7 Search Results for "Heydrich, Sandy"

Document
DOI: 10.4230/LIPIcs.STACS.2026.43
Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal

Authors: Matthias Gehnen and Moritz Stocker

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

Abstract
We introduce the Online Unbounded Knapsack Problem with Removal, a variation of the well-known Online Knapsack Problem. Items, each with a weight and value, arrive online and an algorithm must decide on whether or not to pack them into a knapsack with a fixed weight limit. An item may be packed an arbitrary number of times and items may be removed from the knapsack at any time without cost. The goal is to maximize the total value of items packed, while respecting a weight limit. We show that this is one of the very few natural online knapsack variants that allow for competitive deterministic algorithms in the general setting, by providing an algorithm with competitivity 1.6911. We complement this with a lower bound of 1.5877. We also analyze the proportional setting, where the weight and value of any single item agree, and show that deterministic algorithms can be exactly 3/2-competitive. Lastly, we give lower and upper bounds of 6/5 and 4/3 on the competitivity of randomized algorithms in this setting.
Cite as

Matthias Gehnen and Moritz Stocker. Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 43:1-43:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gehnen_et_al:LIPIcs.STACS.2026.43,
  author =	{Gehnen, Matthias and Stocker, Moritz},
  title =	{{Stealing from the Dragon’s Hoard: Online Unbounded Knapsack With Removal}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{43:1--43:17},
  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.2026.43},
  URN =		{urn:nbn:de:0030-drops-255327},
  doi =		{10.4230/LIPIcs.STACS.2026.43},
  annote =	{Keywords: online problems, online knapsack, unbounded knapsack, removal}
}
Document
DOI: 10.4230/LIPIcs.STACS.2026.56
A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling

Authors: Klaus Jansen and Felix Ohnesorge

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

Abstract
In moldable job scheduling, we are provided m identical machines and n jobs that can be executed on a variable number of machines. The execution time of each job depends on the number of machines assigned to execute that job. For the specific problem of monotone moldable job scheduling, jobs are assumed to have a processing time that is non-increasing in the number of machines. The previous best-known algorithms are: (1) a Polynomial Time Approximation Scheme (PTAS) with time complexity Ω(n^{g(1/ε)}), where g(⋅) is a super-exponential function [Jansen and Thöle '08; Jansen and Land '18], (2) a Fully Polynomial Time Approximation Scheme (FPTAS) for the case of m ≥ 8n/(ε) [Jansen and Land '18], and (3) a 3/2 approximation with time complexity O(nmlog(mn)) [Wu, Zhang, and Chen '23]. We present a new practically efficient algorithm with an approximation ratio of ≈ (1.4593 + ε) and a time complexity of O(nm log 1/(ε)). Our result also applies to the contiguous variant of the problem. In addition to our theoretical results, we implement the presented algorithm and show that the practical performance is significantly better than the theoretical worst-case approximation ratio.
Cite as

Klaus Jansen and Felix Ohnesorge. A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 56:1-56:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jansen_et_al:LIPIcs.STACS.2026.56,
  author =	{Jansen, Klaus and Ohnesorge, Felix},
  title =	{{A Practical 73/50 Approximation for Contiguous Monotone Moldable Job Scheduling}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{56:1--56:20},
  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.2026.56},
  URN =		{urn:nbn:de:0030-drops-255453},
  doi =		{10.4230/LIPIcs.STACS.2026.56},
  annote =	{Keywords: computing, machine scheduling, moldable, polynomial approximation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.10
Improved Approximation Guarantees for Advertisement Placement

Authors: Waldo Gálvez, Roberto Oliva, and Victor Verdugo

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The advertisement placement problem involves selecting and scheduling ads within a timeline that has capacity constraints to maximize profit. Each task is characterized by its height, width, and profit, and must be fully scheduled across multiple time slots. This problem models practical scenarios such as internet advertising and energy management, and it also generalizes classical combinatorial optimization problems like the knapsack and bin packing problems. We present a simple (2+ε)-approximation algorithm for any ε > 0, which improves upon the state-of-the-art 3+ε factor established by Freund and Naor twenty years ago. Our approach combines rounding techniques with dynamic programming and an efficient extension of list scheduling. Furthermore, we enhance this method with linear programming techniques to provide an almost optimal (1+ε)-approximation algorithm under resource augmentation, which allows for a slight increase in time slot capacities.
Cite as

Waldo Gálvez, Roberto Oliva, and Victor Verdugo. Improved Approximation Guarantees for Advertisement Placement. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 10:1-10:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galvez_et_al:LIPIcs.APPROX/RANDOM.2025.10,
  author =	{G\'{a}lvez, Waldo and Oliva, Roberto and Verdugo, Victor},
  title =	{{Improved Approximation Guarantees for Advertisement Placement}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{10:1--10:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.10},
  URN =		{urn:nbn:de:0030-drops-243762},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.10},
  annote =	{Keywords: Advertisement Placement, Two-dimensional Packing, Geometric Knapsack, Resource Allocation}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.30
Exact Methods for the Travelling Salesperson Problem with Self-Deleting Graphs

Authors: Daniel Pekar and J. Christopher Beck

Published in: LIPIcs, Volume 340, 31st International Conference on Principles and Practice of Constraint Programming (CP 2025)

Abstract
Finding the minimal-cost closed loop on a weighted graph where every vertex is visited exactly once is known as the Travelling Salesperson Problem (TSP). In a recently proposed variant, TSP with Self-Deleting graphs (TSP-SD), visiting a vertex i deletes a set of edges in the graph, preventing their subsequent traversal. Due to the dependency between vertex visits and edge deletion, in TSP-SD the feasibility of a cycle depends on the start node. The best performing solution approaches in the literature rely on a simple problem reformulation to find a backward tour where vertex visits add edges rather than delete them. This paper investigates exact model-based approaches, specifically Constraint Programming (CP), Domain-Independent Dynamic Programming (DIDP), and Mixed Integer Linear Programming (MIP) to solve TSP-SD. We show that simple preprocessing can substantially reduce the options for start/end vertex pairs but typically has a limited positive impact on search performance. Our numerical results demonstrate that the difference between the deletion and addition variants is small for CP and MIP but that the reformulation is critical for DIDP performance. Overall, the DIDP addition model is the best of the exact methods on all test instances and outperforms existing heuristic solvers for small and medium-sized instances while trailing in terms of solution quality on larger instances.
Cite as

Daniel Pekar and J. Christopher Beck. Exact Methods for the Travelling Salesperson Problem with Self-Deleting Graphs. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 30:1-30:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{pekar_et_al:LIPIcs.CP.2025.30,
  author =	{Pekar, Daniel and Beck, J. Christopher},
  title =	{{Exact Methods for the Travelling Salesperson Problem with Self-Deleting Graphs}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{30:1--30:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-380-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{340},
  editor =	{de la Banda, Maria Garcia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2025.30},
  URN =		{urn:nbn:de:0030-drops-238914},
  doi =		{10.4230/LIPIcs.CP.2025.30},
  annote =	{Keywords: Decision Diagrams \& Dynamic Programming, Operations Research \& Mathematical Optimization, Modelling \& Modelling Languages}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.104
Improved Approximation Algorithms for Three-Dimensional Bin Packing

Authors: Debajyoti Kar, Arindam Khan, and Malin Rau

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

Abstract
We study three fundamental three-dimensional (3D) geometric packing problems: 3D (Geometric) Bin Packing (3D-BP), 3D Strip Packing (3D-SP), and Minimum Volume Bounding Box (3D-MVBB), where given a set of 3D (rectangular) cuboids, the goal is to find an axis-aligned nonoverlapping packing of all cuboids. In 3D-BP, we need to pack the given cuboids into the minimum number of unit cube bins. In 3D-SP, we need to pack them into a 3D cuboid with a unit square base and minimum height. Finally, in 3D-MVBB, the goal is to pack into a cuboid box of minimum volume. It is NP-hard to even decide whether a set of rectangles can be packed into a unit square bin - giving an (absolute) approximation hardness of 2 for 3D-BP and 3D-SP. The previous best (absolute) approximation for all three problems is by Li and Cheng (SICOMP, 1990), who gave algorithms with approximation ratios of 13, 46/7, and 46/7+ε, respectively, for 3D-BP, 3D-SP, and 3D-MVBB. We provide improved approximation ratios of 6, 6, and 3+ε, respectively, for the three problems, for any constant ε > 0. For 3D-BP, in the asymptotic regime, Bansal, Correa, Kenyon, and Sviridenko (Math. Oper. Res., 2006) showed that there is no asymptotic polynomial-time approximation scheme (APTAS) even when all items have the same height. Caprara (Math. Oper. Res., 2008) gave an asymptotic approximation ratio of T_{∞}² + ε ≈ 2.86, where T_{∞} is the well-known Harmonic constant in Bin Packing. We provide an algorithm with an improved asymptotic approximation ratio of 3 T_{∞}/2 + ε ≈ 2.54. Further, we show that unlike 3D-BP (and 3D-SP), 3D-MVBB admits an APTAS.
Cite as

Debajyoti Kar, Arindam Khan, and Malin Rau. Improved Approximation Algorithms for Three-Dimensional Bin Packing. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 104:1-104:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kar_et_al:LIPIcs.ICALP.2025.104,
  author =	{Kar, Debajyoti and Khan, Arindam and Rau, Malin},
  title =	{{Improved Approximation Algorithms for Three-Dimensional Bin Packing}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{104:1--104:20},
  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.2025.104},
  URN =		{urn:nbn:de:0030-drops-234814},
  doi =		{10.4230/LIPIcs.ICALP.2025.104},
  annote =	{Keywords: Approximation Algorithms, Geometric Packing, Multidimensional Packing}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.60
Improved Approximation Algorithms for Three-Dimensional Knapsack

Authors: Klaus Jansen, Debajyoti Kar, Arindam Khan, K. V. N. Sreenivas, and Malte Tutas

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
We study the three-dimensional Knapsack (3DK) problem, in which we are given a set of axis-aligned cuboids with associated profits and an axis-aligned cube knapsack. The objective is to find a non-overlapping axis-aligned packing (by translation) of the maximum profit subset of cuboids into the cube. The previous best approximation algorithm is due to Diedrich, Harren, Jansen, Thöle, and Thomas (2008), who gave a (7+ε)-approximation algorithm for 3DK and a (5+ε)-approximation algorithm for the variant when the items can be rotated by 90 degrees around any axis, for any constant ε > 0. Chlebík and Chlebíková (2009) showed that the problem does not admit an asymptotic polynomial-time approximation scheme. We provide an improved polynomial-time (139/29+ε) ≈ 4.794-approximation algorithm for 3DK and (30/7+ε) ≈ 4.286-approximation when rotations by 90 degrees are allowed. We also provide improved approximation algorithms for several variants such as the cardinality case (when all items have the same profit) and uniform profit-density case (when the profit of an item is equal to its volume). Our key technical contribution is container packing - a structured packing in 3D such that all items are assigned into a constant number of containers, and each container is packed using a specific strategy based on its type. We first show the existence of highly profitable container packings. Thereafter, we show that one can find near-optimal container packing efficiently using a variant of the Generalized Assignment Problem (GAP).
Cite as

Klaus Jansen, Debajyoti Kar, Arindam Khan, K. V. N. Sreenivas, and Malte Tutas. Improved Approximation Algorithms for Three-Dimensional Knapsack. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 60:1-60:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.SoCG.2025.60,
  author =	{Jansen, Klaus and Kar, Debajyoti and Khan, Arindam and Sreenivas, K. V. N. and Tutas, Malte},
  title =	{{Improved Approximation Algorithms for Three-Dimensional Knapsack}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{60:1--60:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.60},
  URN =		{urn:nbn:de:0030-drops-232126},
  doi =		{10.4230/LIPIcs.SoCG.2025.60},
  annote =	{Keywords: Approximation Algorithms, Hyperrectangle Packing, Multidimensional Knapsack, Three-dimensional Packing}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.41
Beating the Harmonic Lower Bound for Online Bin Packing

Authors: Sandy Heydrich and Rob van Stee

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
In the online bin packing problem, items of sizes in (0,1] arrive online to be packed into bins of size 1. The goal is to minimize the number of used bins. Harmonic++ achieves a competitive ratio of 1.58889 and belongs to the Super Harmonic framework [Seiden, J. ACM, 2002]; a lower bound of Ramanan et al. shows that within this framework, no competitive ratio below 1.58333 can be achieved [Ramanan et al., J. Algorithms, 1989]. In this paper, we present an online bin packing algorithm with asymptotic performance ratio of 1.5815, which constitutes the first improvement in fifteen years and reduces the gap to the lower bound by roughly 15%. We make two crucial changes to the Super Harmonic framework. First, some of the decisions of the algorithm will depend on exact sizes of items, instead of only their types. In particular, for item pairs where the size of one item is in (1/3,1/2] and the other is larger than 1/2 (a large item), when deciding whether to pack such a pair together in one bin, our algorithm does not consider their types, but only checks whether their total size is at most 1. Second, for items with sizes in (1/3,1/2] (medium items), we try to pack the larger items of every type in pairs, while combining the smallest items with large items whenever possible. To do this, we postpone the coloring of medium items (i.e., the decision which items to pack in pairs and which to pack alone) where possible, and later select the smallest ones to be reserved for combining with large items. Additionally, in case such large items arrive early, we pack medium items with them whenever possible. This is a highly unusual idea in the context of Harmonic-like algorithms, which initially seems to preclude analysis (the ratio of items combined with large items is no longer a fixed constant). For the analysis, we carefully mark medium items depending on how they end up packed, enabling us to add crucial constraints to the linear program used by Seiden. We consider the dual, eliminate all but one variable and then solve it with the ellipsoid method using a separation oracle. Our implementation uses additional algorithmic ideas to determine previously hand set parameters automatically and gives certificates for easy verification of the results. We give a lower bound of 1.5766 for algorithms like ours. This shows that fundamentally different ideas will be required to make further improvements
Cite as

Sandy Heydrich and Rob van Stee. Beating the Harmonic Lower Bound for Online Bin Packing. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 41:1-41:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{heydrich_et_al:LIPIcs.ICALP.2016.41,
  author =	{Heydrich, Sandy and van Stee, Rob},
  title =	{{Beating the Harmonic Lower Bound for Online Bin Packing}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{41:1--41:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.41},
  URN =		{urn:nbn:de:0030-drops-63214},
  doi =		{10.4230/LIPIcs.ICALP.2016.41},
  annote =	{Keywords: Bin packing, online algorithms, harmonic algorithm}
}
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