10 Search Results for "Berndt, Sebastian"


Document
PACE Solver Description
PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth

Authors: Max Bannach and Sebastian Berndt

Published in: LIPIcs, Volume 285, 18th International Symposium on Parameterized and Exact Computation (IPEC 2023)


Abstract
This article is a report by the challenge organizers on the 8th Parameterized Algorithms and Computational Experiments Challenge (PACE 2023). As was common in previous iterations of the competition, this year’s iteration implemented an exact and heuristic track for a parameterized problem that has gained attention in the theory community. This year, the problem was to compute the twinwidth of a graph, a recently introduced width parameter that measures the similarity of a graph to a cograph. In the exact track, the competition participants were asked to develop an exact algorithm that can solve as many instances as possible from a benchmark set of 100 instances - with a time limit of 30 minutes per instance. The same task must be accomplished within 5 minutes in the heuristic track. However, the result in this track is not required to be optimal. As in previous iterations, the organizers handed out awards to the best solutions in both tracks and to the best student submissions. New this year is a dedicated theory award that appreciates new theoretical insights found by the participants during the development of their tools.

Cite as

Max Bannach and Sebastian Berndt. PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bannach_et_al:LIPIcs.IPEC.2023.35,
  author =	{Bannach, Max and Berndt, Sebastian},
  title =	{{PACE Solver Description: The PACE 2023 Parameterized Algorithms and Computational Experiments Challenge: Twinwidth}},
  booktitle =	{18th International Symposium on Parameterized and Exact Computation (IPEC 2023)},
  pages =	{35:1--35:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-305-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{285},
  editor =	{Misra, Neeldhara and Wahlstr\"{o}m, Magnus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2023.35},
  URN =		{urn:nbn:de:0030-drops-194548},
  doi =		{10.4230/LIPIcs.IPEC.2023.35},
  annote =	{Keywords: Twinwidth, Algorithm Engineering, FPT, Kernelization}
}
Document
New Support Size Bounds for Integer Programming, Applied to Makespan Minimization on Uniformly Related Machines

Authors: Sebastian Berndt, Hauke Brinkop, Klaus Jansen, Matthias Mnich, and Tobias Stamm

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)


Abstract
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the minimum number of non-zero integer variables in an optimal solution. A hallmark result by Eisenbrand and Shmonin (Oper. Res. Lett. , 2006) shows that any feasible integer linear program (ILP) has a solution with support size s ≤ 2m⋅log(4mΔ), where m is the number of constraints, and Δ is the largest absolute coefficient in any constraint. Our main combinatorial result are improved support size bounds for ILPs. We show that any ILP has a solution with support size s ≤ m⋅(log(3A_max)+√{log(A_max)}), where A_max≔ ‖A‖₁ denotes the 1-norm of the constraint matrix A. Furthermore, we show support bounds in the linearized form s ≤ 2m⋅log(1.46 A_max). Our upper bounds also hold with A_max replaced by √mΔ, which improves on the previously best constants in the linearized form. Our main algorithmic result are the fastest known approximation schemes for fundamental scheduling problems, which use the improved support bounds as one ingredient. We design an efficient approximation scheme (EPTAS) for makespan minimization on uniformly related machines (Q||C_{max}). Our EPTAS yields a (1+ε)-approximation for Q||C_{max} on N jobs in time 2^𝒪(1/ε log³(1/ε)log(log(1/ε))) + 𝒪(N), which improves over the previously fastest algorithm by Jansen, Klein and Verschae (Math. Oper. Res., 2020) with run time 2^𝒪(1/ε log⁴(1/ε)) + N^𝒪(1). Arguably, our approximation scheme is also simpler than all previous EPTASes for Q||C_max, as we reduce the problem to a novel MILP formulation which greatly benefits from the small support.

Cite as

Sebastian Berndt, Hauke Brinkop, Klaus Jansen, Matthias Mnich, and Tobias Stamm. New Support Size Bounds for Integer Programming, Applied to Makespan Minimization on Uniformly Related Machines. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{berndt_et_al:LIPIcs.ISAAC.2023.13,
  author =	{Berndt, Sebastian and Brinkop, Hauke and Jansen, Klaus and Mnich, Matthias and Stamm, Tobias},
  title =	{{New Support Size Bounds for Integer Programming, Applied to Makespan Minimization on Uniformly Related Machines}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.13},
  URN =		{urn:nbn:de:0030-drops-193155},
  doi =		{10.4230/LIPIcs.ISAAC.2023.13},
  annote =	{Keywords: Integer programming, scheduling algorithms, uniformly related machines, makespan minimization}
}
Document
PACE Solver Description
PACE Solver Description: Fluid

Authors: Max Bannach, Sebastian Berndt, Martin Schuster, and Marcel Wienöbst

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)


Abstract
This document describes the heuristic for computing treedepth decompositions of undirected graphs used by our solve fluid. The heuristic runs four different strategies to find a solution and finally outputs the best solution obtained by any of them. Two strategies are score-based and iteratively remove the vertex with the best score. The other two strategies iteratively search for vertex separators and remove them. We also present implementation strategies and data structures that significantly improve the run time complexity and might be interesting on their own.

Cite as

Max Bannach, Sebastian Berndt, Martin Schuster, and Marcel Wienöbst. PACE Solver Description: Fluid. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 27:1-27:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bannach_et_al:LIPIcs.IPEC.2020.27,
  author =	{Bannach, Max and Berndt, Sebastian and Schuster, Martin and Wien\"{o}bst, Marcel},
  title =	{{PACE Solver Description: Fluid}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{27:1--27:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.27},
  URN =		{urn:nbn:de:0030-drops-133300},
  doi =		{10.4230/LIPIcs.IPEC.2020.27},
  annote =	{Keywords: treedepth, heuristics}
}
Document
PACE Solver Description
PACE Solver Description: PID^⋆

Authors: Max Bannach, Sebastian Berndt, Martin Schuster, and Marcel Wienöbst

Published in: LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)


Abstract
This document provides a short overview of our treedepth solver PID^{⋆} in the version that we submitted to the exact track of the PACE challenge 2020. The solver relies on the positive-instance driven dynamic programming (PID) paradigm that was discovered in the light of earlier iterations of the PACE in the context of treewidth. It was recently shown that PID can be used to solve a general class of vertex pursuit-evasion games - which include the game theoretic characterization of treedepth. Our solver PID^{⋆} is build on top of this characterization.

Cite as

Max Bannach, Sebastian Berndt, Martin Schuster, and Marcel Wienöbst. PACE Solver Description: PID^⋆. In 15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 28:1-28:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bannach_et_al:LIPIcs.IPEC.2020.28,
  author =	{Bannach, Max and Berndt, Sebastian and Schuster, Martin and Wien\"{o}bst, Marcel},
  title =	{{PACE Solver Description: PID^⋆}},
  booktitle =	{15th International Symposium on Parameterized and Exact Computation (IPEC 2020)},
  pages =	{28:1--28:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-172-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{180},
  editor =	{Cao, Yixin and Pilipczuk, Marcin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.28},
  URN =		{urn:nbn:de:0030-drops-133312},
  doi =		{10.4230/LIPIcs.IPEC.2020.28},
  annote =	{Keywords: treedepth, positive-instance driven}
}
Document
Solving Packing Problems with Few Small Items Using Rainbow Matchings

Authors: Max Bannach, Sebastian Berndt, Marten Maack, Matthias Mnich, Alexandra Lassota, Malin Rau, and Malte Skambath

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


Abstract
An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation algorithms, but their parameterized complexity has only been investigated barely. For problem instances containing no "small" items, classical matching algorithms yield optimal solutions in polynomial time. In this paper we approach them by their distance from triviality, measuring the problem complexity by the number k of small items. Our main results are fixed-parameter algorithms for vector versions of Bin Packing, Multiple Knapsack, and Bin Covering parameterized by k. The algorithms are randomized with one-sided error and run in time 4^k⋅ k!⋅ n^{O(1)}. To achieve this, we introduce a colored matching problem to which we reduce all these packing problems. The colored matching problem is natural in itself and we expect it to be useful for other applications. We also present a deterministic fixed-parameter algorithm for Bin Covering with run time O((k!)² ⋅ k ⋅ 2^k ⋅ n log(n)).

Cite as

Max Bannach, Sebastian Berndt, Marten Maack, Matthias Mnich, Alexandra Lassota, Malin Rau, and Malte Skambath. Solving Packing Problems with Few Small Items Using Rainbow Matchings. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 11:1-11:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{bannach_et_al:LIPIcs.MFCS.2020.11,
  author =	{Bannach, Max and Berndt, Sebastian and Maack, Marten and Mnich, Matthias and Lassota, Alexandra and Rau, Malin and Skambath, Malte},
  title =	{{Solving Packing Problems with Few Small Items Using Rainbow Matchings}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{11:1--11:14},
  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.2020.11},
  URN =		{urn:nbn:de:0030-drops-126816},
  doi =		{10.4230/LIPIcs.MFCS.2020.11},
  annote =	{Keywords: Bin Packing, Knapsack, matching, fixed-parameter tractable}
}
Document
Online Bin Covering with Limited Migration

Authors: Sebastian Berndt, Leah Epstein, Klaus Jansen, Asaf Levin, Marten Maack, and Lars Rohwedder

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)


Abstract
Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective. In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small epsilon). We therefore resolve the competitiveness of the bin covering problem with migration.

Cite as

Sebastian Berndt, Leah Epstein, Klaus Jansen, Asaf Levin, Marten Maack, and Lars Rohwedder. Online Bin Covering with Limited Migration. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{berndt_et_al:LIPIcs.ESA.2019.18,
  author =	{Berndt, Sebastian and Epstein, Leah and Jansen, Klaus and Levin, Asaf and Maack, Marten and Rohwedder, Lars},
  title =	{{Online Bin Covering with Limited Migration}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{18:1--18:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.18},
  URN =		{urn:nbn:de:0030-drops-111391},
  doi =		{10.4230/LIPIcs.ESA.2019.18},
  annote =	{Keywords: online algorithms, dynamic algorithms, competitive ratio, bin covering, migration factor}
}
Document
Practical Access to Dynamic Programming on Tree Decompositions

Authors: Max Bannach and Sebastian Berndt

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


Abstract
Parameterized complexity theory has lead to a wide range of algorithmic breakthroughs within the last decades, but the practicability of these methods for real-world problems is still not well understood. We investigate the practicability of one of the fundamental approaches of this field: dynamic programming on tree decompositions. Indisputably, this is a key technique in parameterized algorithms and modern algorithm design. Despite the enormous impact of this approach in theory, it still has very little influence on practical implementations. The reasons for this phenomenon are manifold. One of them is the simple fact that such an implementation requires a long chain of non-trivial tasks (as computing the decomposition, preparing it,...). We provide an easy way to implement such dynamic programs that only requires the definition of the update rules. With this interface, dynamic programs for various problems, such as 3-coloring, can be implemented easily in about 100 lines of structured Java code. The theoretical foundation of the success of dynamic programming on tree decompositions is well understood due to Courcelle's celebrated theorem, which states that every MSO-definable problem can be efficiently solved if a tree decomposition of small width is given. We seek to provide practical access to this theorem as well, by presenting a lightweight model-checker for a small fragment of MSO. This fragment is powerful enough to describe many natural problems, and our model-checker turns out to be very competitive against similar state-of-the-art tools.

Cite as

Max Bannach and Sebastian Berndt. Practical Access to Dynamic Programming on Tree Decompositions. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{bannach_et_al:LIPIcs.ESA.2018.6,
  author =	{Bannach, Max and Berndt, Sebastian},
  title =	{{Practical Access to Dynamic Programming on Tree Decompositions}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{6:1--6:13},
  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.2018.6},
  URN =		{urn:nbn:de:0030-drops-94692},
  doi =		{10.4230/LIPIcs.ESA.2018.6},
  annote =	{Keywords: fixed-parameter tractability, treewidth, model-checking}
}
Document
Jdrasil: A Modular Library for Computing Tree Decompositions

Authors: Max Bannach, Sebastian Berndt, and Thorsten Ehlers

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)


Abstract
While the theoretical aspects concerning the computation of tree width - one of the most important graph parameters - are well understood, it is not clear how it can be computed practically. We present the open source Java library Jdrasil that implements several different state of the art algorithms for this task. By experimentally comparing these algorithms, we show that the default choices made in Jdrasil lead to an competitive implementation (it took the third place in the first PACE challenge) while also being easy to use and easy to extend.

Cite as

Max Bannach, Sebastian Berndt, and Thorsten Ehlers. Jdrasil: A Modular Library for Computing Tree Decompositions. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 28:1-28:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{bannach_et_al:LIPIcs.SEA.2017.28,
  author =	{Bannach, Max and Berndt, Sebastian and Ehlers, Thorsten},
  title =	{{Jdrasil: A Modular Library for Computing Tree Decompositions}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{28:1--28:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.28},
  URN =		{urn:nbn:de:0030-drops-76051},
  doi =		{10.4230/LIPIcs.SEA.2017.28},
  annote =	{Keywords: tree width, algorithmic library, experimental evaluation}
}
Document
Hard Communication Channels for Steganography

Authors: Sebastian Berndt and Maciej Liskiewicz

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)


Abstract
This paper considers steganography - the concept of hiding the presence of secret messages in legal communications - in the computational setting and its relation to cryptography. Very recently the first (non-polynomial time) steganographic protocol has been shown which, for any communication channel, is provably secure, reliable, and has nearly optimal bandwidth. The security is unconditional, i.e. it does not rely on any unproven complexity-theoretic assumption. This disproves the claim that the existence of one-way functions and access to a communication channel oracle are both necessary and sufficient conditions for the existence of secure steganography in the sense that secure and reliable steganography exists independently of the existence of one-way functions. In this paper, we prove that this equivalence also does not hold in the more realistic setting, where the stegosystem is polynomial time bounded. We prove this by constructing (a) a channel for which secure steganography exists if and only if one-way functions exist and (b) another channel such that secure steganography implies that no one-way functions exist. We therefore show that security-preserving reductions between cryptography and steganography need to be treated very carefully.

Cite as

Sebastian Berndt and Maciej Liskiewicz. Hard Communication Channels for Steganography. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 16:1-16:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{berndt_et_al:LIPIcs.ISAAC.2016.16,
  author =	{Berndt, Sebastian and Liskiewicz, Maciej},
  title =	{{Hard Communication Channels for Steganography}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{16:1--16:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.16},
  URN =		{urn:nbn:de:0030-drops-67863},
  doi =		{10.4230/LIPIcs.ISAAC.2016.16},
  annote =	{Keywords: provable secure steganography, cryptographic assumptions, pseudoran- dom functions, one-way functions, signature schemes}
}
Document
Fully Dynamic Bin Packing Revisited

Authors: Sebastian Berndt, Klaus Jansen, and Kim-Manuel Klein

Published in: LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)


Abstract
We consider the fully dynamic bin packing problem, where items arrive and depart in an online fashion and repacking of previously packed items is allowed. The goal is, of course, to minimize both the number of bins used as well as the amount of repacking. A recently introduced way of measuring the repacking costs at each timestep is the migration factor, defined as the total size of repacked items divided by the size of an arriving or departing item. Concerning the trade-off between number of bins and migration factor, if we wish to achieve an asymptotic competitive ratio of 1 + epsilon for the number of bins, a relatively simple argument proves a lower bound of Omega(1/epsilon) of the migration factor. We establish a fairly close upper bound of O(1/epsilon^4 log(1/epsilon)) using a new dynamic rounding technique and new ideas to handle small items in a dynamic setting such that no amortization is needed. The running time of our algorithm is polynomial in the number of items n and in 1/epsilon. The previous best trade-off was for an asymptotic competitive ratio of 5/4 for the bins (rather than 1+epsilon) and needed an amortized number of O(log n) repackings (while in our scheme the number of repackings is independent of n and non-amortized).

Cite as

Sebastian Berndt, Klaus Jansen, and Kim-Manuel Klein. Fully Dynamic Bin Packing Revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 135-151, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{berndt_et_al:LIPIcs.APPROX-RANDOM.2015.135,
  author =	{Berndt, Sebastian and Jansen, Klaus and Klein, Kim-Manuel},
  title =	{{Fully Dynamic Bin Packing Revisited}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{135--151},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.135},
  URN =		{urn:nbn:de:0030-drops-53008},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.135},
  annote =	{Keywords: online, bin packing, migration factor, robust, AFPTAS}
}
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