8 Search Results for "Sreenivas, K. V. N."

Document
DOI: 10.4230/LIPIcs.ITCS.2026.86
The Secretary Problem with Predictions and a Chosen Order

Authors: Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We study a learning-augmented variant of the secretary problem, recently introduced by Fujii and Yoshida (2023). In this variant, the decision-maker has access to machine-learned predictions of candidate values in advance. The key challenge is to balance consistency and robustness: when the predictions are accurate, the algorithm should hire a near-best secretary; however, if they are inaccurate, the algorithm should still achieve a bounded competitive ratio. We consider both the standard Random Order Secretary Problem (ROSP), where candidates arrive in a uniform random order, and a more natural model in the learning-augmented setting, where the decision-maker can choose the arrival order based on the predicted candidate values. This model, which we call the Chosen Order Secretary Problem (COSP), can capture scenarios such as an interview schedule that is set by the decision-maker. We propose a novel algorithm that applies to both ROSP and COSP. Building on the approach of Fujii and Yoshida, our method switches from fully trusting predictions to a threshold-based rule when a large deviation of a prediction is observed. Importantly, unlike the algorithm of Fujii and Yoshida, our algorithm uses randomization as part of its decision logic. We show that if ε ∈ [0,1] denotes the maximum multiplicative prediction error, then for ROSP our algorithm achieves competitive ratio max {0.221, (1-ε)/(1+ε)}, improving on a previous bound of max {0.215, (1-ε)/(1+ε)} due to Fujii and Yoshida [Fujii and Yoshida, 2023]. For COSP, our algorithm achieves max {0.262, (1-ε)/(1+ε)}. This surpasses a 0.25 upper bound on the worst-case competitive ratio that applies to the approach of Fujii and Yoshida, and gets closer to the classical secretary benchmark of 1/e ≈ 0.368, which is an upper bound for any algorithm. Our result for COSP highlights the benefit of integrating predictions with arrival-order control in online decision-making.
Cite as

Helia Karisani, Mohammadreza Daneshvaramoli, Hedyeh Beyhaghi, Mohammad Hajiesmaili, and Cameron Musco. The Secretary Problem with Predictions and a Chosen Order. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 86:1-86:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{karisani_et_al:LIPIcs.ITCS.2026.86,
  author =	{Karisani, Helia and Daneshvaramoli, Mohammadreza and Beyhaghi, Hedyeh and Hajiesmaili, Mohammad and Musco, Cameron},
  title =	{{The Secretary Problem with Predictions and a Chosen Order}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{86:1--86:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.86},
  URN =		{urn:nbn:de:0030-drops-253734},
  doi =		{10.4230/LIPIcs.ITCS.2026.86},
  annote =	{Keywords: Secretary problem, learning-augmented algorithms, online algorithms}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2025.38
Fairness and Efficiency in Two-Sided Matching Markets

Authors: Pallavi Jain, Palash Jha, and Shubham Solanki

Published in: LIPIcs, Volume 360, 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)

Abstract
We propose a new fairness notion, motivated by the practical challenge of allocating teaching assistants (TAs) to courses in a department. Each course requires a certain number of TAs and each TA has preferences over the courses they want to assist. Similarly, each course instructor has preferences over the TAs who applied for their course. We demand fairness and efficiency for both sides separately, giving rise to the following criteria: (i) every course gets the required number of TAs and the average utility of the assigned TAs meets a threshold; (ii) the allocation of courses to TAs is envy-free, where a TA envies another TA if the former prefers the latter’s course and has a higher or equal grade in that course. Note that the definition of envy-freeness here differs from the one in the literature, and we call it merit-based envy-freeness. We show that the problem of finding a merit-based envy-free and efficient matching is NP-hard even for very restricted settings, such as two courses and uniform valuations; constant degree, constant capacity of TAs for every course, valuations in the range {0,1,2,3}, identical valuations from TAs, and even more. To find tractable results, we consider some restricted instances, such as, strict valuation of TAs for courses, the difference between the number of positively valued TAs for a course and the capacity, the number of positively valued TAs/courses, types of valuation functions, and obtained some polynomial-time solvable cases, showing the contrast with intractable results. We further studied the problem in the paradigm of parameterized algorithms and designed some exact and approximation algorithms.
Cite as

Pallavi Jain, Palash Jha, and Shubham Solanki. Fairness and Efficiency in Two-Sided Matching Markets. In 45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 360, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jain_et_al:LIPIcs.FSTTCS.2025.38,
  author =	{Jain, Pallavi and Jha, Palash and Solanki, Shubham},
  title =	{{Fairness and Efficiency in Two-Sided Matching Markets}},
  booktitle =	{45th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2025)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-406-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{360},
  editor =	{Aiswarya, C. and Mehta, Ruta and Roy, Subhajit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2025.38},
  URN =		{urn:nbn:de:0030-drops-251186},
  doi =		{10.4230/LIPIcs.FSTTCS.2025.38},
  annote =	{Keywords: Fair Matching, Envy-Freeness, Efficiency}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.26
Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model

Authors: Leah Epstein and Asaf Levin

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
We consider the performance of standard bin packing algorithms in the random order model. We provide an improved lower bound of 1.15582656 on the asymptotic approximation ratio of Best Fit (BF) for randomly ordered inputs. We also show lower bounds on the asymptotic approximation ratio for two bounded space bin packing algorithms in this model, namely for 2-BF and 2-FF. These are well-studied bounded space algorithms and the first one has the same asymptotic worst-case performance as BF. However, the resulting lower bounds on their performances in the random order model are much higher than that of BF.
Cite as

Leah Epstein and Asaf Levin. Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epstein_et_al:LIPIcs.WADS.2025.26,
  author =	{Epstein, Leah and Levin, Asaf},
  title =	{{Lower Bounds for Several Standard Bin Packing Algorithms in the Random Order Model}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.26},
  URN =		{urn:nbn:de:0030-drops-242577},
  doi =		{10.4230/LIPIcs.WADS.2025.26},
  annote =	{Keywords: Bin packing, Best Fit, Random order, Bounded space algorithms}
}
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.FSTTCS.2022.23
Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing

Authors: Arindam Khan, Eklavya Sharma, and K. V. N. Sreenivas

Published in: LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Abstract
We study the generalized multidimensional bin packing problem (GVBP) that generalizes both geometric packing and vector packing. Here, we are given n rectangular items where the i-th item has width w(i), height h(i), and d nonnegative weights v₁(i), v₂(i), …, v_d(i). Our goal is to get an axis-parallel non-overlapping packing of the items into square bins so that for all j ∈ [d], the sum of the j-th weight of items in each bin is at most 1. This is a natural problem arising in logistics, resource allocation, and scheduling. Despite being well-studied in practice, approximation algorithms for this problem have rarely been explored. We first obtain two simple algorithms for GVBP having asymptotic approximation ratios 6(d+1) and 3(1 + ln(d+1) + ε). We then extend the Round-and-Approx (R&A) framework [Bansal et al., 2009; Bansal and Khan, 2014] to wider classes of algorithms, and show how it can be adapted to GVBP. Using more sophisticated techniques, we obtain better approximation algorithms for GVBP, and we get further improvement by combining them with the R&A framework. This gives us an asymptotic approximation ratio of 2(1 + ln((d+4)/2)) + ε for GVBP, which improves to 2.919+ε for the special case of d = 1. We obtain further improvement when the items are allowed to be rotated. We also present algorithms for a generalization of GVBP where the items are high dimensional cuboids.
Cite as

Arindam Khan, Eklavya Sharma, and K. V. N. Sreenivas. Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{khan_et_al:LIPIcs.FSTTCS.2022.23,
  author =	{Khan, Arindam and Sharma, Eklavya and Sreenivas, K. V. N.},
  title =	{{Geometry Meets Vectors: Approximation Algorithms for Multidimensional Packing}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.23},
  URN =		{urn:nbn:de:0030-drops-174151},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.23},
  annote =	{Keywords: Bin packing, rectangle packing, multidimensional packing, approximation algorithms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.12
Near-Optimal Algorithms for Stochastic Online Bin Packing

Authors: Nikhil ^* Ayyadevara, Rajni Dabas, Arindam Khan, and K. V. N. Sreenivas

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study the online bin packing problem under two stochastic settings. In the bin packing problem, we are given n items with sizes in (0,1] and the goal is to pack them into the minimum number of unit-sized bins. First, we study bin packing under the i.i.d. model, where item sizes are sampled independently and identically from a distribution in (0,1]. Both the distribution and the total number of items are unknown. The items arrive one by one and their sizes are revealed upon their arrival and they must be packed immediately and irrevocably in bins of size 1. We provide a simple meta-algorithm that takes an offline α-asymptotic proximation algorithm and provides a polynomial-time (α + ε)-competitive algorithm for online bin packing under the i.i.d. model, where ε > 0 is a small constant. Using the AFPTAS for offline bin packing, we thus provide a linear time (1+ε)-competitive algorithm for online bin packing under i.i.d. model, thus settling the problem. We then study the random-order model, where an adversary specifies the items, but the order of arrival of items is drawn uniformly at random from the set of all permutations of the items. Kenyon’s seminal result [SODA'96] showed that the Best-Fit algorithm has a competitive ratio of at most 3/2 in the random-order model, and conjectured the ratio to be ≈ 1.15. However, it has been a long-standing open problem to break the barrier of 3/2 even for special cases. Recently, Albers et al. [Algorithmica'21] showed an improvement to 5/4 competitive ratio in the special case when all the item sizes are greater than 1/3. For this special case, we settle the analysis by showing that Best-Fit has a competitive ratio of 1. We also make further progress by breaking the barrier of 3/2 for the 3-Partition problem, a notoriously hard special case of bin packing, where all item sizes lie in (1/4,1/2].
Cite as

Nikhil ^* Ayyadevara, Rajni Dabas, Arindam Khan, and K. V. N. Sreenivas. Near-Optimal Algorithms for Stochastic Online Bin Packing. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ayyadevara_et_al:LIPIcs.ICALP.2022.12,
  author =	{Ayyadevara, Nikhil ^* and Dabas, Rajni and Khan, Arindam and Sreenivas, K. V. N.},
  title =	{{Near-Optimal Algorithms for Stochastic Online Bin Packing}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.12},
  URN =		{urn:nbn:de:0030-drops-163532},
  doi =		{10.4230/LIPIcs.ICALP.2022.12},
  annote =	{Keywords: Bin Packing, 3-Partition Problem, Online Algorithms, Random Order Arrival, IID model, Best-Fit Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.78
A PTAS for Packing Hypercubes into a Knapsack

Authors: Klaus Jansen, Arindam Khan, Marvin Lira, and K. V. N. Sreenivas

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study the d-dimensional hypercube knapsack problem ({d}-D Hc-Knapsack) where we are given a set of d-dimensional hypercubes with associated profits, and a knapsack which is a unit d-dimensional hypercube. The goal is to find an axis-aligned non-overlapping packing of a subset of hypercubes such that the profit of the packed hypercubes is maximized. For this problem, Harren (ICALP'06) gave an algorithm with an approximation ratio of (1+1/2^d+ε). For d = 2, Jansen and Solis-Oba (IPCO'08) showed that the problem admits a polynomial-time approximation scheme (PTAS); Heydrich and Wiese (SODA'17) further improved the running time and gave an efficient polynomial-time approximation scheme (EPTAS). Both the results use structural properties of 2-D packing, which do not generalize to higher dimensions. For d > 2, it remains open to obtain a PTAS, and in fact, there has been no improvement since Harren’s result. We settle the problem by providing a PTAS. Our main technical contribution is a structural lemma which shows that any packing of hypercubes can be converted into another structured packing such that a high profitable subset of hypercubes is packed into a constant number of special hypercuboids, called 𝒱-Boxes and 𝒩-Boxes. As a side result, we give an almost optimal algorithm for a variant of the strip packing problem in higher dimensions. This might have applications for other multidimensional geometric packing problems.
Cite as

Klaus Jansen, Arindam Khan, Marvin Lira, and K. V. N. Sreenivas. A PTAS for Packing Hypercubes into a Knapsack. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 78:1-78:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{jansen_et_al:LIPIcs.ICALP.2022.78,
  author =	{Jansen, Klaus and Khan, Arindam and Lira, Marvin and Sreenivas, K. V. N.},
  title =	{{A PTAS for Packing Hypercubes into a Knapsack}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{78:1--78:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.78},
  URN =		{urn:nbn:de:0030-drops-164192},
  doi =		{10.4230/LIPIcs.ICALP.2022.78},
  annote =	{Keywords: Multidimensional knapsack, geometric packing, cube packing, strip packing}
}
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