227 Search Results for "Albers, Susanne"

Volume

LIPIcs, Volume 162

17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

SWAT 2020, June 22-24, 2020, Tórshavn, Faroe Islands

Editors: Susanne Albers

Volume

LIPIcs, Volume 3

26th International Symposium on Theoretical Aspects of Computer Science

STACS 2009, February 26-28, 2009, Freiburg, Germany

Editors: Susanne Albers and Jean-Yves Marion

Volume

LIPIcs, Volume 1

25th International Symposium on Theoretical Aspects of Computer Science

STACS 2008, February 21-23, 2008, Bordeaux, France

Editors: Susanne Albers and Pascal Weil

Document
DOI: 10.4230/LIPIcs.FSCD.2024.24
IMELL Cut Elimination with Linear Overhead

Authors: Beniamino Accattoli and Claudio Sacerdoti Coen

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Recently, Accattoli introduced the Exponential Substitution Calculus (ESC) given by untyped proof terms for Intuitionistic Multiplicative Exponential Linear Logic (IMELL), endowed with rewriting rules at-a-distance for cut elimination. He also introduced a new cut elimination strategy, dubbed the good strategy, and showed that its number of steps is a time cost model with polynomial overhead for ESC/IMELL, and the first such one. Here, we refine Accattoli’s result by introducing an abstract machine for ESC and proving that it implements the good strategy and computes cut-free terms/proofs within a linear overhead.
Cite as

Beniamino Accattoli and Claudio Sacerdoti Coen. IMELL Cut Elimination with Linear Overhead. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 24:1-24:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{accattoli_et_al:LIPIcs.FSCD.2024.24,
  author =	{Accattoli, Beniamino and Sacerdoti Coen, Claudio},
  title =	{{IMELL Cut Elimination with Linear Overhead}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{24:1--24:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.24},
  URN =		{urn:nbn:de:0030-drops-203539},
  doi =		{10.4230/LIPIcs.FSCD.2024.24},
  annote =	{Keywords: Lambda calculus, linear logic, abstract machines}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.4
Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities

Authors: Susanne Albers and Sebastian Schubert

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

Abstract
We study the b-matching problem in bipartite graphs G = (S,R,E). Each vertex s ∈ S is a server with individual capacity b_s. The vertices r ∈ R are requests that arrive online and must be assigned instantly to an eligible server. The goal is to maximize the size of the constructed matching. We assume that G is a (k,d)-graph [J. Naor and D. Wajc, 2018], where k specifies a lower bound on the degree of each server and d is an upper bound on the degree of each request. This setting models matching problems in timely applications. We present tight upper and lower bounds on the performance of deterministic online algorithms. In particular, we develop a new online algorithm via a primal-dual analysis. The optimal competitive ratio tends to 1, for arbitrary k ≥ d, as the server capacities increase. Hence, nearly optimal solutions can be computed online. Our results also hold for the vertex-weighted problem extension, and thus for AdWords and auction problems in which each bidder issues individual, equally valued bids. Our bounds improve the previous best competitive ratios. The asymptotic competitiveness of 1 is a significant improvement over the previous factor of 1-1/e^{k/d}, for the interesting range where k/d ≥ 1 is small. Recall that 1-1/e ≈ 0.63. Matching problems that admit a competitive ratio arbitrarily close to 1 are rare. Prior results rely on randomization or probabilistic input models.
Cite as

Susanne Albers and Sebastian Schubert. Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{albers_et_al:LIPIcs.ESA.2022.4,
  author =	{Albers, Susanne and Schubert, Sebastian},
  title =	{{Tight Bounds for Online Matching in Bounded-Degree Graphs with Vertex Capacities}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.4},
  URN =		{urn:nbn:de:0030-drops-169420},
  doi =		{10.4230/LIPIcs.ESA.2022.4},
  annote =	{Keywords: online algorithms, deterministic algorithms, primal-dual analysis, b-matching, bounded-degree graph, variable vertex capacities, unweighted matching, vertex-weighted matching}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.12
Near-Optimal Algorithms for Stochastic Online Bin Packing

Authors: Nikhil ^* Ayyadevara, Rajni Dabas, Arindam Khan, and K. V. N. Sreenivas

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study the online bin packing problem under two stochastic settings. In the bin packing problem, we are given n items with sizes in (0,1] and the goal is to pack them into the minimum number of unit-sized bins. First, we study bin packing under the i.i.d. model, where item sizes are sampled independently and identically from a distribution in (0,1]. Both the distribution and the total number of items are unknown. The items arrive one by one and their sizes are revealed upon their arrival and they must be packed immediately and irrevocably in bins of size 1. We provide a simple meta-algorithm that takes an offline α-asymptotic proximation algorithm and provides a polynomial-time (α + ε)-competitive algorithm for online bin packing under the i.i.d. model, where ε > 0 is a small constant. Using the AFPTAS for offline bin packing, we thus provide a linear time (1+ε)-competitive algorithm for online bin packing under i.i.d. model, thus settling the problem. We then study the random-order model, where an adversary specifies the items, but the order of arrival of items is drawn uniformly at random from the set of all permutations of the items. Kenyon’s seminal result [SODA'96] showed that the Best-Fit algorithm has a competitive ratio of at most 3/2 in the random-order model, and conjectured the ratio to be ≈ 1.15. However, it has been a long-standing open problem to break the barrier of 3/2 even for special cases. Recently, Albers et al. [Algorithmica'21] showed an improvement to 5/4 competitive ratio in the special case when all the item sizes are greater than 1/3. For this special case, we settle the analysis by showing that Best-Fit has a competitive ratio of 1. We also make further progress by breaking the barrier of 3/2 for the 3-Partition problem, a notoriously hard special case of bin packing, where all item sizes lie in (1/4,1/2].
Cite as

Nikhil ^* Ayyadevara, Rajni Dabas, Arindam Khan, and K. V. N. Sreenivas. Near-Optimal Algorithms for Stochastic Online Bin Packing. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ayyadevara_et_al:LIPIcs.ICALP.2022.12,
  author =	{Ayyadevara, Nikhil ^* and Dabas, Rajni and Khan, Arindam and Sreenivas, K. V. N.},
  title =	{{Near-Optimal Algorithms for Stochastic Online Bin Packing}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.12},
  URN =		{urn:nbn:de:0030-drops-163532},
  doi =		{10.4230/LIPIcs.ICALP.2022.12},
  annote =	{Keywords: Bin Packing, 3-Partition Problem, Online Algorithms, Random Order Arrival, IID model, Best-Fit Algorithm}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2021.52
Machine Covering in the Random-Order Model

Authors: Susanne Albers, Waldo Gálvez, and Maximilian Janke

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)

Abstract
In the Online Machine Covering problem jobs, defined by their sizes, arrive one by one and have to be assigned to m parallel and identical machines, with the goal of maximizing the load of the least-loaded machine. Unfortunately, the classical model allows only fairly pessimistic performance guarantees: The best possible deterministic ratio of m is achieved by the Greedy-strategy, and the best known randomized algorithm has competitive ratio Õ(√m) which cannot be improved by more than a logarithmic factor. Modern results try to mitigate this by studying semi-online models, where additional information about the job sequence is revealed in advance or extra resources are provided to the online algorithm. In this work we study the Machine Covering problem in the recently popular random-order model. Here no extra resources are present, but instead the adversary is weakened in that it can only decide upon the input set while jobs are revealed uniformly at random. It is particularly relevant to Machine Covering where lower bounds are usually associated to highly structured input sequences. We first analyze Graham’s Greedy-strategy in this context and establish that its competitive ratio decreases slightly to Θ(m/(log(m))) which is asymptotically tight. Then, as our main result, we present an improved Õ(∜m)-competitive algorithm for the problem. This result is achieved by exploiting the extra information coming from the random order of the jobs, using sampling techniques to devise an improved mechanism to distinguish jobs that are relatively large from small ones. We complement this result with a first lower bound showing that no algorithm can have a competitive ratio of O(log(m)/{log log(m)}) in the random-order model. This lower bound is achieved by studying a novel variant of the Secretary problem, which could be of independent interest.
Cite as

Susanne Albers, Waldo Gálvez, and Maximilian Janke. Machine Covering in the Random-Order Model. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 52:1-52:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{albers_et_al:LIPIcs.ISAAC.2021.52,
  author =	{Albers, Susanne and G\'{a}lvez, Waldo and Janke, Maximilian},
  title =	{{Machine Covering in the Random-Order Model}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{52:1--52:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.52},
  URN =		{urn:nbn:de:0030-drops-154858},
  doi =		{10.4230/LIPIcs.ISAAC.2021.52},
  annote =	{Keywords: Machine Covering, Online Algorithm, Random-Order, Competitive Analysis, Scheduling}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2021.6
Scheduling in the Secretary Model

Authors: Susanne Albers and Maximilian Janke

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)

Abstract
This paper studies online makespan minimization in the secretary model. Jobs, specified by their processing times, are presented in a uniformly random order. The input size n is known in advance. An online algorithm has to non-preemptively assign each job permanently and irrevocably to one of m parallel and identical machines such that the expected time it takes to process them all, the makespan, is minimized. We give two deterministic algorithms. First, a straightforward adaptation of the semi-online strategy Light Load [Albers and Hellwig, 2012] provides a very simple approach retaining its competitive ratio of 1.75. A new and sophisticated algorithm is 1.535-competitive. These competitive ratios are not only obtained in expectation but, in fact, for all but a very tiny fraction of job orders. Classically, online makespan minimization only considers the worst-case order. Here, no competitive ratio below 1.885 for deterministic algorithms and 1.581 using randomization is possible. The best randomized algorithm so far is 1.916-competitive. Our results show that classical worst-case orders are quite rare and pessimistic for many applications. We complement our results by providing first lower bounds. A competitive ratio obtained on nearly all possible job orders must be at least 1.257. This implies a lower bound of 1.043 for both deterministic and randomized algorithms in the general model.
Cite as

Susanne Albers and Maximilian Janke. Scheduling in the Secretary Model. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{albers_et_al:LIPIcs.FSTTCS.2021.6,
  author =	{Albers, Susanne and Janke, Maximilian},
  title =	{{Scheduling in the Secretary Model}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{6:1--6:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.6},
  URN =		{urn:nbn:de:0030-drops-155172},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.6},
  annote =	{Keywords: Scheduling, makespan minimization, online algorithm, competitive analysis, lower bound, random-order, secretary problem}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2021.2
Optimal Algorithms for Online b-Matching with Variable Vertex Capacities

Authors: Susanne Albers and Sebastian Schubert

Published in: LIPIcs, Volume 207, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)

Abstract
We study the b-matching problem, which generalizes classical online matching introduced by Karp, Vazirani and Vazirani (STOC 1990). Consider a bipartite graph G = (S ̇∪ R,E). Every vertex s ∈ S is a server with a capacity b_s, indicating the number of possible matching partners. The vertices r ∈ R are requests that arrive online and must be matched immediately to an eligible server. The goal is to maximize the cardinality of the constructed matching. In contrast to earlier work, we study the general setting where servers may have arbitrary, individual capacities. We prove that the most natural and simple online algorithms achieve optimal competitive ratios. As for deterministic algorithms, we give a greedy algorithm RelativeBalance and analyze it by extending the primal-dual framework of Devanur, Jain and Kleinberg (SODA 2013). In the area of randomized algorithms we study the celebrated Ranking algorithm by Karp, Vazirani and Vazirani. We prove that the original Ranking strategy, simply picking a random permutation of the servers, achieves an optimal competitiveness of 1-1/e, independently of the server capacities. Hence it is not necessary to resort to a reduction, replacing every server s by b_s vertices of unit capacity and to then run Ranking on this graph with ∑_{s ∈ S} b_s vertices on the left-hand side. From a theoretical point of view our result explores the power of randomization and strictly limits the amount of required randomness. From a practical point of view it leads to more efficient allocation algorithms. Technically, we show that the primal-dual framework of Devanur, Jain and Kleinberg cannot establish a competitiveness better than 1/2 for the original Ranking algorithm, choosing a permutation of the servers. Therefore, we formulate a new configuration LP for the b-matching problem and then conduct a primal-dual analysis. We extend this analysis approach to the vertex-weighted b-matching problem. Specifically, we show that the algorithm PerturbedGreedy by Aggarwal, Goel, Karande and Mehta (SODA 2011), again with a sole randomization over the set of servers, is (1-1/e)-competitive. Together with recent work by Huang and Zhang (STOC 2020), our results demonstrate that configuration LPs can be strictly stronger than standard LPs in the analysis of more complex matching problems.
Cite as

Susanne Albers and Sebastian Schubert. Optimal Algorithms for Online b-Matching with Variable Vertex Capacities. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 2:1-2:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{albers_et_al:LIPIcs.APPROX/RANDOM.2021.2,
  author =	{Albers, Susanne and Schubert, Sebastian},
  title =	{{Optimal Algorithms for Online b-Matching with Variable Vertex Capacities}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021)},
  pages =	{2:1--2:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-207-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{207},
  editor =	{Wootters, Mary and Sanit\`{a}, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2021.2},
  URN =		{urn:nbn:de:0030-drops-146957},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2021.2},
  annote =	{Keywords: Online algorithms, primal-dual analysis, configuration LP, b-matching, variable vertex capacities, unweighted matching, vertex-weighted matching}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.7
Best Fit Bin Packing with Random Order Revisited

Authors: Susanne Albers, Arindam Khan, and Leon Ladewig

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

Abstract
Best Fit is a well known online algorithm for the bin packing problem, where a collection of one-dimensional items has to be packed into a minimum number of unit-sized bins. In a seminal work, Kenyon [SODA 1996] introduced the (asymptotic) random order ratio as an alternative performance measure for online algorithms. Here, an adversary specifies the items, but the order of arrival is drawn uniformly at random. Kenyon’s result establishes lower and upper bounds of 1.08 and 1.5, respectively, for the random order ratio of Best Fit. Although this type of analysis model became increasingly popular in the field of online algorithms, no progress has been made for the Best Fit algorithm after the result of Kenyon. We study the random order ratio of Best Fit and tighten the long-standing gap by establishing an improved lower bound of 1.10. For the case where all items are larger than 1/3, we show that the random order ratio converges quickly to 1.25. It is the existence of such large items that crucially determines the performance of Best Fit in the general case. Moreover, this case is closely related to the classical maximum-cardinality matching problem in the fully online model. As a side product, we show that Best Fit satisfies a monotonicity property on such instances, unlike in the general case. In addition, we initiate the study of the absolute random order ratio for this problem. In contrast to asymptotic ratios, absolute ratios must hold even for instances that can be packed into a small number of bins. We show that the absolute random order ratio of Best Fit is at least 1.3. For the case where all items are larger than 1/3, we derive upper and lower bounds of 21/16 and 1.2, respectively.
Cite as

Susanne Albers, Arindam Khan, and Leon Ladewig. Best Fit Bin Packing with Random Order Revisited. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{albers_et_al:LIPIcs.MFCS.2020.7,
  author =	{Albers, Susanne and Khan, Arindam and Ladewig, Leon},
  title =	{{Best Fit Bin Packing with Random Order Revisited}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{7:1--7:15},
  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.2020.7},
  URN =		{urn:nbn:de:0030-drops-127300},
  doi =		{10.4230/LIPIcs.MFCS.2020.7},
  annote =	{Keywords: Online bin packing, random arrival order, probabilistic analysis}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.68
Scheduling in the Random-Order Model

Authors: Susanne Albers and Maximilian Janke

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

Abstract
Makespan minimization on identical machines is a fundamental problem in online scheduling. The goal is to assign a sequence of jobs to m identical parallel machines so as to minimize the maximum completion time of any job. Already in the 1960s, Graham showed that Greedy is (2-1/m)-competitive [Graham, 1966]. The best deterministic online algorithm currently known achieves a competitive ratio of 1.9201 [Fleischer and Wahl, 2000]. No deterministic online strategy can obtain a competitiveness smaller than 1.88 [Rudin III, 2001]. In this paper, we study online makespan minimization in the popular random-order model, where the jobs of a given input arrive as a random permutation. It is known that Greedy does not attain a competitive factor asymptotically smaller than 2 in this setting [Osborn and Torng, 2008]. We present the first improved performance guarantees. Specifically, we develop a deterministic online algorithm that achieves a competitive ratio of 1.8478. The result relies on a new analysis approach. We identify a set of properties that a random permutation of the input jobs satisfies with high probability. Then we conduct a worst-case analysis of our algorithm, for the respective class of permutations. The analysis implies that the stated competitiveness holds not only in expectation but with high probability. Moreover, it provides mathematical evidence that job sequences leading to higher performance ratios are extremely rare, pathological inputs. We complement the results by lower bounds for the random-order model. We show that no deterministic online algorithm can achieve a competitive ratio smaller than 4/3. Moreover, no deterministic online algorithm can attain a competitiveness smaller than 3/2 with high probability.
Cite as

Susanne Albers and Maximilian Janke. Scheduling in the Random-Order Model. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 68:1-68:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{albers_et_al:LIPIcs.ICALP.2020.68,
  author =	{Albers, Susanne and Janke, Maximilian},
  title =	{{Scheduling in the Random-Order Model}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{68:1--68:18},
  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.2020.68},
  URN =		{urn:nbn:de:0030-drops-124750},
  doi =		{10.4230/LIPIcs.ICALP.2020.68},
  annote =	{Keywords: Scheduling, makespan minimization, online algorithm, competitive analysis, lower bound, random-order}
}
Document
Complete Volume
DOI: 10.4230/LIPIcs.SWAT.2020
LIPIcs, Volume 162, SWAT 2020, Complete Volume

Authors: Susanne Albers

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
LIPIcs, Volume 162, SWAT 2020, Complete Volume
Cite as

17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 1-606, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{albers:LIPIcs.SWAT.2020,
  title =	{{LIPIcs, Volume 162, SWAT 2020, Complete Volume}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{1--606},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020},
  URN =		{urn:nbn:de:0030-drops-122469},
  doi =		{10.4230/LIPIcs.SWAT.2020},
  annote =	{Keywords: LIPIcs, Volume 162, SWAT 2020, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.SWAT.2020.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Susanne Albers

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{albers:LIPIcs.SWAT.2020.0,
  author =	{Albers, Susanne},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{0:i--0:x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.0},
  URN =		{urn:nbn:de:0030-drops-122476},
  doi =		{10.4230/LIPIcs.SWAT.2020.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SWAT.2020.1
Parameterized Complexity of PCA (Invited Talk)

Authors: Fedor V. Fomin, Petr A. Golovach, and Kirill Simonov

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
We discuss some recent progress in the study of Principal Component Analysis (PCA) from the perspective of Parameterized Complexity.
Cite as

Fedor V. Fomin, Petr A. Golovach, and Kirill Simonov. Parameterized Complexity of PCA (Invited Talk). In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, pp. 1:1-1:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{fomin_et_al:LIPIcs.SWAT.2020.1,
  author =	{Fomin, Fedor V. and Golovach, Petr A. and Simonov, Kirill},
  title =	{{Parameterized Complexity of PCA}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{1:1--1:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.1},
  URN =		{urn:nbn:de:0030-drops-122487},
  doi =		{10.4230/LIPIcs.SWAT.2020.1},
  annote =	{Keywords: parameterized complexity, Robust PCA, outlier detection}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SWAT.2020.2
Landscape of Locality (Invited Talk)

Authors: Jukka Suomela

Published in: LIPIcs, Volume 162, 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)

Abstract
The theory of distributed computing aims at understanding which tasks can be solved efficiently in large distributed systems. This forms the basis for our understanding of the modern world, which heavily depends on world-wide communication networks and large-scale distributed computer systems. In distributed computing the key computational resource is communication, and we seek to find out which computational problems can be solved with only a few communication steps. This is directly connected to the concept of locality: in T synchronous communication rounds, all nodes in a network can gather all information in their radius-T neighborhoods, but not any further. Hence the distributed time complexity of a graph problem can be defined in two equivalent ways: it is the number of communication rounds needed to solve the problem, and it is the distance up to which individual nodes need to see in order to choose their own part of the solution. While the locality of graph problems has been studied already since the 1980s, only in the past four years we have started to take big leaps in understanding what the landscape of distributed time complexity looks like and with what kind of tools and techniques we can study it. One concept that has been a driving force in the recent developments is the notion of locally verifiable problems. These are graph problems in which a solution is feasible if and only if it looks valid in all constant-radius neighborhoods; put otherwise, these are problems that could be solved efficiently with a nondeterministic distributed algorithm, and hence they form a natural distributed analogue of class NP. Now the key question is this: if a problem is locally verifiable, is it also locally solvable, and if not, what can we say about its distributed time complexity? Naor and Stockmeyer [SIAM J. Comput. 1995] formalized the idea of locally verifiable problems by introducing the class of LCL problems (locally checkable labeling problems). While the concept is old, and over the years we have seen results related to the locality of many specific LCLs, little was known about the distributed complexity of LCLs in general. By 2015, we had only seen examples of LCLs with localities O(1), Θ(log^* n), and Θ(n), and it was wide open whether these three classes are all that there is. All this started to change rapidly after we proved [Brandt et al., STOC 2016] that there are natural examples of LCLs that have a locality strictly between ω(log^* n) and o(n). The same paper also paved the way for the development of a new general-purpose proof technique for analyzing the locality of locally verifiable problems, namely round elimination. Now after four years of work and a number of papers by several research teams working in the area, we have reached a point in which there is a near-complete picture of the landscape of LCL problems - and it looks nothing like what we would have expected.
Cite as

Jukka Suomela. Landscape of Locality (Invited Talk). In 17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 162, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{suomela:LIPIcs.SWAT.2020.2,
  author =	{Suomela, Jukka},
  title =	{{Landscape of Locality}},
  booktitle =	{17th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2020)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-150-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{162},
  editor =	{Albers, Susanne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2020.2},
  URN =		{urn:nbn:de:0030-drops-122490},
  doi =		{10.4230/LIPIcs.SWAT.2020.2},
  annote =	{Keywords: Theory of distributed computing, Network algorithms, Locality, Distributed time complexity}
}
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