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Documents authored by Verschae, Jose

Found 2 Possible Name Variants:

Verschae, Jose

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.46
A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems

Authors: Andrés Fielbaum, Ignacio Morales, and José Verschae

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Obtaining strong linear relaxations of capacitated covering problems constitute a significant technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on knapsack-cover inequalities has an integrality gap of 2. These inequalities are exploited in more general problems, many of which admit primal-dual approximation algorithms. Inspired by problems from power and transport systems, we introduce a general setting in which items can be taken fractionally to cover a given demand. The cost incurred by an item is given by an arbitrary non-decreasing function of the chosen fraction. We generalize the knapsack-cover inequalities to this setting an use them to obtain a (2+ε)-approximate primal-dual algorithm. Our procedure has a natural interpretation as a bucket-filling algorithm which effectively overcomes the difficulties implied by having different slopes in the cost functions. More precisely, when some superior segment of an item presents a low slope, it helps to increase the priority of inferior segments. We also present a rounding algorithm with an approximation guarantee of 2. We generalize our algorithm to the Unsplittable Flow-Cover problem on a line, also for the setting of fractional items with non-linear costs. For this problem we obtain a (4+ε)-approximation algorithm in polynomial time, almost matching the 4-approximation algorithm known for the classical setting.
Cite as

Andrés Fielbaum, Ignacio Morales, and José Verschae. A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fielbaum_et_al:LIPIcs.ICALP.2020.46,
  author =	{Fielbaum, Andr\'{e}s and Morales, Ignacio and Verschae, Jos\'{e}},
  title =	{{A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.46},
  URN =		{urn:nbn:de:0030-drops-124531},
  doi =		{10.4230/LIPIcs.ICALP.2020.46},
  annote =	{Keywords: Knapsack-Cover Inequalities, Non-Linear Knapsack-Cover, Primal-Dual, Water-Filling Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.82
Maintaining Perfect Matchings at Low Cost

Authors: Jannik Matuschke, Ulrike Schmidt-Kraepelin, and José Verschae

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
The min-cost matching problem suffers from being very sensitive to small changes of the input. Even in a simple setting, e.g., when the costs come from the metric on the line, adding two nodes to the input might change the optimal solution completely. On the other hand, one expects that small changes in the input should incur only small changes on the constructed solutions, measured as the number of modified edges. We introduce a two-stage model where we study the trade-off between quality and robustness of solutions. In the first stage we are given a set of nodes in a metric space and we must compute a perfect matching. In the second stage 2k new nodes appear and we must adapt the solution to a perfect matching for the new instance. We say that an algorithm is (alpha,beta)-robust if the solutions constructed in both stages are alpha-approximate with respect to min-cost perfect matchings, and if the number of edges deleted from the first stage matching is at most beta k. Hence, alpha measures the quality of the algorithm and beta its robustness. In this setting we aim to balance both measures by deriving algorithms for constant alpha and beta. We show that there exists an algorithm that is (3,1)-robust for any metric if one knows the number 2k of arriving nodes in advance. For the case that k is unknown the situation is significantly more involved. We study this setting under the metric on the line and devise a (10,2)-robust algorithm that constructs a solution with a recursive structure that carefully balances cost and redundancy.
Cite as

Jannik Matuschke, Ulrike Schmidt-Kraepelin, and José Verschae. Maintaining Perfect Matchings at Low Cost. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 82:1-82:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{matuschke_et_al:LIPIcs.ICALP.2019.82,
  author =	{Matuschke, Jannik and Schmidt-Kraepelin, Ulrike and Verschae, Jos\'{e}},
  title =	{{Maintaining Perfect Matchings at Low Cost}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{82:1--82:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.82},
  URN =		{urn:nbn:de:0030-drops-106582},
  doi =		{10.4230/LIPIcs.ICALP.2019.82},
  annote =	{Keywords: matchings, robust optimization, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.32
Symmetry Exploitation for Online Machine Covering with Bounded Migration

Authors: Waldo Gálvez, José A. Soto, and José Verschae

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

Abstract
Online models that allow recourse are highly effective in situations where classical models are too pessimistic. One such problem is the online machine covering problem on identical machines. In this setting, jobs arrive one by one and must be assigned to machines with the objective of maximizing the minimum machine load. When a job arrives, we are allowed to reassign some jobs as long as their total size is (at most) proportional to the processing time of the arriving job. The proportionality constant is called the migration factor of the algorithm. By rounding the processing times, which yields useful structural properties for online packing and covering problems, we design first a simple (1.7 + epsilon)-competitive algorithm using a migration factor of O(1/epsilon) which maintains at every arrival a locally optimal solution with respect to the Jump neighborhood. After that, we present as our main contribution a more involved (4/3+epsilon)-competitive algorithm using a migration factor of O~(1/epsilon^3). At every arrival, we run an adaptation of the Largest Processing Time first (LPT) algorithm. Since the new job can cause a complete change of the assignment of smaller jobs in both cases, a low migration factor is achieved by carefully exploiting the highly symmetric structure obtained by the rounding procedure.
Cite as

Waldo Gálvez, José A. Soto, and José Verschae. Symmetry Exploitation for Online Machine Covering with Bounded Migration. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{galvez_et_al:LIPIcs.ESA.2018.32,
  author =	{G\'{a}lvez, Waldo and Soto, Jos\'{e} A. and Verschae, Jos\'{e}},
  title =	{{Symmetry Exploitation for Online Machine Covering with Bounded Migration}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.32},
  URN =		{urn:nbn:de:0030-drops-94959},
  doi =		{10.4230/LIPIcs.ESA.2018.32},
  annote =	{Keywords: Machine Covering, Bounded Migration, Online, Scheduling, LPT}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.31
A Local-Search Algorithm for Steiner Forest

Authors: Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, and José Verschae

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by, e.g., the elegant primal-dual algorithm of Agrawal, Klein, and Ravi from 1995. We give a local-search-based constant-factor approximation for the problem. Local search brings in new techniques to an area that has for long not seen any improvements and might be a step towards a combinatorial algorithm for the more general survivable network design problem. Moreover, local search was an essential tool to tackle the dynamic MST/Steiner Tree problem, whereas dynamic Steiner Forest is still wide open. It is easy to see that any constant factor local search algorithm requires steps that add/drop many edges together. We propose natural local moves which, at each step, either (a) add a shortest path in the current graph and then drop a bunch of inessential edges, or (b) add a set of edges to the current solution. This second type of moves is motivated by the potential function we use to measure progress, combining the cost of the solution with a penalty for each connected component. Our carefully-chosen local moves and potential function work in tandem to eliminate bad local minima that arise when using more traditional local moves. Our analysis first considers the case where the local optimum is a single tree, and shows optimality w.r.t. moves that add a single edge (and drop a set of edges) is enough to bound the locality gap. For the general case, we show how to "project" the optimal solution onto the different trees of the local optimum without incurring too much cost (and this argument uses optimality w.r.t. both kinds of moves), followed by a tree-by-tree argument. We hope both the potential function, and our analysis techniques will be useful to develop and analyze local-search algorithms in other contexts.
Cite as

Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, and José Verschae. A Local-Search Algorithm for Steiner Forest. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gro_et_al:LIPIcs.ITCS.2018.31,
  author =	{Gro{\ss}, Martin and Gupta, Anupam and Kumar, Amit and Matuschke, Jannik and Schmidt, Daniel R. and Schmidt, Melanie and Verschae, Jos\'{e}},
  title =	{{A Local-Search Algorithm for Steiner Forest}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.31},
  URN =		{urn:nbn:de:0030-drops-83134},
  doi =		{10.4230/LIPIcs.ITCS.2018.31},
  annote =	{Keywords: Local Search, Steiner Forest, Approximation Algorithms, Network Design}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.31
A QPTAS for the General Scheduling Problem with Identical Release Dates

Authors: Antonios Antoniadis, Ruben Hoeksma, Julie Meißner, José Verschae, and Andreas Wiese

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
The General Scheduling Problem (GSP) generalizes scheduling problems with sum of cost objectives such as weighted flow time and weighted tardiness. Given a set of jobs with processing times, release dates, and job dependent cost functions, we seek to find a minimum cost preemptive schedule on a single machine. The best known algorithm for this problem and also for weighted flow time/tardiness is an O(loglog P)-approximation (where P denotes the range of the job processing times), while the best lower bound shows only strong NP-hardness. When release dates are identical there is also a gap: the problem remains strongly NP-hard and the best known approximation algorithm has a ratio of e+\epsilon (running in quasi-polynomial time). We reduce the latter gap by giving a QPTAS if the numbers in the input are quasi-polynomially bounded, ruling out the existence of an APX-hardness proof unless NP\subseteq DTIME(2^polylog(n)). Our techniques are based on the QPTAS known for the UFP-Cover problem, a particular case of GSP where we must pick a subset of intervals (jobs) on the real line with associated heights and costs. If an interval is selected, its height will help cover a given demand on any point contained within the interval. We reduce our problem to a generalization of UFP-Cover and use a sophisticated divide-and-conquer procedure with interdependent non-symmetric subproblems. We also present a pseudo-polynomial time approximation scheme for two variants of UFP-Cover. For the case of agreeable intervals we give an algorithm based on a new dynamic programming approach which might be useful for other problems of this type. The second one is a resource augmentation setting where we are allowed to slightly enlarge each interval.
Cite as

Antonios Antoniadis, Ruben Hoeksma, Julie Meißner, José Verschae, and Andreas Wiese. A QPTAS for the General Scheduling Problem with Identical Release Dates. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{antoniadis_et_al:LIPIcs.ICALP.2017.31,
  author =	{Antoniadis, Antonios and Hoeksma, Ruben and Mei{\ss}ner, Julie and Verschae, Jos\'{e} and Wiese, Andreas},
  title =	{{A QPTAS for the General Scheduling Problem with Identical Release Dates}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.31},
  URN =		{urn:nbn:de:0030-drops-74575},
  doi =		{10.4230/LIPIcs.ICALP.2017.31},
  annote =	{Keywords: Generalized Scheduling, QPTAS, Unsplittable Flows}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.72
Closing the Gap for Makespan Scheduling via Sparsification Techniques

Authors: Klaus Jansen, Kim-Manuel Klein, and José Verschae

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Makespan scheduling on identical machines is one of the most basic and fundamental packing problem studied in the discrete optimization literature. It asks for an assignment of n jobs to a set of m identical machines that minimizes the makespan. The problem is strongly NPhard, and thus we do not expect a (1 + epsilon)-approximation algorithm with a running time that depends polynomially on 1/epsilon. Furthermore, Chen et al. [Chen/JansenZhang, SODA'13] recently showed that a running time of 2^{1/epsilon}^{1-delta} + poly(n) for any delta > 0 would imply that the Exponential Time Hypothesis (ETH) fails. A long sequence of algorithms have been developed that try to obtain low dependencies on 1/epsilon, the better of which achieves a running time of 2^{~O(1/epsilon^{2})} + O(n*log(n)) [Jansen, SIAM J. Disc. Math. 2010]. In this paper we obtain an algorithm with a running time of 2^{~O(1/epsilon)} + O(n*log(n)), which is tight under ETH up to logarithmic factors on the exponent. Our main technical contribution is a new structural result on the configuration-IP. More precisely, we show the existence of a highly symmetric and sparse optimal solution, in which all but a constant number of machines are assigned a configuration with small support. This structure can then be exploited by integer programming techniques and enumeration. We believe that our structural result is of independent interest and should find applications to other settings. In particular, we show how the structure can be applied to the minimum makespan problem on related machines and to a larger class of objective functions on parallel machines. For all these cases we obtain an efficient PTAS with running time 2^{~O(1/epsilon)} + poly(n).
Cite as

Klaus Jansen, Kim-Manuel Klein, and José Verschae. Closing the Gap for Makespan Scheduling via Sparsification Techniques. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 72:1-72:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jansen_et_al:LIPIcs.ICALP.2016.72,
  author =	{Jansen, Klaus and Klein, Kim-Manuel and Verschae, Jos\'{e}},
  title =	{{Closing the Gap for Makespan Scheduling via Sparsification Techniques}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{72:1--72:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.72},
  URN =		{urn:nbn:de:0030-drops-62122},
  doi =		{10.4230/LIPIcs.ICALP.2016.72},
  annote =	{Keywords: scheduling, approximation, PTAS, makespan, ETH}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.74
Min-Sum Scheduling Under Precedence Constraints

Authors: Andreas S. Schulz and José Verschae

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is that some jobs can only be processed after others. In this paper, we give the first approximation algorithms for min-sum scheduling with (nonnegative, non-decreasing) non-linear functions and general precedence constraints. In particular, for 1|prec|sum w_j f(C_j), we propose a polynomial-time universal algorithm that performs well for all functions f simultaneously. Its approximation guarantee is 2 for all concave functions, at worst. We also provide a (non-universal) polynomial-time algorithm for the more general case 1|prec|sum f_j(C_j). The performance guarantee is no worse than 2+epsilon for all concave functions. Our results match the best bounds known for the case of linear functions, a widely studied problem, and considerably extend the results for minimizing sum w_jf(C_j) without precedence constraints.
Cite as

Andreas S. Schulz and José Verschae. Min-Sum Scheduling Under Precedence Constraints. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 74:1-74:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{schulz_et_al:LIPIcs.ESA.2016.74,
  author =	{Schulz, Andreas S. and Verschae, Jos\'{e}},
  title =	{{Min-Sum Scheduling Under Precedence Constraints}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{74:1--74:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.74},
  URN =		{urn:nbn:de:0030-drops-64157},
  doi =		{10.4230/LIPIcs.ESA.2016.74},
  annote =	{Keywords: scheduling, approximation algorithms, linear programming relaxations, precedence constraints}
}
Document
DOI: 10.4230/DagSemProc.10071.13
Scheduling periodic tasks in a hard real-time environment

Authors: Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier, Martin Skutella, Jose Verschae, and Andreas Wiese

Published in: Dagstuhl Seminar Proceedings, Volume 10071, Scheduling (2010)

Abstract
We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks $ au_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $ au_i$ releases a job of running time $c_i$ at each time $a_i + kcdot p_i, , k in mathbb{N}_0$ and a collision occurs if two jobs are simultaneously active on the same machine. We shed some light on the complexity and approximability landscape of this problem. Although the problem cannot be approximated within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i | p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads to a 2-approximation. This result is tight, even asymptotically.
Cite as

Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier, Martin Skutella, Jose Verschae, and Andreas Wiese. Scheduling periodic tasks in a hard real-time environment. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{eisenbrand_et_al:DagSemProc.10071.13,
  author =	{Eisenbrand, Friedrich and H\"{a}hnle, Nicolai and Niemeier, Martin and Skutella, Martin and Verschae, Jose and Wiese, Andreas},
  title =	{{Scheduling periodic tasks in a hard real-time environment}},
  booktitle =	{Scheduling},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10071},
  editor =	{Susanne Albers and Sanjoy K. Baruah and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.13},
  URN =		{urn:nbn:de:0030-drops-25348},
  doi =		{10.4230/DagSemProc.10071.13},
  annote =	{Keywords: Real-Time Scheduling, Periodic scheduling problem, Periodic maintenance problem, Approximation hardness, Approximation algorithm}
}
Document
DOI: 10.4230/DagSemProc.09261.4
A Robust PTAS for the Parallel Machine Covering Problem

Authors: Martin Skutella and Jose Verschae

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract
In general, combinatorial optimization problems are unstable: slight changes on the instance of a problem can render huge changes in the optimal solution. Thus, a natural question arises: Can we achieve stability if we only maintain approximate solutions?. In this talk I will first formalize these ideas, and then show some results on the parallel machine covering problem. In particular I will derive a robust PTAS, i.e., I will show how to construct a solution that is not only $(1-epsilon)$-approximate, but is also stable. That is, if the instance is changed by adding or removing a job, then we can construct a new near-optimal solution by only slightly modifying the previous one.
Cite as

Martin Skutella and Jose Verschae. A Robust PTAS for the Parallel Machine Covering Problem. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{skutella_et_al:DagSemProc.09261.4,
  author =	{Skutella, Martin and Verschae, Jose},
  title =	{{A Robust PTAS for the Parallel Machine Covering Problem}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.4},
  URN =		{urn:nbn:de:0030-drops-21609},
  doi =		{10.4230/DagSemProc.09261.4},
  annote =	{Keywords: Stability, approximation schemes, online algorithms}
}

Verschae, José

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.46
A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems

Authors: Andrés Fielbaum, Ignacio Morales, and José Verschae

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
Obtaining strong linear relaxations of capacitated covering problems constitute a significant technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on knapsack-cover inequalities has an integrality gap of 2. These inequalities are exploited in more general problems, many of which admit primal-dual approximation algorithms. Inspired by problems from power and transport systems, we introduce a general setting in which items can be taken fractionally to cover a given demand. The cost incurred by an item is given by an arbitrary non-decreasing function of the chosen fraction. We generalize the knapsack-cover inequalities to this setting an use them to obtain a (2+ε)-approximate primal-dual algorithm. Our procedure has a natural interpretation as a bucket-filling algorithm which effectively overcomes the difficulties implied by having different slopes in the cost functions. More precisely, when some superior segment of an item presents a low slope, it helps to increase the priority of inferior segments. We also present a rounding algorithm with an approximation guarantee of 2. We generalize our algorithm to the Unsplittable Flow-Cover problem on a line, also for the setting of fractional items with non-linear costs. For this problem we obtain a (4+ε)-approximation algorithm in polynomial time, almost matching the 4-approximation algorithm known for the classical setting.
Cite as

Andrés Fielbaum, Ignacio Morales, and José Verschae. A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 46:1-46:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fielbaum_et_al:LIPIcs.ICALP.2020.46,
  author =	{Fielbaum, Andr\'{e}s and Morales, Ignacio and Verschae, Jos\'{e}},
  title =	{{A Water-Filling Primal-Dual Algorithm for Approximating Non-Linear Covering Problems}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{46:1--46:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.46},
  URN =		{urn:nbn:de:0030-drops-124531},
  doi =		{10.4230/LIPIcs.ICALP.2020.46},
  annote =	{Keywords: Knapsack-Cover Inequalities, Non-Linear Knapsack-Cover, Primal-Dual, Water-Filling Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.82
Maintaining Perfect Matchings at Low Cost

Authors: Jannik Matuschke, Ulrike Schmidt-Kraepelin, and José Verschae

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
The min-cost matching problem suffers from being very sensitive to small changes of the input. Even in a simple setting, e.g., when the costs come from the metric on the line, adding two nodes to the input might change the optimal solution completely. On the other hand, one expects that small changes in the input should incur only small changes on the constructed solutions, measured as the number of modified edges. We introduce a two-stage model where we study the trade-off between quality and robustness of solutions. In the first stage we are given a set of nodes in a metric space and we must compute a perfect matching. In the second stage 2k new nodes appear and we must adapt the solution to a perfect matching for the new instance. We say that an algorithm is (alpha,beta)-robust if the solutions constructed in both stages are alpha-approximate with respect to min-cost perfect matchings, and if the number of edges deleted from the first stage matching is at most beta k. Hence, alpha measures the quality of the algorithm and beta its robustness. In this setting we aim to balance both measures by deriving algorithms for constant alpha and beta. We show that there exists an algorithm that is (3,1)-robust for any metric if one knows the number 2k of arriving nodes in advance. For the case that k is unknown the situation is significantly more involved. We study this setting under the metric on the line and devise a (10,2)-robust algorithm that constructs a solution with a recursive structure that carefully balances cost and redundancy.
Cite as

Jannik Matuschke, Ulrike Schmidt-Kraepelin, and José Verschae. Maintaining Perfect Matchings at Low Cost. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 82:1-82:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{matuschke_et_al:LIPIcs.ICALP.2019.82,
  author =	{Matuschke, Jannik and Schmidt-Kraepelin, Ulrike and Verschae, Jos\'{e}},
  title =	{{Maintaining Perfect Matchings at Low Cost}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{82:1--82:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.82},
  URN =		{urn:nbn:de:0030-drops-106582},
  doi =		{10.4230/LIPIcs.ICALP.2019.82},
  annote =	{Keywords: matchings, robust optimization, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.32
Symmetry Exploitation for Online Machine Covering with Bounded Migration

Authors: Waldo Gálvez, José A. Soto, and José Verschae

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

Abstract
Online models that allow recourse are highly effective in situations where classical models are too pessimistic. One such problem is the online machine covering problem on identical machines. In this setting, jobs arrive one by one and must be assigned to machines with the objective of maximizing the minimum machine load. When a job arrives, we are allowed to reassign some jobs as long as their total size is (at most) proportional to the processing time of the arriving job. The proportionality constant is called the migration factor of the algorithm. By rounding the processing times, which yields useful structural properties for online packing and covering problems, we design first a simple (1.7 + epsilon)-competitive algorithm using a migration factor of O(1/epsilon) which maintains at every arrival a locally optimal solution with respect to the Jump neighborhood. After that, we present as our main contribution a more involved (4/3+epsilon)-competitive algorithm using a migration factor of O~(1/epsilon^3). At every arrival, we run an adaptation of the Largest Processing Time first (LPT) algorithm. Since the new job can cause a complete change of the assignment of smaller jobs in both cases, a low migration factor is achieved by carefully exploiting the highly symmetric structure obtained by the rounding procedure.
Cite as

Waldo Gálvez, José A. Soto, and José Verschae. Symmetry Exploitation for Online Machine Covering with Bounded Migration. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{galvez_et_al:LIPIcs.ESA.2018.32,
  author =	{G\'{a}lvez, Waldo and Soto, Jos\'{e} A. and Verschae, Jos\'{e}},
  title =	{{Symmetry Exploitation for Online Machine Covering with Bounded Migration}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.32},
  URN =		{urn:nbn:de:0030-drops-94959},
  doi =		{10.4230/LIPIcs.ESA.2018.32},
  annote =	{Keywords: Machine Covering, Bounded Migration, Online, Scheduling, LPT}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.31
A Local-Search Algorithm for Steiner Forest

Authors: Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, and José Verschae

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
In the Steiner Forest problem, we are given a graph and a collection of source-sink pairs, and the goal is to find a subgraph of minimum total length such that all pairs are connected. The problem is APX-Hard and can be 2-approximated by, e.g., the elegant primal-dual algorithm of Agrawal, Klein, and Ravi from 1995. We give a local-search-based constant-factor approximation for the problem. Local search brings in new techniques to an area that has for long not seen any improvements and might be a step towards a combinatorial algorithm for the more general survivable network design problem. Moreover, local search was an essential tool to tackle the dynamic MST/Steiner Tree problem, whereas dynamic Steiner Forest is still wide open. It is easy to see that any constant factor local search algorithm requires steps that add/drop many edges together. We propose natural local moves which, at each step, either (a) add a shortest path in the current graph and then drop a bunch of inessential edges, or (b) add a set of edges to the current solution. This second type of moves is motivated by the potential function we use to measure progress, combining the cost of the solution with a penalty for each connected component. Our carefully-chosen local moves and potential function work in tandem to eliminate bad local minima that arise when using more traditional local moves. Our analysis first considers the case where the local optimum is a single tree, and shows optimality w.r.t. moves that add a single edge (and drop a set of edges) is enough to bound the locality gap. For the general case, we show how to "project" the optimal solution onto the different trees of the local optimum without incurring too much cost (and this argument uses optimality w.r.t. both kinds of moves), followed by a tree-by-tree argument. We hope both the potential function, and our analysis techniques will be useful to develop and analyze local-search algorithms in other contexts.
Cite as

Martin Groß, Anupam Gupta, Amit Kumar, Jannik Matuschke, Daniel R. Schmidt, Melanie Schmidt, and José Verschae. A Local-Search Algorithm for Steiner Forest. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gro_et_al:LIPIcs.ITCS.2018.31,
  author =	{Gro{\ss}, Martin and Gupta, Anupam and Kumar, Amit and Matuschke, Jannik and Schmidt, Daniel R. and Schmidt, Melanie and Verschae, Jos\'{e}},
  title =	{{A Local-Search Algorithm for Steiner Forest}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.31},
  URN =		{urn:nbn:de:0030-drops-83134},
  doi =		{10.4230/LIPIcs.ITCS.2018.31},
  annote =	{Keywords: Local Search, Steiner Forest, Approximation Algorithms, Network Design}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.31
A QPTAS for the General Scheduling Problem with Identical Release Dates

Authors: Antonios Antoniadis, Ruben Hoeksma, Julie Meißner, José Verschae, and Andreas Wiese

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract
The General Scheduling Problem (GSP) generalizes scheduling problems with sum of cost objectives such as weighted flow time and weighted tardiness. Given a set of jobs with processing times, release dates, and job dependent cost functions, we seek to find a minimum cost preemptive schedule on a single machine. The best known algorithm for this problem and also for weighted flow time/tardiness is an O(loglog P)-approximation (where P denotes the range of the job processing times), while the best lower bound shows only strong NP-hardness. When release dates are identical there is also a gap: the problem remains strongly NP-hard and the best known approximation algorithm has a ratio of e+\epsilon (running in quasi-polynomial time). We reduce the latter gap by giving a QPTAS if the numbers in the input are quasi-polynomially bounded, ruling out the existence of an APX-hardness proof unless NP\subseteq DTIME(2^polylog(n)). Our techniques are based on the QPTAS known for the UFP-Cover problem, a particular case of GSP where we must pick a subset of intervals (jobs) on the real line with associated heights and costs. If an interval is selected, its height will help cover a given demand on any point contained within the interval. We reduce our problem to a generalization of UFP-Cover and use a sophisticated divide-and-conquer procedure with interdependent non-symmetric subproblems. We also present a pseudo-polynomial time approximation scheme for two variants of UFP-Cover. For the case of agreeable intervals we give an algorithm based on a new dynamic programming approach which might be useful for other problems of this type. The second one is a resource augmentation setting where we are allowed to slightly enlarge each interval.
Cite as

Antonios Antoniadis, Ruben Hoeksma, Julie Meißner, José Verschae, and Andreas Wiese. A QPTAS for the General Scheduling Problem with Identical Release Dates. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{antoniadis_et_al:LIPIcs.ICALP.2017.31,
  author =	{Antoniadis, Antonios and Hoeksma, Ruben and Mei{\ss}ner, Julie and Verschae, Jos\'{e} and Wiese, Andreas},
  title =	{{A QPTAS for the General Scheduling Problem with Identical Release Dates}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.31},
  URN =		{urn:nbn:de:0030-drops-74575},
  doi =		{10.4230/LIPIcs.ICALP.2017.31},
  annote =	{Keywords: Generalized Scheduling, QPTAS, Unsplittable Flows}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.72
Closing the Gap for Makespan Scheduling via Sparsification Techniques

Authors: Klaus Jansen, Kim-Manuel Klein, and José Verschae

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract
Makespan scheduling on identical machines is one of the most basic and fundamental packing problem studied in the discrete optimization literature. It asks for an assignment of n jobs to a set of m identical machines that minimizes the makespan. The problem is strongly NPhard, and thus we do not expect a (1 + epsilon)-approximation algorithm with a running time that depends polynomially on 1/epsilon. Furthermore, Chen et al. [Chen/JansenZhang, SODA'13] recently showed that a running time of 2^{1/epsilon}^{1-delta} + poly(n) for any delta > 0 would imply that the Exponential Time Hypothesis (ETH) fails. A long sequence of algorithms have been developed that try to obtain low dependencies on 1/epsilon, the better of which achieves a running time of 2^{~O(1/epsilon^{2})} + O(n*log(n)) [Jansen, SIAM J. Disc. Math. 2010]. In this paper we obtain an algorithm with a running time of 2^{~O(1/epsilon)} + O(n*log(n)), which is tight under ETH up to logarithmic factors on the exponent. Our main technical contribution is a new structural result on the configuration-IP. More precisely, we show the existence of a highly symmetric and sparse optimal solution, in which all but a constant number of machines are assigned a configuration with small support. This structure can then be exploited by integer programming techniques and enumeration. We believe that our structural result is of independent interest and should find applications to other settings. In particular, we show how the structure can be applied to the minimum makespan problem on related machines and to a larger class of objective functions on parallel machines. For all these cases we obtain an efficient PTAS with running time 2^{~O(1/epsilon)} + poly(n).
Cite as

Klaus Jansen, Kim-Manuel Klein, and José Verschae. Closing the Gap for Makespan Scheduling via Sparsification Techniques. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 72:1-72:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{jansen_et_al:LIPIcs.ICALP.2016.72,
  author =	{Jansen, Klaus and Klein, Kim-Manuel and Verschae, Jos\'{e}},
  title =	{{Closing the Gap for Makespan Scheduling via Sparsification Techniques}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{72:1--72:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.72},
  URN =		{urn:nbn:de:0030-drops-62122},
  doi =		{10.4230/LIPIcs.ICALP.2016.72},
  annote =	{Keywords: scheduling, approximation, PTAS, makespan, ETH}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.74
Min-Sum Scheduling Under Precedence Constraints

Authors: Andreas S. Schulz and José Verschae

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is that some jobs can only be processed after others. In this paper, we give the first approximation algorithms for min-sum scheduling with (nonnegative, non-decreasing) non-linear functions and general precedence constraints. In particular, for 1|prec|sum w_j f(C_j), we propose a polynomial-time universal algorithm that performs well for all functions f simultaneously. Its approximation guarantee is 2 for all concave functions, at worst. We also provide a (non-universal) polynomial-time algorithm for the more general case 1|prec|sum f_j(C_j). The performance guarantee is no worse than 2+epsilon for all concave functions. Our results match the best bounds known for the case of linear functions, a widely studied problem, and considerably extend the results for minimizing sum w_jf(C_j) without precedence constraints.
Cite as

Andreas S. Schulz and José Verschae. Min-Sum Scheduling Under Precedence Constraints. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 74:1-74:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{schulz_et_al:LIPIcs.ESA.2016.74,
  author =	{Schulz, Andreas S. and Verschae, Jos\'{e}},
  title =	{{Min-Sum Scheduling Under Precedence Constraints}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{74:1--74:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.74},
  URN =		{urn:nbn:de:0030-drops-64157},
  doi =		{10.4230/LIPIcs.ESA.2016.74},
  annote =	{Keywords: scheduling, approximation algorithms, linear programming relaxations, precedence constraints}
}
Document
DOI: 10.4230/DagSemProc.10071.13
Scheduling periodic tasks in a hard real-time environment

Authors: Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier, Martin Skutella, Jose Verschae, and Andreas Wiese

Published in: Dagstuhl Seminar Proceedings, Volume 10071, Scheduling (2010)

Abstract
We consider a real-time scheduling problem that occurs in the design of software-based aircraft control. The goal is to distribute tasks $ au_i=(c_i,p_i)$ on a minimum number of identical machines and to compute offsets $a_i$ for the tasks such that no collision occurs. A task $ au_i$ releases a job of running time $c_i$ at each time $a_i + kcdot p_i, , k in mathbb{N}_0$ and a collision occurs if two jobs are simultaneously active on the same machine. We shed some light on the complexity and approximability landscape of this problem. Although the problem cannot be approximated within a factor of $n^{1-varepsilon}$ for any $varepsilon>0$, an interesting restriction is much more tractable: If the periods are dividing (for each $i,j$ one has $p_i | p_j$ or $p_j | p_i$), the problem allows for a better structured representation of solutions, which leads to a 2-approximation. This result is tight, even asymptotically.
Cite as

Friedrich Eisenbrand, Nicolai Hähnle, Martin Niemeier, Martin Skutella, Jose Verschae, and Andreas Wiese. Scheduling periodic tasks in a hard real-time environment. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{eisenbrand_et_al:DagSemProc.10071.13,
  author =	{Eisenbrand, Friedrich and H\"{a}hnle, Nicolai and Niemeier, Martin and Skutella, Martin and Verschae, Jose and Wiese, Andreas},
  title =	{{Scheduling periodic tasks in a hard real-time environment}},
  booktitle =	{Scheduling},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10071},
  editor =	{Susanne Albers and Sanjoy K. Baruah and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.13},
  URN =		{urn:nbn:de:0030-drops-25348},
  doi =		{10.4230/DagSemProc.10071.13},
  annote =	{Keywords: Real-Time Scheduling, Periodic scheduling problem, Periodic maintenance problem, Approximation hardness, Approximation algorithm}
}
Document
DOI: 10.4230/DagSemProc.09261.4
A Robust PTAS for the Parallel Machine Covering Problem

Authors: Martin Skutella and Jose Verschae

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract
In general, combinatorial optimization problems are unstable: slight changes on the instance of a problem can render huge changes in the optimal solution. Thus, a natural question arises: Can we achieve stability if we only maintain approximate solutions?. In this talk I will first formalize these ideas, and then show some results on the parallel machine covering problem. In particular I will derive a robust PTAS, i.e., I will show how to construct a solution that is not only $(1-epsilon)$-approximate, but is also stable. That is, if the instance is changed by adding or removing a job, then we can construct a new near-optimal solution by only slightly modifying the previous one.
Cite as

Martin Skutella and Jose Verschae. A Robust PTAS for the Parallel Machine Covering Problem. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{skutella_et_al:DagSemProc.09261.4,
  author =	{Skutella, Martin and Verschae, Jose},
  title =	{{A Robust PTAS for the Parallel Machine Covering Problem}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.4},
  URN =		{urn:nbn:de:0030-drops-21609},
  doi =		{10.4230/DagSemProc.09261.4},
  annote =	{Keywords: Stability, approximation schemes, online algorithms}
}
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