4 Search Results for "Land, Kati"

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
DOI: 10.4230/LIPIcs.ITCS.2026.50
On the PTAS Complexity of Multidimensional Knapsack

Authors: Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi

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

Abstract
We study the d-dimensional knapsack problem. We are given a set of items, each with a d-dimensional cost vector and a profit, along with a d-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A polynomial-time approximation scheme (PTAS) with running time n^{Θ(d/{ε})} has long been known for this problem, where {ε} is the error parameter and n is the encoding size. Despite decades of active research, the best running time of a PTAS has remained O(n^{⌈ d/{ε} ⌉ - d}). Unfortunately, existing lower bounds only cover the special case with two dimensions d = 2, and do not answer whether there is a n^{o(d/({ε)})}-time PTAS for larger values of d. In this work, we show that the running times of the best-known PTAS cannot be improved up to a polylogarithmic factor assuming the Exponential Time Hypothesis (ETH). Our techniques are based on a robust reduction from 2-CSP, which embeds 2-CSP constraints into a desired number of dimensions. Then, using a recent result of [Bafna Karthik and Minzer, STOC'25], we succeed in exhibiting tight trade-off between d and {ε} for all regimes of the parameters assuming d is sufficiently large. Informally, our result also shows that under ETH, for any function f there is no f(d/({ε)}) ⋅ n^{õ(d/({ε)})}-time (1-{ε})-approximation for d-dimensional knapsack, where n is the number of items and õ hides polylogarithmic factors in d/({ε)}.
Cite as

Ilan Doron-Arad, Ariel Kulik, and Pasin Manurangsi. On the PTAS Complexity of Multidimensional Knapsack. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 50:1-50:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{doronarad_et_al:LIPIcs.ITCS.2026.50,
  author =	{Doron-Arad, Ilan and Kulik, Ariel and Manurangsi, Pasin},
  title =	{{On the PTAS Complexity of Multidimensional Knapsack}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{50:1--50:22},
  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.2026.50},
  URN =		{urn:nbn:de:0030-drops-253377},
  doi =		{10.4230/LIPIcs.ITCS.2026.50},
  annote =	{Keywords: d-dimensional Knapsack, Multidimensional Knapsack, PTAS, CSP}
}
Document
DOI: 10.4230/LIPIcs.CP.2025.26
Parallel MIP Solving with Dynamic Task Decomposition

Authors: Peng Lin, Shaowei Cai, Mengchuan Zou, and Shengqi Chen

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

Abstract
Mixed Integer Programming (MIP) is a foundational model in operations research. Although significant progress has been made in enhancing sequential MIP solvers through sophisticated techniques and heuristics, remarkable developments in computing resources have made parallel solving a promising direction for performance improvement. In this work, we propose a novel parallel MIP solving framework that employs dynamic task decomposition in a divide-and-conquer paradigm. Our framework incorporates a hardness estimate heuristic to identify challenging solving tasks and a reward decaying mechanism to reinforce the task decomposition decision. We apply our framework to two state-of-the-art open-source MIP solvers, SCIP and HiGHS, yielding efficient parallel solvers. Extensive experiments on the full MIPLIB benchmark, using up to 128 cores, demonstrate that our framework yields substantial performance improvements over modern divide-and-conquer parallel solvers. Moreover, our parallel solvers have established new best known solutions for 16 open MIPLIB instances.
Cite as

Peng Lin, Shaowei Cai, Mengchuan Zou, and Shengqi Chen. Parallel MIP Solving with Dynamic Task Decomposition. In 31st International Conference on Principles and Practice of Constraint Programming (CP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 340, pp. 26:1-26:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lin_et_al:LIPIcs.CP.2025.26,
  author =	{Lin, Peng and Cai, Shaowei and Zou, Mengchuan and Chen, Shengqi},
  title =	{{Parallel MIP Solving with Dynamic Task Decomposition}},
  booktitle =	{31st International Conference on Principles and Practice of Constraint Programming (CP 2025)},
  pages =	{26:1--26:19},
  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.2025.26},
  URN =		{urn:nbn:de:0030-drops-238871},
  doi =		{10.4230/LIPIcs.CP.2025.26},
  annote =	{Keywords: Mixed Integer Programming, Parallel Computing, Complete Search, Task Decomposition}
}
Document
DOI: 10.4230/LIPIcs.SWAT.2016.24
Estimating The Makespan of The Two-Valued Restricted Assignment Problem

Authors: Klaus Jansen, Kati Land, and Marten Maack

Published in: LIPIcs, Volume 53, 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)

Abstract
We consider a special case of the scheduling problem on unrelated machines, namely the Restricted Assignment Problem with two different processing times. We show that the configuration LP has an integrality gap of at most 5/3 ~ 1.667 for this problem. This allows us to estimate the optimal makespan within a factor of 5/3, improving upon the previously best known estimation algorithm with ratio 11/6 ~ 1.833 due to Chakrabarty, Khanna, and Li.
Cite as

Klaus Jansen, Kati Land, and Marten Maack. Estimating The Makespan of The Two-Valued Restricted Assignment Problem. In 15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 53, pp. 24:1-24:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jansen_et_al:LIPIcs.SWAT.2016.24,
  author =	{Jansen, Klaus and Land, Kati and Maack, Marten},
  title =	{{Estimating The Makespan of The Two-Valued Restricted Assignment Problem}},
  booktitle =	{15th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2016)},
  pages =	{24:1--24:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-011-8},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{53},
  editor =	{Pagh, Rasmus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2016.24},
  URN =		{urn:nbn:de:0030-drops-60467},
  doi =		{10.4230/LIPIcs.SWAT.2016.24},
  annote =	{Keywords: unrelated scheduling, restricted assignment, configuration LP, integrality gap, estimation algorithm}
}
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