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Documents authored by Pruhs, Kirk

Document
DOI: 10.4230/LIPIcs.ICDT.2024.11
On the Convergence Rate of Linear Datalog ^∘ over Stable Semirings

Authors: Sungjin Im, Benjamin Moseley, Hung Ngo, and Kirk Pruhs

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

Abstract
Datalog^∘ is an extension of Datalog, where instead of a program being a collection of union of conjunctive queries over the standard Boolean semiring, a program may now be a collection of sum-product queries over an arbitrary commutative partially ordered pre-semiring. Datalog^∘ is more powerful than Datalog in that its additional algebraic structure alows for supporting recursion with aggregation. At the same time, Datalog^∘ retains the syntactic and semantic simplicity of Datalog: Datalog^∘ has declarative least fixpoint semantics. The least fixpoint can be found via the naïve evaluation algorithm that repeatedly applies the immediate consequence operator until no further change is possible. It was shown in [Mahmoud Abo Khamis et al., 2022] that, when the underlying semiring is p-stable, then the naïve evaluation of any Datalog^∘ program over the semiring converges in a finite number of steps. However, the upper bounds on the rate of convergence were exponential in the number n of ground IDB atoms. This paper establishes polynomial upper bounds on the convergence rate of the naïve algorithm on linear Datalog^∘ programs, which is quite common in practice. In particular, the main result of this paper is that the convergence rate of linear Datalog^∘ programs under any p-stable semiring is O(pn³). Furthermore, we show a matching lower bound by constructing a p-stable semiring and a linear Datalog^∘ program that requires Ω(pn³) iterations for the naïve iteration algorithm to converge. Next, we study the convergence rate in terms of the number of elements in the semiring for linear Datalog^∘ programs. When L is the number of elements, the convergence rate is bounded by O(pn log L). This significantly improves the convergence rate for small L. We show a nearly matching lower bound as well.
Cite as

Sungjin Im, Benjamin Moseley, Hung Ngo, and Kirk Pruhs. On the Convergence Rate of Linear Datalog ^∘ over Stable Semirings. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 11:1-11:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{im_et_al:LIPIcs.ICDT.2024.11,
  author =	{Im, Sungjin and Moseley, Benjamin and Ngo, Hung and Pruhs, Kirk},
  title =	{{On the Convergence Rate of Linear Datalog ^∘ over Stable Semirings}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{11:1--11:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.11},
  URN =		{urn:nbn:de:0030-drops-197939},
  doi =		{10.4230/LIPIcs.ICDT.2024.11},
  annote =	{Keywords: Datalog, convergence rate, semiring}
}
Document
DOI: 10.4230/LIPIcs.ESA.2021.62
An Efficient Reduction of a Gammoid to a Partition Matroid

Authors: Marilena Leichter, Benjamin Moseley, and Kirk Pruhs

Published in: LIPIcs, Volume 204, 29th Annual European Symposium on Algorithms (ESA 2021)

Abstract
Our main contribution is a polynomial-time algorithm to reduce a k-colorable gammoid to a (2k-2)-colorable partition matroid. It is known that there are gammoids that can not be reduced to any (2k-3)-colorable partition matroid, so this result is tight. We then discuss how such a reduction can be used to obtain polynomial-time algorithms with better approximation ratios for various natural problems related to coloring and list coloring the intersection of matroids.
Cite as

Marilena Leichter, Benjamin Moseley, and Kirk Pruhs. An Efficient Reduction of a Gammoid to a Partition Matroid. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 62:1-62:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{leichter_et_al:LIPIcs.ESA.2021.62,
  author =	{Leichter, Marilena and Moseley, Benjamin and Pruhs, Kirk},
  title =	{{An Efficient Reduction of a Gammoid to a Partition Matroid}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{62:1--62:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2021.62},
  URN =		{urn:nbn:de:0030-drops-146432},
  doi =		{10.4230/LIPIcs.ESA.2021.62},
  annote =	{Keywords: Matroid, Gammoid, Reduction, Algorithms}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.6
An Approximation Algorithm for the Matrix Tree Multiplication Problem

Authors: Mahmoud Abo-Khamis, Ryan Curtin, Sungjin Im, Benjamin Moseley, Hung Ngo, Kirk Pruhs, and Alireza Samadian

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We consider the Matrix Tree Multiplication problem. This problem is a generalization of the classic Matrix Chain Multiplication problem covered in the dynamic programming chapter of many introductory algorithms textbooks. An instance of the Matrix Tree Multiplication problem consists of a rooted tree with a matrix associated with each edge. The output is, for each leaf in the tree, the product of the matrices on the chain/path from the root to that leaf. Matrix multiplications that are shared between various chains need only be computed once, potentially being shared between different root to leaf chains. Algorithms are evaluated by the number of scalar multiplications performed. Our main result is a linear time algorithm for which the number of scalar multiplications performed is at most 15 times the optimal number of scalar multiplications.
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Mahmoud Abo-Khamis, Ryan Curtin, Sungjin Im, Benjamin Moseley, Hung Ngo, Kirk Pruhs, and Alireza Samadian. An Approximation Algorithm for the Matrix Tree Multiplication Problem. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abokhamis_et_al:LIPIcs.MFCS.2021.6,
  author =	{Abo-Khamis, Mahmoud and Curtin, Ryan and Im, Sungjin and Moseley, Benjamin and Ngo, Hung and Pruhs, Kirk and Samadian, Alireza},
  title =	{{An Approximation Algorithm for the Matrix Tree Multiplication Problem}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.6},
  URN =		{urn:nbn:de:0030-drops-144464},
  doi =		{10.4230/LIPIcs.MFCS.2021.6},
  annote =	{Keywords: Matrix Multiplication, Approximation Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.97
Relational Algorithms for k-Means Clustering

Authors: Benjamin Moseley, Kirk Pruhs, Alireza Samadian, and Yuyan Wang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows represent the data points. The running time is potentially exponentially smaller than N, the number of data points to be clustered that the relational database represents. Few relational algorithms are known and this paper offers techniques for designing relational algorithms as well as characterizing their limitations. We show that given two data points as cluster centers, if we cluster points according to their closest centers, it is NP-Hard to approximate the number of points in the clusters on a general relational input. This is trivial for conventional data inputs and this result exemplifies that standard algorithmic techniques may not be directly applied when designing an efficient relational algorithm. This paper then introduces a new method that leverages rejection sampling and the k-means++ algorithm to construct a O(1)-approximate k-means solution.
Cite as

Benjamin Moseley, Kirk Pruhs, Alireza Samadian, and Yuyan Wang. Relational Algorithms for k-Means Clustering. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 97:1-97:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{moseley_et_al:LIPIcs.ICALP.2021.97,
  author =	{Moseley, Benjamin and Pruhs, Kirk and Samadian, Alireza and Wang, Yuyan},
  title =	{{Relational Algorithms for k-Means Clustering}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{97:1--97:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.97},
  URN =		{urn:nbn:de:0030-drops-141668},
  doi =		{10.4230/LIPIcs.ICALP.2021.97},
  annote =	{Keywords: k-means, clustering, approximation, big-data, databases}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.145
Matroid Coflow Scheduling

Authors: Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Manish Purohit

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

Abstract
We consider the matroid coflow scheduling problem, where each job is comprised of a set of flows and the family of sets that can be scheduled at any time form a matroid. Our main result is a polynomial-time algorithm that yields a 2-approximation for the objective of minimizing the weighted completion time. This result is tight assuming P != NP. As a by-product we also obtain the first (2+epsilon)-approximation algorithm for the preemptive concurrent open shop scheduling problem.
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Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Manish Purohit. Matroid Coflow Scheduling. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 145:1-145:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{im_et_al:LIPIcs.ICALP.2019.145,
  author =	{Im, Sungjin and Moseley, Benjamin and Pruhs, Kirk and Purohit, Manish},
  title =	{{Matroid Coflow Scheduling}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{145:1--145:13},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.145},
  URN =		{urn:nbn:de:0030-drops-107213},
  doi =		{10.4230/LIPIcs.ICALP.2019.145},
  annote =	{Keywords: Coflow Scheduling, Concurrent Open Shop, Matroid Scheduling}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.ESA.2017
LIPIcs, Volume 87, ESA'17, Complete Volume

Authors: Kirk Pruhs and Christian Sohler

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
LIPIcs, Volume 87, ESA'17, Complete Volume
Cite as

25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{pruhs_et_al:LIPIcs.ESA.2017,
  title =	{{LIPIcs, Volume 87, ESA'17, Complete Volume}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017},
  URN =		{urn:nbn:de:0030-drops-79096},
  doi =		{10.4230/LIPIcs.ESA.2017},
  annote =	{Keywords: Data Structures, Nonnumerical Algorithms and Problems, Optimization, Discrete Mathematics, Mathematical Software, AlgorithmsProblem Solving, Control Methods, and Search, Computational Geometry and Object Modeling}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.ESA.2017.0
Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers

Authors: Kirk Pruhs and Christian Sohler

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers
Cite as

25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{pruhs_et_al:LIPIcs.ESA.2017.0,
  author =	{Pruhs, Kirk and Sohler, Christian},
  title =	{{Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{0:i--0:xx},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.0},
  URN =		{urn:nbn:de:0030-drops-78147},
  doi =		{10.4230/LIPIcs.ESA.2017.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}
}
Document
DOI: 10.4230/LIPIcs.ESA.2017.51
Minimizing Maximum Flow Time on Related Machines via Dynamic Posted Pricing

Authors: Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Clifford Stein

Published in: LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Abstract
We consider a setting where selfish agents want to schedule jobs on related machines. The agent submitting a job picks a server that minimizes a linear combination of the server price and the resulting response time for that job on the selected server. The manager's task is to maintain server prices to (approximately) optimize the maximum response time, which is a measure of social good. We show that the existence of a pricing scheme with certain competitiveness is equivalent to the existence of a monotone immediate-dispatch algorithm. Our main result is a monotone immediate-dispatch algorithm that is O(1)-competitive with respect to the maximum response time.
Cite as

Sungjin Im, Benjamin Moseley, Kirk Pruhs, and Clifford Stein. Minimizing Maximum Flow Time on Related Machines via Dynamic Posted Pricing. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 51:1-51:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{im_et_al:LIPIcs.ESA.2017.51,
  author =	{Im, Sungjin and Moseley, Benjamin and Pruhs, Kirk and Stein, Clifford},
  title =	{{Minimizing Maximum Flow Time on Related Machines via  Dynamic Posted Pricing}},
  booktitle =	{25th Annual European Symposium on Algorithms (ESA 2017)},
  pages =	{51:1--51:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-049-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{87},
  editor =	{Pruhs, Kirk and Sohler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.51},
  URN =		{urn:nbn:de:0030-drops-78287},
  doi =		{10.4230/LIPIcs.ESA.2017.51},
  annote =	{Keywords: Posted pricing scheme, online scheduling, related machines, maximum flow time, competitiveness analysis}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.96
A 2-Competitive Algorithm For Online Convex Optimization With Switching Costs

Authors: Nikhil Bansal, Anupam Gupta, Ravishankar Krishnaswamy, Kirk Pruhs, Kevin Schewior, and Cliff Stein

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

Abstract
We consider a natural online optimization problem set on the real line. The state of the online algorithm at each integer time is a location on the real line. At each integer time, a convex function arrives online. In response, the online algorithm picks a new location. The cost paid by the online algorithm for this response is the distance moved plus the value of the function at the final destination. The objective is then to minimize the aggregate cost over all time. The motivating application is rightsizing power-proportional data centers. We give a 2-competitive algorithm for this problem. We also give a 3-competitive memoryless algorithm, and show that this is the best competitive ratio achievable by a deterministic memoryless algorithm. Finally we show that this online problem is strictly harder than the standard ski rental problem.
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Nikhil Bansal, Anupam Gupta, Ravishankar Krishnaswamy, Kirk Pruhs, Kevin Schewior, and Cliff Stein. A 2-Competitive Algorithm For Online Convex Optimization With Switching Costs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 96-109, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{bansal_et_al:LIPIcs.APPROX-RANDOM.2015.96,
  author =	{Bansal, Nikhil and Gupta, Anupam and Krishnaswamy, Ravishankar and Pruhs, Kirk and Schewior, Kevin and Stein, Cliff},
  title =	{{A 2-Competitive Algorithm For Online Convex Optimization With Switching Costs}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{96--109},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.96},
  URN =		{urn:nbn:de:0030-drops-52970},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.96},
  annote =	{Keywords: Stochastic, Scheduling}
}
Document
DOI: 10.4230/LIPIcs.STACS.2015.474
Stochastic Scheduling of Heavy-tailed Jobs

Authors: Sungjin Im, Benjamin Moseley, and Kirk Pruhs

Published in: LIPIcs, Volume 30, 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)

Abstract
We revisit the classical stochastic scheduling problem of nonpreemptively scheduling n jobs so as to minimize total completion time on m identical machines, P \mid \mid \mathbb{E} \sum C_j in the standard 3-field scheduling notation. Previously it was only known how to obtain reasonable approximation if jobs sizes have low variability. However, distributions commonly arising in practice have high variability, and the upper bounds on the approximation ratio for the previous algorithms for such distributions can be even inverse-polynomial in the maximum possible job size. We start by showing that the natural list scheduling algorithm Shortest Expected Processing Time (SEPT) has a bad approximation ratio for high variability jobs. We observe that a simple randomized rounding of a natural linear programming relaxation is a (1+\epsilon)-machine O(1)-approximation assuming the number of machines is at least logarithmic in the number of jobs. Turning to the case of a modest number of machines, we develop a list scheduling algorithm that is O(\log^2 n + m \log n)-approximate. Our results together imply a (1+\epsilon)-machine O(\log^2 n )-approximation for an arbitrary number of machines. Intuitively our list scheduling algorithm finds an ordering that not only takes the expected size of a job into account, but also takes into account the probability that job will be big.
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Sungjin Im, Benjamin Moseley, and Kirk Pruhs. Stochastic Scheduling of Heavy-tailed Jobs. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 474-486, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{im_et_al:LIPIcs.STACS.2015.474,
  author =	{Im, Sungjin and Moseley, Benjamin and Pruhs, Kirk},
  title =	{{Stochastic Scheduling of Heavy-tailed Jobs}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{474--486},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-78-1},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{30},
  editor =	{Mayr, Ernst W. and Ollinger, Nicolas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.474},
  URN =		{urn:nbn:de:0030-drops-49359},
  doi =		{10.4230/LIPIcs.STACS.2015.474},
  annote =	{Keywords: stochastic scheduling, completion time, approximation}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.63
Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-off Schedules

Authors: Antonios Antoniadis, Neal Barcelo, Mario Consuegra, Peter Kling, Michael Nugent, Kirk Pruhs, and Michele Scquizzato

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract
We give a polynomial time algorithm to compute an optimal energy and fractional weighted flow trade-off schedule for a speed-scalable processor with discrete speeds. Our algorithm uses a geometric approach that is based on structural properties obtained from a primal-dual formulation of the problem.
Cite as

Antonios Antoniadis, Neal Barcelo, Mario Consuegra, Peter Kling, Michael Nugent, Kirk Pruhs, and Michele Scquizzato. Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-off Schedules. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 63-74, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{antoniadis_et_al:LIPIcs.STACS.2014.63,
  author =	{Antoniadis, Antonios and Barcelo, Neal and Consuegra, Mario and Kling, Peter and Nugent, Michael and Pruhs, Kirk and Scquizzato, Michele},
  title =	{{Efficient Computation of Optimal Energy and Fractional Weighted Flow Trade-off Schedules}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{63--74},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.63},
  URN =		{urn:nbn:de:0030-drops-44474},
  doi =		{10.4230/LIPIcs.STACS.2014.63},
  annote =	{Keywords: scheduling, flow time, energy efficiency, speed scaling, primal-dual}
}
Document
DOI: 10.4230/DagRep.3.3.24
Scheduling (Dagstuhl Seminar 13111)

Authors: Susanne Albers, Onno J. Boxma, and Kirk Pruhs

Published in: Dagstuhl Reports, Volume 3, Issue 3 (2013)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 13111 "Scheduling". The primary objective of the seminar is to facilitate dialog and collaboration between researchers in two different mathematically-oriented scheduling research communities, the stochastic scheduling and queuing community, and the worst-case approximation scheduling community.
Cite as

Susanne Albers, Onno J. Boxma, and Kirk Pruhs. Scheduling (Dagstuhl Seminar 13111). In Dagstuhl Reports, Volume 3, Issue 3, pp. 24-50, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@Article{albers_et_al:DagRep.3.3.24,
  author =	{Albers, Susanne and Boxma, Onno J. and Pruhs, Kirk},
  title =	{{Scheduling (Dagstuhl Seminar 13111)}},
  pages =	{24--50},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2013},
  volume =	{3},
  number =	{3},
  editor =	{Albers, Susanne and Boxma, Onno J. and Pruhs, Kirk},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.3.3.24},
  URN =		{urn:nbn:de:0030-drops-40244},
  doi =		{10.4230/DagRep.3.3.24},
  annote =	{Keywords: Scheduling, Algorithms, Stochastic, Optimization, Queuing}
}
Document
DOI: 10.4230/DagSemProc.10261.3
An Experimental Comparison of Speed Scaling Algorithms with Deadline Feasibility Constraints

Authors: Ahmed Abousamra, David P. Bunde, and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 10261, Algorithm Engineering (2010)

Abstract
We consider the first, and most well studied, speed scaling problem in the algorithmic literature: where the scheduling quality of service measure is a deadline feasibility constraint, and where the power objective is to minimize the total energy used. Four online algorithms for this problem have been proposed in the algorithmic literature. Based on the best upper bound that can be proved on the competitive ratio, the ranking of the online algorithms from best to worst is: $qOA$, $OA$, $AVR$, $BKP$. As a test case on the effectiveness of competitive analysis to predict the best online algorithm, we report on an experimental ``horse race'' between these algorithms using instances based on web server traces. Our main conclusion is that the ranking of our algorithms based on their performance in our experiments is identical to the order predicted by competitive analysis. This ranking holds over a large range of possible power functions, and even if the power objective is temperature.
Cite as

Ahmed Abousamra, David P. Bunde, and Kirk Pruhs. An Experimental Comparison of Speed Scaling Algorithms with Deadline Feasibility Constraints. In Algorithm Engineering. Dagstuhl Seminar Proceedings, Volume 10261, pp. 1-22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{abousamra_et_al:DagSemProc.10261.3,
  author =	{Abousamra, Ahmed and Bunde, David P. and Pruhs, Kirk},
  title =	{{An Experimental Comparison of Speed Scaling Algorithms with Deadline Feasibility Constraints}},
  booktitle =	{Algorithm Engineering},
  pages =	{1--22},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10261},
  editor =	{Giuseppe F. Italiano and David S. Johnson and Petra Mutzel and Peter Sanders},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10261.3},
  URN =		{urn:nbn:de:0030-drops-27971},
  doi =		{10.4230/DagSemProc.10261.3},
  annote =	{Keywords: Scheduling, Speed Scaling, Experimental Algorithms, Power Management}
}
Document
DOI: 10.4230/DagSemProc.10071.1
10071 Abstracts Collection – Scheduling

Authors: Susanne Albers, Sanjoy K. Baruah, Rolf H. Möhring, and Kirk Pruhs

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

Abstract
From 14.02. to 19.02.2010, the Dagstuhl Seminar 10071 ``Scheduling '' was held in Schloss Dagstuhl-Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Susanne Albers, Sanjoy K. Baruah, Rolf H. Möhring, and Kirk Pruhs. 10071 Abstracts Collection – Scheduling. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{albers_et_al:DagSemProc.10071.1,
  author =	{Albers, Susanne and Baruah, Sanjoy K. and M\"{o}hring, Rolf  H. and Pruhs, Kirk},
  title =	{{10071 Abstracts Collection – Scheduling}},
  booktitle =	{Scheduling},
  pages =	{1--12},
  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-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.1},
  URN =		{urn:nbn:de:0030-drops-25479},
  doi =		{10.4230/DagSemProc.10071.1},
  annote =	{Keywords: Scheduling, real-time, complexity, approximation algorithms}
}
Document
DOI: 10.4230/DagSemProc.10071.2
10071 Executive Summary – Scheduling

Authors: Susanne Albers, Sanjoy K. Baruah, Rolf H. Möhring, and Kirk Pruhs

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

Abstract
The primary objectives of this seminar were to bring together leading researchers working on scheduling problems in three different research communities – operations research, theoretical computer science, and real-time systems – to expose each community to the important problems addressed by the other communities; to enable and encourage cooperation among the researchers; and to facilitate a transfer of solution techniques from each community to the others.
Cite as

Susanne Albers, Sanjoy K. Baruah, Rolf H. Möhring, and Kirk Pruhs. 10071 Executive Summary – Scheduling. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{albers_et_al:DagSemProc.10071.2,
  author =	{Albers, Susanne and Baruah, Sanjoy K. and M\"{o}hring, Rolf  H. and Pruhs, Kirk},
  title =	{{10071 Executive Summary – Scheduling}},
  booktitle =	{Scheduling},
  pages =	{1--2},
  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-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.2},
  URN =		{urn:nbn:de:0030-drops-25417},
  doi =		{10.4230/DagSemProc.10071.2},
  annote =	{Keywords: Scheduling, real-time, complexity, approximation algorithms}
}
Document
DOI: 10.4230/DagSemProc.10071.3
10071 Open Problems – Scheduling

Authors: Jim Anderson, Björn Andersson, Yossi Azar, Nikhil Bansal, Enrico Bini, Marek Chrobak, José Correa, Liliana Cucu-Grosjean, Rob Davis, Arvind Easwaran, Jeff Edmonds, Shelby Funk, Sathish Gopalakrishnan, Han Hoogeveen, Claire Mathieu, Nicole Megow, Seffi Naor, Kirk Pruhs, Maurice Queyranne, Adi Rosén, Nicolas Schabanel, Jiří Sgall, René Sitters, Sebastian Stiller, Marc Uetz, Tjark Vredeveld, and Gerhard J. Woeginger

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

Abstract
Collection of the open problems presented at the scheduling seminar.
Cite as

Jim Anderson, Björn Andersson, Yossi Azar, Nikhil Bansal, Enrico Bini, Marek Chrobak, José Correa, Liliana Cucu-Grosjean, Rob Davis, Arvind Easwaran, Jeff Edmonds, Shelby Funk, Sathish Gopalakrishnan, Han Hoogeveen, Claire Mathieu, Nicole Megow, Seffi Naor, Kirk Pruhs, Maurice Queyranne, Adi Rosén, Nicolas Schabanel, Jiří Sgall, René Sitters, Sebastian Stiller, Marc Uetz, Tjark Vredeveld, and Gerhard J. Woeginger. 10071 Open Problems – Scheduling. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{anderson_et_al:DagSemProc.10071.3,
  author =	{Anderson, Jim and Andersson, Bj\"{o}rn and Azar, Yossi and Bansal, Nikhil and Bini, Enrico and Chrobak, Marek and Correa, Jos\'{e} and Cucu-Grosjean, Liliana and Davis, Rob and Easwaran, Arvind and Edmonds, Jeff and Funk, Shelby and Gopalakrishnan, Sathish and Hoogeveen, Han and Mathieu, Claire and Megow, Nicole and Naor, Seffi and Pruhs, Kirk and Queyranne, Maurice and Ros\'{e}n, Adi and Schabanel, Nicolas and Sgall, Ji\v{r}{\'\i} and Sitters, Ren\'{e} and Stiller, Sebastian and Uetz, Marc and Vredeveld, Tjark and Woeginger, Gerhard J.},
  title =	{{10071 Open Problems – Scheduling}},
  booktitle =	{Scheduling},
  pages =	{1--24},
  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-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.3},
  URN =		{urn:nbn:de:0030-drops-25367},
  doi =		{10.4230/DagSemProc.10071.3},
  annote =	{Keywords: Open problems, scheduling}
}
Document
DOI: 10.4230/DagSemProc.10071.12
Scalably Scheduling Processes with Arbitrary Speedup Curves

Authors: Jeff Edmonds and Kirk Pruhs

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

Abstract
We give a scalable ((1+\epsilon)-speed O(1)-competitive) nonclairvoyant algorithm for scheduling jobs with sublinear nondecreasing speed-up curves on multiple processors with the objective of average response time.
Cite as

Jeff Edmonds and Kirk Pruhs. Scalably Scheduling Processes with Arbitrary Speedup Curves. In Scheduling. Dagstuhl Seminar Proceedings, Volume 10071, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{edmonds_et_al:DagSemProc.10071.12,
  author =	{Edmonds, Jeff and Pruhs, Kirk},
  title =	{{Scalably Scheduling Processes with Arbitrary Speedup Curves}},
  booktitle =	{Scheduling},
  pages =	{1--9},
  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-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.10071.12},
  URN =		{urn:nbn:de:0030-drops-25463},
  doi =		{10.4230/DagSemProc.10071.12},
  annote =	{Keywords: Scheduling}
}
Document
DOI: 10.4230/LIPIcs.STACS.2009.1815
Nonclairvoyant Speed Scaling for Flow and Energy

Authors: Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)

Abstract
We study online nonclairvoyant speed scaling to minimize total flow time plus energy. We first consider the traditional model where the power function is $P(s)=s^\alpha$. We give a nonclairvoyant algorithm that is shown to be $O(\alpha^3)$-competitive. We then show an $\Omega( \alpha^{1/3-\epsilon} )$ lower bound on the competitive ratio of any nonclairvoyant algorithm. We also show that there are power functions for which no nonclairvoyant algorithm can be $O(1)$-competitive.
Cite as

Ho-Leung Chan, Jeff Edmonds, Tak-Wah Lam, Lap-Kei Lee, Alberto Marchetti-Spaccamela, and Kirk Pruhs. Nonclairvoyant Speed Scaling for Flow and Energy. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 255-264, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{chan_et_al:LIPIcs.STACS.2009.1815,
  author =	{Chan, Ho-Leung and Edmonds, Jeff and Lam, Tak-Wah and Lee, Lap-Kei and Marchetti-Spaccamela, Alberto and Pruhs, Kirk},
  title =	{{Nonclairvoyant Speed Scaling for Flow and Energy}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{255--264},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1815},
  URN =		{urn:nbn:de:0030-drops-18151},
  doi =		{10.4230/LIPIcs.STACS.2009.1815},
  annote =	{Keywords: }
}
Document
DOI: 10.4230/DagSemProc.08071.1
08071 Abstracts Collection – Scheduling

Authors: Jane W. S. Liu, Rolf H. Möhring, and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 8071, Scheduling (2008)

Abstract
From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Jane W. S. Liu, Rolf H. Möhring, and Kirk Pruhs. 08071 Abstracts Collection – Scheduling. In Scheduling. Dagstuhl Seminar Proceedings, Volume 8071, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{liu_et_al:DagSemProc.08071.1,
  author =	{Liu, Jane W. S. and M\"{o}hring, Rolf H. and Pruhs, Kirk},
  title =	{{08071 Abstracts Collection – Scheduling}},
  booktitle =	{Scheduling},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8071},
  editor =	{Jane W. S. Liu and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08071.1},
  URN =		{urn:nbn:de:0030-drops-14897},
  doi =		{10.4230/DagSemProc.08071.1},
  annote =	{Keywords: Scheduling, real-time, supply chain}
}
Document
DOI: 10.4230/DagSemProc.08071.2
08071 Executive Summary – Scheduling

Authors: Jane W. S. Liu, Rolf H. Möhring, and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 8071, Scheduling (2008)

Abstract
Scheduling is a form of decision making that involves allocating scarce resources to achieve some objective. The study of scheduling dates back to at least the 1950’s when operations research researchers studied problems of managing activities in a workshop. Computer systems researchers started studying scheduling in the 1960’s in the development of operating systems and time-critical applications.
Cite as

Jane W. S. Liu, Rolf H. Möhring, and Kirk Pruhs. 08071 Executive Summary – Scheduling. In Scheduling. Dagstuhl Seminar Proceedings, Volume 8071, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{liu_et_al:DagSemProc.08071.2,
  author =	{Liu, Jane W. S. and M\"{o}hring, Rolf H. and Pruhs, Kirk},
  title =	{{08071 Executive Summary – Scheduling}},
  booktitle =	{Scheduling},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8071},
  editor =	{Jane W. S. Liu and Rolf H. M\"{o}hring and Kirk Pruhs},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.08071.2},
  URN =		{urn:nbn:de:0030-drops-14871},
  doi =		{10.4230/DagSemProc.08071.2},
  annote =	{Keywords: Scheduling, real-time, supply chain}
}
Document
DOI: 10.4230/DagSemProc.07261.1
07261 Abstracts Collection – Fair Division

Authors: Steven J. Brams and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
From 24.06. to 29.06.2007, the Dagstuhl Seminar 07261 % generate automatically ``Fair Division'' % generate automatically was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Steven J. Brams and Kirk Pruhs. 07261 Abstracts Collection – Fair Division. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brams_et_al:DagSemProc.07261.1,
  author =	{Brams, Steven J. and Pruhs, Kirk},
  title =	{{07261 Abstracts Collection – Fair Division}},
  booktitle =	{Fair Division},
  pages =	{1--16},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.1},
  URN =		{urn:nbn:de:0030-drops-12444},
  doi =		{10.4230/DagSemProc.07261.1},
  annote =	{Keywords: Economics, Fairness, Allocation, Political Science}
}
Document
DOI: 10.4230/DagSemProc.07261.2
07261 Summary – Fair Division

Authors: Steven J. Brams and Kirk Pruhs

Published in: Dagstuhl Seminar Proceedings, Volume 7261, Fair Division (2007)

Abstract
The problem of fair division – dividing goods or "bads" (e.g., costs) among entities in an impartial and equitable way – is one of the most important problems that society faces. A Google search on the phrase "fair allocation" returns over 100K links, referring to the division of sports tickets, health resources, computer networking resources, voting power, intellectual property licenses, costs of environmental improvements, etc.
Cite as

Steven J. Brams and Kirk Pruhs. 07261 Summary – Fair Division. In Fair Division. Dagstuhl Seminar Proceedings, Volume 7261, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{brams_et_al:DagSemProc.07261.2,
  author =	{Brams, Steven J. and Pruhs, Kirk},
  title =	{{07261 Summary  – Fair Division}},
  booktitle =	{Fair Division},
  pages =	{1--3},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7261},
  editor =	{Steven Brams and Kirk Pruhs and Gerhard Woeginger},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07261.2},
  URN =		{urn:nbn:de:0030-drops-12434},
  doi =		{10.4230/DagSemProc.07261.2},
  annote =	{Keywords: Economics, Fairness, Allocation, Political Science}
}
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