9 Search Results for "Balogh, János"

Document
DOI: 10.4230/LIPIcs.SoCG.2026.52
Online Packing of Orthogonal Polygons

Authors: Tim Gerlach, Benjamin Hennies, and Linda Kleist

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
While rectangular and box-shaped objects dominate the classic discourse of theoretic investigations, a fascinating frontier lies in packing more complex shapes. Given recent insights that convex polygons do not allow for constant competitive online algorithms for diverse variants under translation, we study orthogonal polygons, in particular of small complexity. For translational packings of orthogonal 6-gons, we show that the competitive ratio of any online algorithm that aims to pack the items into a minimal number of unit bins is in Ω(n/(log n)), where n denotes the number of objects. In contrast, we show that constant competitive algorithms exist when the orthogonal 6-gons are symmetric or small. For (orthogonally convex) orthogonal 8-gons, we show that the trivial n-competitive algorithm, which places each item in its own bin, is best-possible, i.e., every online algorithm has an asymptotic competitive ratio of at least n. This implies that for general orthogonal polygons, the trivial algorithm is best possible. Interestingly, for packing degenerate orthogonal polygons (with thickness 0), called skeletons, the change in complexity is even more drastic. While constant competitive algorithms for 6-skeletons exist, no online algorithm for 8-skeletons achieves a competitive ratio better than n. For other packing variants of orthogonal 6-gons under translation, our insights imply the following consequences. The asymptotic competitive ratio of any online algorithm is in Ω(n/(log n)) for strip packing, and there exist online algorithms with competitive ratios in O(1) for perimeter packing, or in O(√n) for minimizing the area of the bounding box. Moreover, the critical packing density is positive (if every object individually fits into the interior of a unit bin).
Cite as

Tim Gerlach, Benjamin Hennies, and Linda Kleist. Online Packing of Orthogonal Polygons. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 52:1-52:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gerlach_et_al:LIPIcs.SoCG.2026.52,
  author =	{Gerlach, Tim and Hennies, Benjamin and Kleist, Linda},
  title =	{{Online Packing of Orthogonal Polygons}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{52:1--52:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.52},
  URN =		{urn:nbn:de:0030-drops-258589},
  doi =		{10.4230/LIPIcs.SoCG.2026.52},
  annote =	{Keywords: Packing, orthogonal polygon, algorithm, offline, online, competitive ratio, bin packing, strip packing, perimeter packing, critical density, 6-gon, 8-gon, L-shape, Z-shape, skeleton}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.63
Unavoidable Patterns and Plane Paths in Dense Topological Graphs

Authors: Balázs Keszegh, Andrew Suk, Gábor Tardos, and Ji Zeng

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
Let C_{s,t} be the complete bipartite geometric graph, with s and t vertices on two distinct parallel lines respectively, and all s t straight-line edges drawn between them. In this paper, we show that every complete bipartite simple topological graph, with parts of size 2(k-1)⁴ + 1 and 2^{k^{5k}}, contains a topological subgraph weakly isomorphic to C_{k,k}. As a corollary, every n-vertex simple topological graph not containing a plane path of length k has at most O_k(n^{2 - 8/k⁴}) edges. When k = 3, we obtain a stronger bound by showing that every n-vertex simple topological graph not containing a plane path of length 3 has at most O(n^{4/3}) edges. We also prove that x-monotone simple topological graphs not containing a plane path of length 3 have at most a linear number of edges.
Cite as

Balázs Keszegh, Andrew Suk, Gábor Tardos, and Ji Zeng. Unavoidable Patterns and Plane Paths in Dense Topological Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 63:1-63:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{keszegh_et_al:LIPIcs.SoCG.2026.63,
  author =	{Keszegh, Bal\'{a}zs and Suk, Andrew and Tardos, G\'{a}bor and Zeng, Ji},
  title =	{{Unavoidable Patterns and Plane Paths in Dense Topological Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{63:1--63:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.63},
  URN =		{urn:nbn:de:0030-drops-258706},
  doi =		{10.4230/LIPIcs.SoCG.2026.63},
  annote =	{Keywords: graph drawing, topological graph, bipartite geometric graph, forbidden subgraph, extremal graph, thrackle}
}
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.ESA.2025.27
Online Makespan Scheduling Under Scenarios

Authors: Ekin Ergen

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

Abstract
We consider a natural extension of online makespan scheduling on identical parallel machines by introducing scenarios. A scenario is a subset of jobs, and the task of our problem is to find a global assignment of the jobs to machines so that the maximum makespan under a scenario, i.e., the maximum makespan of any schedule restricted to a scenario, is minimized. For varying values of the number of scenarios and machines, we explore the competitiveness of online algorithms. We prove tight and near-tight bounds, several of which are achieved through novel constructions. In particular, we leverage the interplay between the unit processing time case of our problem and the hypergraph coloring problem both ways: We use hypergraph coloring techniques to steer an adversarial family of instances proving lower bounds for our problem, which in turn leads to lower bounds for several variants of online hypergraph coloring.
Cite as

Ekin Ergen. Online Makespan Scheduling Under Scenarios. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 27:1-27:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ergen:LIPIcs.ESA.2025.27,
  author =	{Ergen, Ekin},
  title =	{{Online Makespan Scheduling Under Scenarios}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{27:1--27:16},
  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.2025.27},
  URN =		{urn:nbn:de:0030-drops-244950},
  doi =		{10.4230/LIPIcs.ESA.2025.27},
  annote =	{Keywords: online scheduling, scenario-based model, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.50
Immersions and Albertson’s Conjecture

Authors: Jacob Fox, János Pach, and Andrew Suk

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

Abstract
A graph is said to contain K_k (a clique of size k) as a weak immersion if it has k vertices, pairwise connected by edge-disjoint paths. In 1989, Lescure and Meyniel made the following conjecture related to Hadwiger’s conjecture: Every graph of chromatic number k contains K_k as a weak immersion. We prove this conjecture for graphs with at most 1.4(k-1) vertices. As an application, we make some progress on Albertson’s conjecture on crossing numbers of graphs, according to which every graph G with chromatic number k satisfies cr(G) ≥ cr(K_k). In particular, we show that the conjecture is true for all graphs of chromatic number k, provided that they have at most 1.4(k-1) vertices and k is sufficiently large.
Cite as

Jacob Fox, János Pach, and Andrew Suk. Immersions and Albertson’s Conjecture. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 50:1-50:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fox_et_al:LIPIcs.SoCG.2025.50,
  author =	{Fox, Jacob and Pach, J\'{a}nos and Suk, Andrew},
  title =	{{Immersions and Albertson’s Conjecture}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{50:1--50:10},
  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.2025.50},
  URN =		{urn:nbn:de:0030-drops-232022},
  doi =		{10.4230/LIPIcs.SoCG.2025.50},
  annote =	{Keywords: Immersions, crossing numbers, chromatic number}
}
Document
DOI: 10.4230/LIPIcs.FUN.2024.28
No Tiling of the 70 × 70 Square with Consecutive Squares

Authors: Jiří Sgall, János Balogh, József Békési, György Dósa, Lars Magnus Hvattum, and Zsolt Tuza

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)

Abstract
The total area of the 24 squares of sizes 1,2,…,24 is equal to the area of the 70× 70 square. Can this equation be demonstrated by a tiling of the 70× 70 square with the 24 squares of sizes 1,2,…,24? The answer is "NO", no such tiling exists. This has been demonstrated by computer search. However, until now, no proof without use of computer was given. We fill this gap and give a complete combinatorial proof.
Cite as

Jiří Sgall, János Balogh, József Békési, György Dósa, Lars Magnus Hvattum, and Zsolt Tuza. No Tiling of the 70 × 70 Square with Consecutive Squares. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 28:1-28:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{sgall_et_al:LIPIcs.FUN.2024.28,
  author =	{Sgall, Ji\v{r}{\'\i} and Balogh, J\'{a}nos and B\'{e}k\'{e}si, J\'{o}zsef and D\'{o}sa, Gy\"{o}rgy and Hvattum, Lars Magnus and Tuza, Zsolt},
  title =	{{No Tiling of the 70 × 70 Square with Consecutive Squares}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{28:1--28:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.28},
  URN =		{urn:nbn:de:0030-drops-199362},
  doi =		{10.4230/LIPIcs.FUN.2024.28},
  annote =	{Keywords: square packing, Gardner’s problem, combinatorial proof}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.8
Truly Asymptotic Lower Bounds for Online Vector Bin Packing

Authors: János Balogh, Ilan Reuven Cohen, Leah Epstein, and Asaf Levin

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
In this work, we consider online d-dimensional vector bin packing. It is known that no algorithm can have a competitive ratio of o(d/log² d) in the absolute sense, although upper bounds for this problem have always been presented in the asymptotic sense. Since variants of bin packing are traditionally studied with respect to the asymptotic measure, and since the two measures are different, we focus on the asymptotic measure and prove new lower bounds of the asymptotic competitive ratio. The existing lower bounds prior to this work were known to be smaller than 3, even for very large d. Here, we significantly improved on the best known lower bounds of the asymptotic competitive ratio (and as a byproduct, on the absolute competitive ratio) for online vector packing of vectors with d ≥ 3 dimensions, for every dimension d. To obtain these results, we use several different constructions, one of which is an adaptive construction with a lower bound of Ω(√d). Our main result is that the lower bound of Ω(d/log² d) on the competitive ratio holds also in the asymptotic sense. This result holds also against randomized algorithms, and requires a careful adaptation of constructions for online coloring, rather than simple black-box reductions.
Cite as

János Balogh, Ilan Reuven Cohen, Leah Epstein, and Asaf Levin. Truly Asymptotic Lower Bounds for Online Vector Bin Packing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 8:1-8:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{balogh_et_al:LIPIcs.APPROX/RANDOM.2021.8,
  author =	{Balogh, J\'{a}nos and Cohen, Ilan Reuven and Epstein, Leah and Levin, Asaf},
  title =	{{Truly Asymptotic Lower Bounds for Online Vector Bin Packing}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{8:1--8:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.8},
  URN =		{urn:nbn:de:0030-drops-147013},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.8},
  annote =	{Keywords: Bin packing, online algorithms, approximation algorithms, vector packing}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.5
A New and Improved Algorithm for Online Bin Packing

Authors: János Balogh, József Békési, György Dósa, Leah Epstein, and Asaf Levin

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

Abstract
We revisit the classic online bin packing problem studied in the half-century. In this problem, items of positive sizes no larger than 1 are presented one by one to be packed into subsets called bins of total sizes no larger than 1, such that every item is assigned to a bin before the next item is presented. We use online partitioning of items into classes based on sizes, as in previous work, but we also apply a new method where items of one class can be packed into more than two types of bins, where a bin type is defined according to the number of such items grouped together. Additionally, we allow the smallest class of items to be packed in multiple kinds of bins, and not only into their own bins. We combine this with the approach of packing of sufficiently big items according to their exact sizes. Finally, we simplify the analysis of such algorithms, allowing the analysis to be based on the most standard weight functions. This simplified analysis allows us to study the algorithm which we defined based on all these ideas. This leads us to the design and analysis of the first algorithm of asymptotic competitive ratio strictly below 1.58, specifically, we break this barrier by providing an algorithm AH (Advanced Harmonic) whose asymptotic competitive ratio does not exceed 1.57829. Our main contribution is the introduction of the simple analysis based on weight function to analyze the state of the art online algorithms for the classic online bin packing problem. The previously used analytic tool named weight system was too complicated for the community in this area to adjust it for other problems and other algorithmic tools that are needed in order to improve the current best algorithms. We show that the weight system based analysis is not needed for the analysis of the current algorithms for the classic online bin packing problem. The importance of a simple analysis is demonstrated by analyzing several new features together with all existing techniques, and by proving a better competitive ratio than the previously best one.
Cite as

János Balogh, József Békési, György Dósa, Leah Epstein, and Asaf Levin. A New and Improved Algorithm for Online Bin Packing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 5:1-5:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{balogh_et_al:LIPIcs.ESA.2018.5,
  author =	{Balogh, J\'{a}nos and B\'{e}k\'{e}si, J\'{o}zsef and D\'{o}sa, Gy\"{o}rgy and Epstein, Leah and Levin, Asaf},
  title =	{{A New and Improved Algorithm for Online Bin Packing}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{5:1--5:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.5},
  URN =		{urn:nbn:de:0030-drops-94686},
  doi =		{10.4230/LIPIcs.ESA.2018.5},
  annote =	{Keywords: Bin packing, online algorithms, competitive analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.10
Online Bin Packing with Cardinality Constraints Resolved

Authors: Janos Balogh, Jozsef Bekesi, Gyorgy Dosa, Leah Epstein, and Asaf Levin

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
Cardinality constrained bin packing or bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k >= 2, items having sizes in (0,1] associated with them are presented one by one to be packed into unit capacity bins, such that the capacities of bins are not exceeded, and no bin receives more than k items. We resolve the online problem in the sense that we prove a lower bound of 2 on the overall asymptotic competitive ratio. This closes the long standing open problem of finding the value of the best possible overall asymptotic competitive ratio, since an algorithm of an absolute competitive ratio 2 for any fixed value of k is known. Additionally, we significantly improve the known lower bounds on the asymptotic competitive ratio for every specific value of k. The novelty of our constructions is based on full adaptivity that creates large gaps between item sizes. Thus, our lower bound inputs do not follow the common practice for online bin packing problems of having a known in advance input consisting of batches for which the algorithm needs to be competitive on every prefix of the input. Last, we show a lower bound strictly larger than 2 on the asymptotic competitive ratio of the online 2-dimensional vector packing problem, and thus provide for the first time a lower bound larger than 2 on the asymptotic competitive ratio for the vector packing problem in any fixed dimension.
Cite as

Janos Balogh, Jozsef Bekesi, Gyorgy Dosa, Leah Epstein, and Asaf Levin. Online Bin Packing with Cardinality Constraints Resolved. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 10:1-10:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{balogh_et_al:LIPIcs.ESA.2017.10,
  author =	{Balogh, Janos and Bekesi, Jozsef and Dosa, Gyorgy and Epstein, Leah and Levin, Asaf},
  title =	{{Online Bin Packing with Cardinality Constraints Resolved}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{10:1--10:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.10},
  URN =		{urn:nbn:de:0030-drops-78514},
  doi =		{10.4230/LIPIcs.ESA.2017.10},
  annote =	{Keywords: Online algorithms, bin packing, cardinality constraints, lower bounds}
}
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