11 Search Results for "Maack, Marten"

Document
Invited Talk
DOI: 10.4230/LIPIcs.IPEC.2025.1
A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk)

Authors: Martin Koutecký

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Integer Programming (IP) is a fundamental but computationally hard problem. Still, certain efficiently solvable subclasses have been identified over time, most notably totally unimodular IPs in the 1950s, and fixed-dimension IPs in the 1980s. Starting around the year 2000, a stream of research has identified block-structured IPs as yet another tractable subclass. In this paper, we give a brief and incomplete review of this history, with a focus on several of the author’s contributions.
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Martin Koutecký. A Brief History of Parameterized Algorithms for Block-Structured Integer Programs (Invited Talk). In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{koutecky:LIPIcs.IPEC.2025.1,
  author =	{Kouteck\'{y}, Martin},
  title =	{{A Brief History of Parameterized Algorithms for Block-Structured Integer Programs}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.1},
  URN =		{urn:nbn:de:0030-drops-251338},
  doi =		{10.4230/LIPIcs.IPEC.2025.1},
  annote =	{Keywords: Integer Programming, Parameterized Algorithm, Graver Basis, Treedepth, n-fold, tree-fold, 2-stage stochastic, multistage stochastic, Mixed-Integer Programming}
}
Document
DOI: 10.4230/LIPIcs.IPEC.2025.15
New Algorithm for Combinatorial n-Folds and Applications

Authors: Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas

Published in: LIPIcs, Volume 358, 20th International Symposium on Parameterized and Exact Computation (IPEC 2025)

Abstract
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address n-fold ILPs where the matrix 𝒜 has a specific structure, i.e., where the blocks in the lower part of 𝒜 consist only of the row vectors (1,… ,1). In this paper, we propose an approach tailored to exactly these combinatorial n-folds. We utilize a divide and conquer approach to separate the original problem such that the right-hand side iteratively decreases in size. We show that this decrease in size can be calculated such that we only need to consider a bounded amount of possible right-hand sides. This, in turn, lets us efficiently combine solutions of the smaller right-hand sides to solve the original problem. We can decide the feasibility of, and also optimally solve, such problems in time (n r Δ)^O(r) log(‖b‖_∞), where n is the number of blocks, r the number of rows in the upper blocks and Δ = ‖A‖_∞. We complement the algorithm by discussing applications of the n-fold ILPs with the specific structure we require. We consider the problems of (i) scheduling on uniform machines, (ii) closest string and (iii) (graph) imbalance. Regarding (i), our algorithm results in running times of p_max^O(d)|I|^O(1), matching a lower bound derived via ETH. For (ii) we achieve running times matching the current state-of-the-art in the general case. In contrast to the state-of-the-art, our result can leverage a bounded number of column-types to yield an improved running time. For (iii), we improve the parameter dependency on the size of the vertex cover.
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Klaus Jansen, Kai Kahler, Lis Pirotton, and Malte Tutas. New Algorithm for Combinatorial n-Folds and Applications. In 20th International Symposium on Parameterized and Exact Computation (IPEC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 358, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{jansen_et_al:LIPIcs.IPEC.2025.15,
  author =	{Jansen, Klaus and Kahler, Kai and Pirotton, Lis and Tutas, Malte},
  title =	{{New Algorithm for Combinatorial n-Folds and Applications}},
  booktitle =	{20th International Symposium on Parameterized and Exact Computation (IPEC 2025)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-407-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{358},
  editor =	{Agrawal, Akanksha and van Leeuwen, Erik Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2025.15},
  URN =		{urn:nbn:de:0030-drops-251472},
  doi =		{10.4230/LIPIcs.IPEC.2025.15},
  annote =	{Keywords: integer linear programming, n-fold, parameterized complexity, scheduling, uniform machines}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.112
Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns

Authors: Alexandra Lassota and Koen Ligthart

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

Abstract
We study integer linear programs (ILP) of the form min{c^⊤ x | Ax = b,l ≤ x ≤ u,x ∈ ℤⁿ} and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the well-established approach of capturing the hardness of a problem by the distance to triviality. The generalized matching problem is an ILP where each column of the constraint matrix has 1-norm of at most 2. It captures several well-known polynomial time solvable problems such as matching and flow problems. We parameterize by the size of variable and constraint backdoors, which measure the least number of columns or rows that must be deleted to obtain a generalized matching ILP. This extends generalized matching problems by allowing a parameterized number of additional arbitrary variables or constraints, yielding a novel parameter. We present the following results: (i) a fixed-parameter tractable (FPT) algorithm for ILPs parameterized by the size p of a minimum variable backdoor to generalized matching; (ii) a randomized slice-wise polynomial (XP) time algorithm for ILPs parameterized by the size h of a minimum constraint backdoor to generalized matching as long as c and A are encoded in unary; (iii) we complement (ii) by proving that solving an ILP is W[1]-hard when parameterized by h even when c,A,l,u have coefficients of constant size. To obtain (i), we prove a variant of lattice-convexity of the degree sequences of weighted b-matchings, which we study in the light of SBO jump M-convex functions. This allows us to model the matching part as a polyhedral constraint on the integer backdoor variables. The resulting ILP is solved in FPT time using an integer programming algorithm. For (ii), the randomized XP time algorithm is obtained by pseudo-polynomially reducing the problem to the exact matching problem. To prevent an exponential blowup in terms of the encoding length of b, we bound the Graver complexity of the constraint matrix and employ a Graver augmentation local search framework. The hardness result (iii) is obtained through a parameterized reduction from ILP with h constraints and coefficients encoded in unary.
Cite as

Alexandra Lassota and Koen Ligthart. Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 112:1-112:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lassota_et_al:LIPIcs.ICALP.2025.112,
  author =	{Lassota, Alexandra and Ligthart, Koen},
  title =	{{Parameterized Algorithms for Matching Integer Programs with Additional Rows and Columns}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{112:1--112:18},
  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.2025.112},
  URN =		{urn:nbn:de:0030-drops-234895},
  doi =		{10.4230/LIPIcs.ICALP.2025.112},
  annote =	{Keywords: Integer Programming, fixed-parameter Tractability, polyhedral Optimization, Matchings}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2025.87
When to Give up on a Parallel Implementation

Authors: Nathan S. Sheffield and Alek Westover

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
In the Serial Parallel Decision Problem (SPDP), introduced by Kuszmaul and Westover [SPAA'24], an algorithm receives a series of tasks online, and must choose for each between a serial implementation and a parallelizable (but less efficient) implementation. Kuszmaul and Westover describe three decision models: (1) Instantly-committing schedulers must decide on arrival, irrevocably, which implementation of the task to run. (2) Eventually-committing schedulers can delay their decision beyond a task’s arrival time, but cannot revoke their decision once made. (3) Never-committing schedulers are always free to abandon their progress on the task and start over using a different implementation. Kuszmaul and Westover gave a simple instantly-committing scheduler whose total completion time is 3-competitive with the offline optimal schedule, and proved two lower bounds: no eventually-committing scheduler can have competitive ratio better than ϕ ≈ 1.618 in general, and no instantly-committing scheduler can have competitive ratio better than 2 in general. They conjectured that the three decision models should admit different competitive ratios, but left upper bounds below 3 in any model as an open problem. In this paper, we show that the powers of instantly, eventually, and never committing schedulers are distinct, at least in the "massively parallel regime". The massively parallel regime of the SPDP is the special case where the number of available processors is asymptotically larger than the number of tasks to process, meaning that the work associated with running a task in serial is negligible compared to its runtime. In this regime, we show (1) The optimal competitive ratio for instantly-committing schedulers is 2, (2) The optimal competitive ratio for eventually-committing schedulers lies in [1.618, 1.678], (3) The optimal competitive ratio for never-committing schedulers lies in [1.366, 1.500]. We additionally show that our instantly-committing scheduler is also 2-competitive outside of the massively parallel regime, giving proof-of-concept that results in the massively parallel regime can be translated to hold with fewer processors.
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Nathan S. Sheffield and Alek Westover. When to Give up on a Parallel Implementation. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 87:1-87:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sheffield_et_al:LIPIcs.ITCS.2025.87,
  author =	{Sheffield, Nathan S. and Westover, Alek},
  title =	{{When to Give up on a Parallel Implementation}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{87:1--87:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.87},
  URN =		{urn:nbn:de:0030-drops-227154},
  doi =		{10.4230/LIPIcs.ITCS.2025.87},
  annote =	{Keywords: Scheduling, Multi-Processor, Online-Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.77
(In-)Approximability Results for Interval, Resource Restricted, and Low Rank Scheduling

Authors: Marten Maack, Simon Pukrop, and Anna Rodriguez Rasmussen

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We consider variants of the restricted assignment problem where a set of jobs has to be assigned to a set of machines, for each job a size and a set of eligible machines is given, and the jobs may only be assigned to eligible machines with the goal of makespan minimization. For the variant with interval restrictions, where the machines can be arranged on a path such that each job is eligible on a subpath, we present the first better than 2-approximation and an improved inapproximability result. In particular, we give a (2-1/24)-approximation and show that no better than 9/8-approximation is possible, unless P=NP. Furthermore, we consider restricted assignment with R resource restrictions and rank D unrelated scheduling. In the former problem, a machine may process a job if it can meet its resource requirements regarding R (renewable) resources. In the latter, the size of a job is dependent on the machine it is assigned to and the corresponding processing time matrix has rank at most D. The problem with interval restrictions includes the 1 resource variant, is encompassed by the 2 resource variant, and regarding approximation the R resource variant is essentially a special case of the rank R+1 problem. We show that no better than 3/2, 8/7, and 3/2-approximation is possible (unless P=NP) for the 3 resource, 2 resource, and rank 3 variant, respectively. Both the approximation result for the interval case and the inapproximability result for the rank 3 variant are solutions to open challenges stated in previous works. Lastly, we also consider the reverse objective, that is, maximizing the minimal load any machine receives, and achieve similar results.
Cite as

Marten Maack, Simon Pukrop, and Anna Rodriguez Rasmussen. (In-)Approximability Results for Interval, Resource Restricted, and Low Rank Scheduling. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 77:1-77:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{maack_et_al:LIPIcs.ESA.2022.77,
  author =	{Maack, Marten and Pukrop, Simon and Rasmussen, Anna Rodriguez},
  title =	{{(In-)Approximability Results for Interval, Resource Restricted, and Low Rank Scheduling}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{77:1--77:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva 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.2022.77},
  URN =		{urn:nbn:de:0030-drops-170152},
  doi =		{10.4230/LIPIcs.ESA.2022.77},
  annote =	{Keywords: Scheduling, Restricted Assignment, Approximation, Inapproximability}
}
Document
DOI: 10.4230/LIPIcs.STACS.2022.28
Cardinality Constrained Scheduling in Online Models

Authors: Leah Epstein, Alexandra Lassota, Asaf Levin, Marten Maack, and Lars Rohwedder

Published in: LIPIcs, Volume 219, 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)

Abstract
Makespan minimization on parallel identical machines is a classical and intensively studied problem in scheduling, and a classic example for online algorithm analysis with Graham’s famous list scheduling algorithm dating back to the 1960s. In this problem, jobs arrive over a list and upon an arrival, the algorithm needs to assign the job to a machine. The goal is to minimize the makespan, that is, the maximum machine load. In this paper, we consider the variant with an additional cardinality constraint: The algorithm may assign at most k jobs to each machine where k is part of the input. While the offline (strongly NP-hard) variant of cardinality constrained scheduling is well understood and an EPTAS exists here, no non-trivial results are known for the online variant. We fill this gap by making a comprehensive study of various different online models. First, we show that there is a constant competitive algorithm for the problem and further, present a lower bound of 2 on the competitive ratio of any online algorithm. Motivated by the lower bound, we consider a semi-online variant where upon arrival of a job of size p, we are allowed to migrate jobs of total size at most a constant times p. This constant is called the migration factor of the algorithm. Algorithms with small migration factors are a common approach to bridge the performance of online algorithms and offline algorithms. One can obtain algorithms with a constant migration factor by rounding the size of each incoming job and then applying an ordinal algorithm to the resulting rounded instance. With this in mind, we also consider the framework of ordinal algorithms and characterize the competitive ratio that can be achieved using the aforementioned approaches. More specifically, we show that in both cases, one can get a competitive ratio that is strictly lower than 2, which is the bound from the standard online setting. On the other hand, we prove that no PTAS is possible.
Cite as

Leah Epstein, Alexandra Lassota, Asaf Levin, Marten Maack, and Lars Rohwedder. Cardinality Constrained Scheduling in Online Models. In 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 219, pp. 28:1-28:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{epstein_et_al:LIPIcs.STACS.2022.28,
  author =	{Epstein, Leah and Lassota, Alexandra and Levin, Asaf and Maack, Marten and Rohwedder, Lars},
  title =	{{Cardinality Constrained Scheduling in Online Models}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{28:1--28:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.28},
  URN =		{urn:nbn:de:0030-drops-158385},
  doi =		{10.4230/LIPIcs.STACS.2022.28},
  annote =	{Keywords: Cardinality Constrained Scheduling, Makespan Minimization, Online Algorithms, Lower Bounds, Pure Online, Migration, Ordinal Algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.11
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
DOI: 10.4230/LIPIcs.STACS.2020.5
Inapproximability Results for Scheduling with Interval and Resource Restrictions

Authors: Marten Maack and Klaus Jansen

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
In the restricted assignment problem, the input consists of a set of machines and a set of jobs each with a processing time and a subset of eligible machines. The goal is to find an assignment of the jobs to the machines minimizing the makespan, that is, the maximum summed up processing time any machine receives. Herein, jobs should only be assigned to those machines on which they are eligible. It is well-known that there is no polynomial time approximation algorithm with an approximation guarantee of less than 1.5 for the restricted assignment problem unless P=NP. In this work, we show hardness results for variants of the restricted assignment problem with particular types of restrictions. For the case of interval restrictions - where the machines can be totally ordered such that jobs are eligible on consecutive machines - we show that there is no polynomial time approximation scheme (PTAS) unless P=NP. The question of whether a PTAS for this variant exists was stated as an open problem before, and PTAS results for special cases of this variant are known. Furthermore, we consider a variant with resource restriction where the sets of eligible machines are of the following form: There is a fixed number of (renewable) resources, each machine has a capacity, and each job a demand for each resource. A job is eligible on a machine if its demand is at most as big as the capacity of the machine for each resource. For one resource, this problem has been intensively studied under several different names and is known to admit a PTAS, and for two resources the variant with interval restrictions is contained as a special case. Moreover, the version with multiple resources is closely related to makespan minimization on parallel machines with a low rank processing time matrix. We show that there is no polynomial time approximation algorithm with a rate smaller than 48/47 ≈ 1.02 or 1.5 for scheduling with resource restrictions with 2 or 4 resources, respectively, unless P=NP. All our results can be extended to the so called Santa Claus variants of the problems where the goal is to maximize the minimal processing time any machine receives.
Cite as

Marten Maack and Klaus Jansen. Inapproximability Results for Scheduling with Interval and Resource Restrictions. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 5:1-5:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{maack_et_al:LIPIcs.STACS.2020.5,
  author =	{Maack, Marten and Jansen, Klaus},
  title =	{{Inapproximability Results for Scheduling with Interval and Resource Restrictions}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{5:1--5:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.5},
  URN =		{urn:nbn:de:0030-drops-118663},
  doi =		{10.4230/LIPIcs.STACS.2020.5},
  annote =	{Keywords: Scheduling, Restricted Assignment, Approximation, Inapproximability, PTAS}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.18
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
DOI: 10.4230/LIPIcs.ITCS.2019.44
Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times

Authors: Klaus Jansen, Kim-Manuel Klein, Marten Maack, and Malin Rau

Published in: LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Abstract
Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems, where a set of items has to be placed in multiple target locations. Herein a configuration describes a possible placement on one of the target locations, and the IP is used to chose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and therefore be solved efficiently. As an application, we consider scheduling problems with setup times, in which a set of jobs has to be scheduled on a set of identical machines, with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f(1/epsilon) x poly(|I|) with a single exponential term in f for the first and a double exponential one for the second case. Previously, only constant factor approximations of 5/3 and 4/3 + epsilon respectively were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.
Cite as

Klaus Jansen, Kim-Manuel Klein, Marten Maack, and Malin Rau. Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{jansen_et_al:LIPIcs.ITCS.2019.44,
  author =	{Jansen, Klaus and Klein, Kim-Manuel and Maack, Marten and Rau, Malin},
  title =	{{Empowering the Configuration-IP - New PTAS Results for Scheduling with Setups Times}},
  booktitle =	{10th Innovations in Theoretical Computer Science Conference (ITCS 2019)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{124},
  editor =	{Blum, Avrim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.44},
  URN =		{urn:nbn:de:0030-drops-101375},
  doi =		{10.4230/LIPIcs.ITCS.2019.44},
  annote =	{Keywords: Parallel Machines, Setup Time, EPTAS, n-fold integer programming}
}
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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