Tree with Uncertainty}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{49:1--49:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.49},
  URN =		{urn:nbn:de:0030-drops-169872},
  doi =		{10.4230/LIPIcs.ESA.2022.49},
  annote =	{Keywords: explorable uncertainty, queries, untrusted predictions}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.18
Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

Authors: Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, and Andreas Wiese

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of maximum total value that can be packed into the knapsacks without exceeding the capacities. We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing input. More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items. As the optimal and any approximate solution may change drastically, we maintain implicit solutions and support polylogarithmic time query operations that can return the computed solution value and the packing of any given item. While dynamic algorithms are well-studied in the context of graph problems, there is hardly any work on packing problems (and generally much less on non-graph problems). Motivated by the theoretical interest in knapsack problems and their practical relevance, our work bridges this gap.
Cite as

Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, and Andreas Wiese. Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{eberle_et_al:LIPIcs.FSTTCS.2021.18,
  author =	{Eberle, Franziska and Megow, Nicole and N\"{o}lke, Lukas and Simon, Bertrand and Wiese, Andreas},
  title =	{{Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.18},
  URN =		{urn:nbn:de:0030-drops-155297},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.18},
  annote =	{Keywords: Fully dynamic algorithms, knapsack problem, approximation schemes}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.10
Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty

Authors: Evripidis Bampis, Christoph Dürr, Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter

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

Abstract
Given a hypergraph with uncertain node weights following known probability distributions, we study the problem of querying as few nodes as possible until the identity of a node with minimum weight can be determined for each hyperedge. Querying a node has a cost and reveals the precise weight of the node, drawn from the given probability distribution. Using competitive analysis, we compare the expected query cost of an algorithm with the expected cost of an optimal query set for the given instance. For the general case, we give a polynomial-time f(α)-competitive algorithm, where f(α) ∈ [1.618+ε,2] depends on the approximation ratio α for an underlying vertex cover problem. We also show that no algorithm using a similar approach can be better than 1.5-competitive. Furthermore, we give polynomial-time 4/3-competitive algorithms for bipartite graphs with arbitrary query costs and for hypergraphs with a single hyperedge and uniform query costs, with matching lower bounds.
Cite as

Evripidis Bampis, Christoph Dürr, Thomas Erlebach, Murilo Santos de Lima, Nicole Megow, and Jens Schlöter. Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bampis_et_al:LIPIcs.ESA.2021.10,
  author =	{Bampis, Evripidis and D\"{u}rr, Christoph and Erlebach, Thomas and de Lima, Murilo Santos and Megow, Nicole and Schl\"{o}ter, Jens},
  title =	{{Orienting (Hyper)graphs Under Explorable Stochastic Uncertainty}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{10:1--10:18},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.10},
  URN =		{urn:nbn:de:0030-drops-145910},
  doi =		{10.4230/LIPIcs.ESA.2021.10},
  annote =	{Keywords: Explorable uncertainty, queries, stochastic optimization, graph orientation, selection problems}
}
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