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**Published in:** LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

We study the fundamental online k-server problem in a learning-augmented setting. While in the traditional online model, an algorithm has no information about the request sequence, we assume that there is given some advice (e.g. machine-learned predictions) on an algorithm’s decision. There is, however, no guarantee on the quality of the prediction and it might be far from being correct.
Our main result is a learning-augmented variation of the well-known Double Coverage algorithm for k-server on the line (Chrobak et al., SIDMA 1991) in which we integrate predictions as well as our trust into their quality. We give an error-dependent competitive ratio, which is a function of a user-defined confidence parameter, and which interpolates smoothly between an optimal consistency, the performance in case that all predictions are correct, and the best-possible robustness regardless of the prediction quality. When given good predictions, we improve upon known lower bounds for online algorithms without advice. We further show that our algorithm achieves for any k an almost optimal consistency-robustness tradeoff, within a class of deterministic algorithms respecting local and memoryless properties.
Our algorithm outperforms a previously proposed (more general) learning-augmented algorithm. It is remarkable that the previous algorithm crucially exploits memory, whereas our algorithm is memoryless. Finally, we demonstrate in experiments the practicability and the superior performance of our algorithm on real-world data.

Alexander Lindermayr, Nicole Megow, and Bertrand Simon. Double Coverage with Machine-Learned Advice. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 99:1-99:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lindermayr_et_al:LIPIcs.ITCS.2022.99, author = {Lindermayr, Alexander and Megow, Nicole and Simon, Bertrand}, title = {{Double Coverage with Machine-Learned Advice}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {99:1--99:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-217-4}, ISSN = {1868-8969}, year = {2022}, volume = {215}, editor = {Braverman, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.99}, URN = {urn:nbn:de:0030-drops-156954}, doi = {10.4230/LIPIcs.ITCS.2022.99}, annote = {Keywords: online k-server problem, competitive analysis, learning-augmented algorithms, untrusted predictions, consistency, robustness} }

Document

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

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.

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} }

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**Published in:** LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

We consider the problem of computing a Steiner tree of minimum cost under a k-hop constraint which requires the depth of the tree to be at most k. Our main result is an exact algorithm for metrics induced by graphs of bounded treewidth that runs in time n^O(k). For the special case of a path, we give a simple algorithm that solves the problem in polynomial time, even if k is part of the input. The main result can be used to obtain, in quasi-polynomial time, a near-optimal solution that violates the k-hop constraint by at most one hop for more general metrics induced by graphs of bounded highway dimension and bounded doubling dimension.

Martin Böhm, Ruben Hoeksma, Nicole Megow, Lukas Nölke, and Bertrand Simon. Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bohm_et_al:LIPIcs.MFCS.2020.18, author = {B\"{o}hm, Martin and Hoeksma, Ruben and Megow, Nicole and N\"{o}lke, Lukas and Simon, Bertrand}, title = {{Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics}}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)}, pages = {18:1--18:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-159-7}, ISSN = {1868-8969}, year = {2020}, volume = {170}, editor = {Esparza, Javier and Kr\'{a}l', Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.18}, URN = {urn:nbn:de:0030-drops-126870}, doi = {10.4230/LIPIcs.MFCS.2020.18}, annote = {Keywords: k-hop Steiner tree, dynamic programming, bounded treewidth} }

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**Published in:** OASIcs, Volume 77, Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2020)

Static (offline) techniques for mapping applications given by task graphs to MPSoC systems often deliver overly pessimistic and thus suboptimal results w.r.t. exploiting time slack in order to minimize the energy consumption. This holds true in particular in case computation times of tasks may be workload-dependent and becoming known only at runtime or in case of conditionally executed tasks or scenarios. This paper studies and quantitatively evaluates different classes of algorithms for scheduling periodic applications given by task graphs (i.e., DAGs) with precedence constraints and a global deadline on homogeneous MPSoCs purely at runtime on a per-instance base. We present and analyze algorithms providing provably optimal results as well as approximation algorithms with proven guarantees on the achieved energy savings. For problem instances taken from realistic embedded system benchmarks as well as synthetic scalable problems, we provide results on the computation time and quality of each algorithm to perform a) scheduling and b) voltage/speed assignments for each task at runtime. In our portfolio, we distinguish as well continuous and discrete speed (e.g., DVFS-related) assignment problems. In summary, the presented ties between theory (algorithmic complexity and optimality) and execution time analysis deliver important insights on the practical usability of the presented algorithms for runtime optimization of task scheduling and speed assignment on MPSoCs.

Bertrand Simon, Joachim Falk, Nicole Megow, and Jürgen Teich. Energy Minimization in DAG Scheduling on MPSoCs at Run-Time: Theory and Practice. In Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2020). Open Access Series in Informatics (OASIcs), Volume 77, pp. 2:1-2:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{simon_et_al:OASIcs.NG-RES.2020.2, author = {Simon, Bertrand and Falk, Joachim and Megow, Nicole and Teich, J\"{u}rgen}, title = {{Energy Minimization in DAG Scheduling on MPSoCs at Run-Time: Theory and Practice}}, booktitle = {Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2020)}, pages = {2:1--2:13}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-136-8}, ISSN = {2190-6807}, year = {2020}, volume = {77}, editor = {Bertogna, Marko and Terraneo, Federico}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.NG-RES.2020.2}, URN = {urn:nbn:de:0030-drops-117781}, doi = {10.4230/OASIcs.NG-RES.2020.2}, annote = {Keywords: energy minimization, speed scaling, precedence graphs, scheduling, critical path, MPSoC} }

Document

**Published in:** LIPIcs, Volume 49, 8th International Conference on Fun with Algorithms (FUN 2016)

This paper formalizes a resource-allocation problem that is all too familiar to the seasoned program-committee member. For each submission j that the PC member has the honor of reviewing, there is a choice. The PC member can spend the time to review submission j in detail on his/her own at a cost of C_i. Alternatively, the PC member can spend the time to identify and contact peers, hoping to recruit them as subreviewers, at a cost of 1 per subreviewer. These potential subreviewers have a certain probability of rejecting each review request, and this probability increases as time goes on. Once the PC member runs out of time or unasked experts, he/she is forced to review the paper without outside assistance.
This paper gives optimal solutions to several variations of the scheduling-reviewers problem. Most of the solutions from this paper are based on an iterated log function of C_i. In particular, with k rounds, the optimal solution sends the k-iterated log of C_i requests in the first round, the (k-1)-iterated log in the second round, and so forth. One of the contributions of this paper is solving this problem exactly, even when rejection probabilities may increase.
Naturally, PC members must make an integral number of subreview requests. This paper gives, as an intermediate result, a linear-time algorithm to transform the artificial problem in which one can send fractional requests into the less-artificial problem in which one sends an integral number of requests. Finally, this paper considers the case where the PC member knows nothing about the probability that a potential subreviewer agrees to review the paper. This paper gives an approximation algorithm for this case, whose bounds improve as the number of rounds increases.

Michael A. Bender, Samuel McCauley, Bertrand Simon, Shikha Singh, and Frédéric Vivien. Resource Optimization for Program Committee Members: A Subreview Article. In 8th International Conference on Fun with Algorithms (FUN 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 49, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{bender_et_al:LIPIcs.FUN.2016.7, author = {Bender, Michael A. and McCauley, Samuel and Simon, Bertrand and Singh, Shikha and Vivien, Fr\'{e}d\'{e}ric}, title = {{Resource Optimization for Program Committee Members: A Subreview Article}}, booktitle = {8th International Conference on Fun with Algorithms (FUN 2016)}, pages = {7:1--7:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-005-7}, ISSN = {1868-8969}, year = {2016}, volume = {49}, editor = {Demaine, Erik D. and Grandoni, Fabrizio}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2016.7}, URN = {urn:nbn:de:0030-drops-58872}, doi = {10.4230/LIPIcs.FUN.2016.7}, annote = {Keywords: Scheduling, Delegation, Subreviews} }

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