10 Search Results for "Hoeksma, Ruben"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.8
Speed-Robust Scheduling Revisited

Authors: Josef Minařík and Jiří Sgall

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
Speed-robust scheduling is the following two-stage problem of scheduling n jobs on m uniformly related machines. In the first stage, the algorithm receives the value of m and the processing times of n jobs; it has to partition the jobs into b groups called bags. In the second stage, the machine speeds are revealed and the bags are assigned to the machines, i.e., the algorithm produces a schedule where all the jobs in the same bag are assigned to the same machine. The objective is to minimize the makespan (the length of the schedule). The algorithm is compared to the optimal schedule and it is called ρ-robust, if its makespan is always at most ρ times the optimal one. Our main result is an improved bound for equal-size jobs for b = m. We give an upper bound of 1.6. This improves previous bound of 1.8 and it is almost tight in the light of previous lower bound of 1.58. Second, for infinitesimally small jobs, we give tight upper and lower bounds for the case when b ≥ m. This generalizes and simplifies the previous bounds for b = m. Finally, we introduce a new special case with relatively small jobs for which we give an algorithm whose robustness is close to that of infinitesimal jobs and thus gives better than 2-robust for a large class of inputs.
Cite as

Josef Minařík and Jiří Sgall. Speed-Robust Scheduling Revisited. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 8:1-8:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{minarik_et_al:LIPIcs.APPROX/RANDOM.2024.8,
  author =	{Mina\v{r}{\'\i}k, Josef and Sgall, Ji\v{r}{\'\i}},
  title =	{{Speed-Robust Scheduling Revisited}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{8:1--8:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.8},
  URN =		{urn:nbn:de:0030-drops-210010},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.8},
  annote =	{Keywords: scheduling, approximation algorithms, makespan, uniform speeds}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.14
Scheduling on a Stochastic Number of Machines

Authors: Moritz Buchem, Franziska Eberle, Hugo Kooki Kasuya Rosado, Kevin Schewior, and Andreas Wiese

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract
We consider a new scheduling problem on parallel identical machines in which the number of machines is initially not known, but it follows a given probability distribution. Only after all jobs are assigned to a given number of bags, the actual number of machines is revealed. Subsequently, the jobs need to be assigned to the machines without splitting the bags. This is the stochastic version of a related problem introduced by Stein and Zhong [SODA 2018, TALG 2020] and it is, for example, motivated by bundling jobs that need to be scheduled by data centers. We present two PTASs for the stochastic setting, computing job-to-bag assignments that (i) minimize the expected maximum machine load and (ii) maximize the expected minimum machine load (like in the Santa Claus problem), respectively. The former result follows by careful enumeration combined with known PTASs. For the latter result, we introduce an intricate dynamic program that we apply to a suitably rounded instance.
Cite as

Moritz Buchem, Franziska Eberle, Hugo Kooki Kasuya Rosado, Kevin Schewior, and Andreas Wiese. Scheduling on a Stochastic Number of Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 14:1-14:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{buchem_et_al:LIPIcs.APPROX/RANDOM.2024.14,
  author =	{Buchem, Moritz and Eberle, Franziska and Kasuya Rosado, Hugo Kooki and Schewior, Kevin and Wiese, Andreas},
  title =	{{Scheduling on a Stochastic Number of Machines}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.14},
  URN =		{urn:nbn:de:0030-drops-210073},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.14},
  annote =	{Keywords: scheduling, approximation algorithms, stochastic machines, makespan, max-min fair allocation, dynamic programming}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.4
Tighter Worst-Case Response Time Bounds for Jitter-Based Self-Suspension Analysis

Authors: Mario Günzel, Georg von der Brüggen, and Jian-Jia Chen

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
Tasks are called self-suspending if they can yield their ready state (specifically, releasing the processor while having highest priority) despite being incomplete, for instance, to offload computation to an external device or when waiting on access rights for shared resources or data. This self-suspending behavior requires special treatment when applying analytical results to compute worst-case response time bounds. One typical treatment is modeling self-suspension as release jitter in a so-called jitter-based analysis. The state of the art, when considering task-level fixed-priority scheduling, individually quantifies the jitter term of each higher-priority task by its worst-case response time minus its worst-case execution time. This work tightens the jitter term by taking the execution behavior of the other higher-priority tasks into account. Our improved jitter-based analysis analytically dominates the previous jitter-based analysis. Moreover, an evaluation for synthetically generated sporadic tasks demonstrates that this jitter term results in tighter worst-case response time bounds for self-suspending tasks. We observe an improvement for up to 55.89 % of the tasksets compared to the previous jitter-based analysis.
Cite as

Mario Günzel, Georg von der Brüggen, and Jian-Jia Chen. Tighter Worst-Case Response Time Bounds for Jitter-Based Self-Suspension Analysis. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 4:1-4:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{gunzel_et_al:LIPIcs.ECRTS.2024.4,
  author =	{G\"{u}nzel, Mario and von der Br\"{u}ggen, Georg and Chen, Jian-Jia},
  title =	{{Tighter Worst-Case Response Time Bounds for Jitter-Based Self-Suspension Analysis}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{4:1--4:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.4},
  URN =		{urn:nbn:de:0030-drops-203074},
  doi =		{10.4230/LIPIcs.ECRTS.2024.4},
  annote =	{Keywords: Worst-Case Response Time, WCRT, Jitter, Self-Suspension, Analysis}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.81
Oracle-Augmented Prophet Inequalities

Authors: Sariel Har-Peled, Elfarouk Harb, and Vasilis Livanos

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In the classical prophet inequality setting, a gambler is given a sequence of n random variables X₁, … , X_n, taken from known distributions, observes their values in adversarial order and selects one of them, immediately after it is being observed, aiming to select a value that is as high as possible. The classical prophet inequality shows a strategy that guarantees a value at least half of the value of an omniscience prophet that always picks the maximum, and this ratio is optimal. Here, we generalize the prophet inequality, allowing the gambler some additional information about the future that is otherwise privy only to the prophet. Specifically, at any point in the process, the gambler is allowed to query an oracle 𝒪. The oracle responds with a single bit answer: YES if the current realization is greater than the remaining realizations, and NO otherwise. We show that the oracle model with m oracle calls is equivalent to the Top-1-of-(m+1) model when the objective is maximizing the probability of selecting the maximum. This equivalence fails to hold when the objective is maximizing the competitive ratio, but we still show that any algorithm for the oracle model implies an equivalent competitive ratio for the Top-1-of-(m+1) model. We resolve the oracle model for any m, giving tight lower and upper bound on the best possible competitive ratio compared to an almighty adversary. As a consequence, we provide new results as well as improvements on known results for the Top-1-of-m model.
Cite as

Sariel Har-Peled, Elfarouk Harb, and Vasilis Livanos. Oracle-Augmented Prophet Inequalities. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 81:1-81:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{harpeled_et_al:LIPIcs.ICALP.2024.81,
  author =	{Har-Peled, Sariel and Harb, Elfarouk and Livanos, Vasilis},
  title =	{{Oracle-Augmented Prophet Inequalities}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{81:1--81:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.81},
  URN =		{urn:nbn:de:0030-drops-202245},
  doi =		{10.4230/LIPIcs.ICALP.2024.81},
  annote =	{Keywords: prophet inequalities, predictions, top-1-of-k model}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.18
Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics

Authors: Martin Böhm, Ruben Hoeksma, Nicole Megow, Lukas Nölke, and Bertrand Simon

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

Abstract
We consider the problem of computing a Steiner tree of minimum cost under a k-hop constraint which requires the depth of the tree to be at most k. Our main result is an exact algorithm for metrics induced by graphs of bounded treewidth that runs in time n^O(k). For the special case of a path, we give a simple algorithm that solves the problem in polynomial time, even if k is part of the input. The main result can be used to obtain, in quasi-polynomial time, a near-optimal solution that violates the k-hop constraint by at most one hop for more general metrics induced by graphs of bounded highway dimension and bounded doubling dimension.
Cite as

Martin Böhm, Ruben Hoeksma, Nicole Megow, Lukas Nölke, and Bertrand Simon. Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 18:1-18:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{bohm_et_al:LIPIcs.MFCS.2020.18,
  author =	{B\"{o}hm, Martin and Hoeksma, Ruben and Megow, Nicole and N\"{o}lke, Lukas and Simon, Bertrand},
  title =	{{Computing a Minimum-Cost k-Hop Steiner Tree in Tree-Like Metrics}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{18:1--18:15},
  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.2020.18},
  URN =		{urn:nbn:de:0030-drops-126870},
  doi =		{10.4230/LIPIcs.MFCS.2020.18},
  annote =	{Keywords: k-hop Steiner tree, dynamic programming, bounded treewidth}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.8
On the Complexity of Anchored Rectangle Packing

Authors: Antonios Antoniadis, Felix Biermeier, Andrés Cristi, Christoph Damerius, Ruben Hoeksma, Dominik Kaaser, Peter Kling, and Lukas Nölke

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

Abstract
In the Anchored Rectangle Packing (ARP) problem, we are given a set of points P in the unit square [0,1]^2 and seek a maximum-area set of axis-aligned interior-disjoint rectangles S, each of which is anchored at a point p in P. In the most prominent variant - Lower-Left-Anchored Rectangle Packing (LLARP) - rectangles are anchored in their lower-left corner. Freedman [W. T. Tutte (Ed.), 1969] conjectured in 1969 that, if (0,0) in P, then there is a LLARP that covers an area of at least 0.5. Somewhat surprisingly, this conjecture remains open to this day, with the best known result covering an area of 0.091 [Dumitrescu and Tóth, 2015]. Maybe even more surprisingly, it is not known whether LLARP - or any ARP-problem with only one anchor - is NP-hard. In this work, we first study the Center-Anchored Rectangle Packing (CARP) problem, where rectangles are anchored in their center. We prove NP-hardness and provide a PTAS. In fact, our PTAS applies to any ARP problem where the anchor lies in the interior of the rectangles. Afterwards, we turn to the LLARP problem and investigate two different resource-augmentation settings: In the first we allow an epsilon-perturbation of the input P, whereas in the second we permit an epsilon-overlap between rectangles. For the former setting, we give an algorithm that covers at least as much area as an optimal solution of the original problem. For the latter, we give an (1 - epsilon)-approximation.
Cite as

Antonios Antoniadis, Felix Biermeier, Andrés Cristi, Christoph Damerius, Ruben Hoeksma, Dominik Kaaser, Peter Kling, and Lukas Nölke. On the Complexity of Anchored Rectangle Packing. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{antoniadis_et_al:LIPIcs.ESA.2019.8,
  author =	{Antoniadis, Antonios and Biermeier, Felix and Cristi, Andr\'{e}s and Damerius, Christoph and Hoeksma, Ruben and Kaaser, Dominik and Kling, Peter and N\"{o}lke, Lukas},
  title =	{{On the Complexity of Anchored Rectangle Packing}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{8:1--8:14},
  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.2019.8},
  URN =		{urn:nbn:de:0030-drops-111297},
  doi =		{10.4230/LIPIcs.ESA.2019.8},
  annote =	{Keywords: anchored rectangle, rectangle packing, resource augmentation, PTAS, NP, hardness}
}
Document
Artifact
DOI: 10.4230/DARTS.5.1.6
Scheduling Self-Suspending Tasks: New and Old Results (Artifact)

Authors: Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen

Published in: DARTS, Volume 5, Issue 1, Special Issue of the 31st Euromicro Conference on Real-Time Systems (ECRTS 2019)

Abstract
In computing systems, a job may suspend itself (before it finishes its execution) when it has to wait for certain results from other (usually external) activities. For real-time systems, such self-suspension behavior has been shown to induce performance degradation. Hence, the researchers in the real-time systems community have devoted themselves to the design and analysis of scheduling algorithms that can alleviate the performance penalty due to self-suspension behavior. As self-suspension and delegation of parts of a job to non-bottleneck resources is pretty natural in many applications, researchers in the operations research (OR) community have also explored scheduling algorithms for systems with such suspension behavior, called the master-slave problem in the OR community. This paper first reviews the results for the master-slave problem in the OR literature and explains their impact on several long-standing problems for scheduling self-suspending real-time tasks. For frame-based periodic real-time tasks, in which the periods of all tasks are identical and all jobs related to one frame are released synchronously, we explore different approximation metrics with respect to resource augmentation factors under different scenarios for both uniprocessor and multiprocessor systems, and demonstrate that different approximation metrics can create different levels of difficulty for the approximation. Our experimental results show that such more carefully designed schedules can significantly outperform the state-of-the-art.
Cite as

Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen. Scheduling Self-Suspending Tasks: New and Old Results (Artifact). In Special Issue of the 31st Euromicro Conference on Real-Time Systems (ECRTS 2019). Dagstuhl Artifacts Series (DARTS), Volume 5, Issue 1, pp. 6:1-6:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@Article{chen_et_al:DARTS.5.1.6,
  author =	{Chen, Jian-Jia and Hahn, Tobias and Hoeksma, Ruben and Megow, Nicole and von der Br\"{u}ggen, Georg},
  title =	{{Scheduling Self-Suspending Tasks: New and Old Results}},
  pages =	{6:1--6:3},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2019},
  volume =	{5},
  number =	{1},
  editor =	{Chen, Jian-Jia and Hahn, Tobias and Hoeksma, Ruben and Megow, Nicole and von der Br\"{u}ggen, Georg},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DARTS.5.1.6},
  URN =		{urn:nbn:de:0030-drops-107349},
  doi =		{10.4230/DARTS.5.1.6},
  annote =	{Keywords: Self-suspension, master-slave problem, computational complexity, speedup factors}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2019.16
Scheduling Self-Suspending Tasks: New and Old Results

Authors: Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen

Published in: LIPIcs, Volume 133, 31st Euromicro Conference on Real-Time Systems (ECRTS 2019)

Abstract
In computing systems, a job may suspend itself (before it finishes its execution) when it has to wait for certain results from other (usually external) activities. For real-time systems, such self-suspension behavior has been shown to induce performance degradation. Hence, the researchers in the real-time systems community have devoted themselves to the design and analysis of scheduling algorithms that can alleviate the performance penalty due to self-suspension behavior. As self-suspension and delegation of parts of a job to non-bottleneck resources is pretty natural in many applications, researchers in the operations research (OR) community have also explored scheduling algorithms for systems with such suspension behavior, called the master-slave problem in the OR community. This paper first reviews the results for the master-slave problem in the OR literature and explains their impact on several long-standing problems for scheduling self-suspending real-time tasks. For frame-based periodic real-time tasks, in which the periods of all tasks are identical and all jobs related to one frame are released synchronously, we explore different approximation metrics with respect to resource augmentation factors under different scenarios for both uniprocessor and multiprocessor systems, and demonstrate that different approximation metrics can create different levels of difficulty for the approximation. Our experimental results show that such more carefully designed schedules can significantly outperform the state-of-the-art.
Cite as

Jian-Jia Chen, Tobias Hahn, Ruben Hoeksma, Nicole Megow, and Georg von der Brüggen. Scheduling Self-Suspending Tasks: New and Old Results. In 31st Euromicro Conference on Real-Time Systems (ECRTS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 133, pp. 16:1-16:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{chen_et_al:LIPIcs.ECRTS.2019.16,
  author =	{Chen, Jian-Jia and Hahn, Tobias and Hoeksma, Ruben and Megow, Nicole and von der Br\"{u}ggen, Georg},
  title =	{{Scheduling Self-Suspending Tasks: New and Old Results}},
  booktitle =	{31st Euromicro Conference on Real-Time Systems (ECRTS 2019)},
  pages =	{16:1--16:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-110-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{133},
  editor =	{Quinton, Sophie},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2019.16},
  URN =		{urn:nbn:de:0030-drops-107532},
  doi =		{10.4230/LIPIcs.ECRTS.2019.16},
  annote =	{Keywords: Self-suspension, master-slave problem, computational complexity, speedup factors}
}
Document
DOI: 10.4230/LIPIcs.FUN.2018.12
SUPERSET: A (Super)Natural Variant of the Card Game SET

Authors: Fábio Botler, Andrés Cristi, Ruben Hoeksma, Kevin Schewior, and Andreas Tönnis

Published in: LIPIcs, Volume 100, 9th International Conference on Fun with Algorithms (FUN 2018)

Abstract
We consider Superset, a lesser-known yet interesting variant of the famous card game Set. Here, players look for Supersets instead of Sets, that is, the symmetric difference of two Sets that intersect in exactly one card. In this paper, we pose questions that have been previously posed for Set and provide answers to them; we also show relations between Set and Superset. For the regular Set deck, which can be identified with F^3_4, we give a proof for the fact that the maximum number of cards that can be on the table without having a Superset is 9. This solves an open question posed by McMahon et al. in 2016. For the deck corresponding to F^3_d, we show that this number is Omega(1.442^d) and O(1.733^d). We also compute probabilities of the presence of a superset in a collection of cards drawn uniformly at random. Finally, we consider the computational complexity of deciding whether a multi-value version of Set or Superset is contained in a given set of cards, and show an FPT-reduction from the problem for Set to that for Superset, implying W[1]-hardness of the problem for Superset.
Cite as

Fábio Botler, Andrés Cristi, Ruben Hoeksma, Kevin Schewior, and Andreas Tönnis. SUPERSET: A (Super)Natural Variant of the Card Game SET. In 9th International Conference on Fun with Algorithms (FUN 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 100, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{botler_et_al:LIPIcs.FUN.2018.12,
  author =	{Botler, F\'{a}bio and Cristi, Andr\'{e}s and Hoeksma, Ruben and Schewior, Kevin and T\"{o}nnis, Andreas},
  title =	{{SUPERSET: A (Super)Natural Variant of the Card Game SET}},
  booktitle =	{9th International Conference on Fun with Algorithms (FUN 2018)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-067-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{100},
  editor =	{Ito, Hiro and Leonardi, Stefano and Pagli, Linda and Prencipe, Giuseppe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2018.12},
  URN =		{urn:nbn:de:0030-drops-88035},
  doi =		{10.4230/LIPIcs.FUN.2018.12},
  annote =	{Keywords: SET, SUPERSET, card game, cap set, affine geometry, computational complexity}
}
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)

Copy BibTex To Clipboard

@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}
}
  • Refine by Author
  • 6 Hoeksma, Ruben
  • 3 Chen, Jian-Jia
  • 3 Megow, Nicole
  • 3 von der Brüggen, Georg
  • 2 Antoniadis, Antonios
  • Show More...

  • Refine by Classification
  • 3 Computer systems organization → Real-time systems
  • 2 Theory of computation → Scheduling algorithms
  • 1 Computer systems organization → Embedded systems
  • 1 Mathematics of computing → Combinatorial optimization
  • 1 Mathematics of computing → Combinatoric problems
  • Show More...

  • Refine by Keyword
  • 3 computational complexity
  • 2 Self-suspension
  • 2 approximation algorithms
  • 2 dynamic programming
  • 2 makespan
  • Show More...

  • Refine by Type
  • 10 document

  • Refine by Publication Year
  • 4 2024
  • 3 2019
  • 1 2017
  • 1 2018
  • 1 2020

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact