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Documents authored by Královič, Rastislav

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Královic, Rastislav

Document
Complete Volume
DOI: 10.4230/LIPIcs.MFCS.2024
LIPIcs, Volume 306, MFCS 2024, Complete Volume

Authors: Rastislav Královič and Antonín Kučera

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
LIPIcs, Volume 306, MFCS 2024, Complete Volume
Cite as

49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 1-1362, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{kralovic_et_al:LIPIcs.MFCS.2024,
  title =	{{LIPIcs, Volume 306, MFCS 2024, Complete Volume}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{1--1362},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024},
  URN =		{urn:nbn:de:0030-drops-205555},
  doi =		{10.4230/LIPIcs.MFCS.2024},
  annote =	{Keywords: LIPIcs, Volume 306, MFCS 2024, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.MFCS.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Rastislav Královič and Antonín Kučera

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

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

49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kralovic_et_al:LIPIcs.MFCS.2024.0,
  author =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.0},
  URN =		{urn:nbn:de:0030-drops-205568},
  doi =		{10.4230/LIPIcs.MFCS.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.30
Randomization in Non-Uniform Finite Automata

Authors: Pavol Ďuriš, Rastislav Královič, Richard Královič, Dana Pardubská, Martin Pašen, and Peter Rossmanith

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

Abstract
The non-uniform version of Turing machines with an extra advice input tape that depends on the length of the input but not the input itself is a well-studied model in complexity theory. We investigate the same notion of non-uniformity in weaker models, namely one-way finite automata. In particular, we are interested in the power of two-sided bounded-error randomization, and how it compares to determinism and non-determinism. We show that for unlimited advice, randomization is strictly stronger than determinism, and strictly weaker than non-determinism. However, when the advice is restricted to polynomial length, the landscape changes: the expressive power of determinism and randomization does not change, but the power of non-determinism is reduced to the extent that it becomes incomparable with randomization.
Cite as

Pavol Ďuriš, Rastislav Královič, Richard Královič, Dana Pardubská, Martin Pašen, and Peter Rossmanith. Randomization in Non-Uniform Finite Automata. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{duris_et_al:LIPIcs.MFCS.2020.30,
  author =	{\v{D}uri\v{s}, Pavol and Kr\'{a}lovi\v{c}, Rastislav and Kr\'{a}lovi\v{c}, Richard and Pardubsk\'{a}, Dana and Pa\v{s}en, Martin and Rossmanith, Peter},
  title =	{{Randomization in Non-Uniform Finite Automata}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{30:1--30:13},
  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.2020.30},
  URN =		{urn:nbn:de:0030-drops-126987},
  doi =		{10.4230/LIPIcs.MFCS.2020.30},
  annote =	{Keywords: finite automata, non-uniform computation, randomization}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2017.14
Treasure Hunt with Barely Communicating Agents

Authors: Stefan Dobrev, Rastislav Královic, and Dana Pardubská

Published in: LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017)

Abstract
We consider the problem of fault-tolerant parallel exhaustive search, a.k.a. “Treasure Hunt”, introduced by Fraigniaud, Korman and Rodeh in [13]: Imagine an infinite list of “boxes”, one of which contains a “treasure”. The ordering of the boxes reflects the importance of finding the treasure in a given box. There are k agents, whose goal is to locate the treasure in the least amount of time. The system is synchronous; at every step, an agent can ”open” a box and see whether the treasure is there. The hunt finishes when the first agent locates the treasure. The original paper [13] considers non-cooperating randomized agents, out of which at most f can fail, with the failure pattern determined by an adversary. In this paper, we consider deterministic agents and investigate two failure models: The failing-agents model from [13] and a “black hole” model: At most f boxes contain “black holes”, placed by the adversary. When an agent opens a box containing a black hole, the agent disappears without an observable trace. The crucial distinction, however, is that we consider “barely communicating” or “indirectly weakly communicating” agents: When an agent opens a box, it can tell whether the box has been previously opened. There are no other means of direct or indirect communication between the agents. We show that adding even such weak means of communication has very strong impact on the solvability and complexity of the Treasure Hunt problem. In particular, in the failing agents model it allows the agents to be 1-competitive w.r.t. an optimal algorithm which does not know the location of the treasure, but is instantly notified of agent failures. In the black holes model (where there is no deterministic solution for non-communicating agents even in the presence of a single black hole) we show a lower bound of 2f + 1 and an upper bound of 4f + 1 for the number of agents needed to solve Treasure Hunt in presence of up to f black holes, as well as partial results about the hunt time in the presence of few black holes.
Cite as

Stefan Dobrev, Rastislav Královic, and Dana Pardubská. Treasure Hunt with Barely Communicating Agents. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dobrev_et_al:LIPIcs.OPODIS.2017.14,
  author =	{Dobrev, Stefan and Kr\'{a}lovic, Rastislav and Pardubsk\'{a}, Dana},
  title =	{{Treasure Hunt with Barely Communicating Agents}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-061-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{95},
  editor =	{Aspnes, James and Bessani, Alysson and Felber, Pascal and Leit\~{a}o, Jo\~{a}o},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.14},
  URN =		{urn:nbn:de:0030-drops-86346},
  doi =		{10.4230/LIPIcs.OPODIS.2017.14},
  annote =	{Keywords: parallel exhaustive search, treasure hunt, fault-tolerant search, weak coordination, black holes}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.59
Advice Complexity of the Online Induced Subgraph Problem

Authors: Dennis Komm, Rastislav Královic, Richard Královic, and Christian Kudahl

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples include maximum independent set, maximum planar graph, maximum clique, minimum feedback vertex set, and many others. In online versions of these problems, the vertices of the graph are presented in an adversarial order, and with each vertex, the online algorithm must irreversibly decide whether to include it into the constructed subgraph, based only on the subgraph induced by the vertices presented so far. We study the properties that are common to all these problems by investigating a generalized problem: for an arbitrary but fixed hereditary property pi, find some maximal induced subgraph having pi. We investigate this problem from the point of view of advice complexity, i.e., we ask how some additional information about the yet unrevealed parts of the input can influence the solution quality. We evaluate the information in a quantitative way by considering the best possible advice of given size that describes the unknown input. Using a result from Boyar et al. [STACS 2015, LIPIcs 30], we give a tight trade-off relationship stating that, for inputs of length n, roughly n/c bits of advice are both needed and sufficient to obtain a solution with competitive ratio c, regardless of the choice of pi, for any c (possibly a function of n). This complements the results from Bartal et al. [SIAM Journal on Computing 36(2), 2006] stating that, without any advice, even a randomized algorithm cannot achieve a competitive ratio better than Omega(n^{1-log_{4}3-o(1)}). Surprisingly, for a given cohereditary property pi and the objective to find a minimum subgraph having pi, the advice complexity varies significantly with the choice of pi. We also consider a preemptive online model, inspired by some applications mainly in networking and scheduling, where the decision of the algorithm is not completely irreversible. In particular, the algorithm may discard some vertices previously assigned to the constructed set, but discarded vertices cannot be reinserted into the set. We show that, for the maximum induced subgraph problem, preemption does not significantly help by giving a lower bound of Omega(n/(c^2log c)) on the bits of advice that are needed to obtain competitive ratio c, where c is any increasing function bounded from above by sqrt(n/log n). We also give a linear lower bound for c close to 1.
Cite as

Dennis Komm, Rastislav Královic, Richard Královic, and Christian Kudahl. Advice Complexity of the Online Induced Subgraph Problem. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 59:1-59:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{komm_et_al:LIPIcs.MFCS.2016.59,
  author =	{Komm, Dennis and Kr\'{a}lovic, Rastislav and Kr\'{a}lovic, Richard and Kudahl, Christian},
  title =	{{Advice Complexity of the Online Induced Subgraph Problem}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{59:1--59:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.59},
  URN =		{urn:nbn:de:0030-drops-64713},
  doi =		{10.4230/LIPIcs.MFCS.2016.59},
  annote =	{Keywords: online algorithms, advice complexity, induced subgraph problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.470
Randomized Online Algorithms with High Probability Guarantees

Authors: Dennis Komm, Rastislav Královic, Richard Královic, and Tobias Mömke

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

Abstract
We study the relationship between the competitive ratio and the tail distribution of randomized online problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like paging, k-server and metrical task systems on finite metrics, and show that for these problems it is possible to obtain, given an algorithm with constant expected competitive ratio, another algorithm that achieves the same solution quality up to an arbitrarily small constant error with high probability; the "high probability" statement is in terms of the optimal cost. Furthermore, we show that our assumptions are tight in the sense that removing any of them allows for a counterexample to the theorem.
Cite as

Dennis Komm, Rastislav Královic, Richard Královic, and Tobias Mömke. Randomized Online Algorithms with High Probability Guarantees. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 470-481, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{komm_et_al:LIPIcs.STACS.2014.470,
  author =	{Komm, Dennis and Kr\'{a}lovic, Rastislav and Kr\'{a}lovic, Richard and M\"{o}mke, Tobias},
  title =	{{Randomized Online Algorithms with High Probability Guarantees}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{470--481},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.470},
  URN =		{urn:nbn:de:0030-drops-44803},
  doi =		{10.4230/LIPIcs.STACS.2014.470},
  annote =	{Keywords: Online Algorithms, Randomization, High Probability}
}

Královič, Rastislav

Document
Complete Volume
DOI: 10.4230/LIPIcs.MFCS.2024
LIPIcs, Volume 306, MFCS 2024, Complete Volume

Authors: Rastislav Královič and Antonín Kučera

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
LIPIcs, Volume 306, MFCS 2024, Complete Volume
Cite as

49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 1-1362, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Proceedings{kralovic_et_al:LIPIcs.MFCS.2024,
  title =	{{LIPIcs, Volume 306, MFCS 2024, Complete Volume}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{1--1362},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024},
  URN =		{urn:nbn:de:0030-drops-205555},
  doi =		{10.4230/LIPIcs.MFCS.2024},
  annote =	{Keywords: LIPIcs, Volume 306, MFCS 2024, Complete Volume}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.MFCS.2024.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Rastislav Královič and Antonín Kučera

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

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

49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kralovic_et_al:LIPIcs.MFCS.2024.0,
  author =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.0},
  URN =		{urn:nbn:de:0030-drops-205568},
  doi =		{10.4230/LIPIcs.MFCS.2024.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.30
Randomization in Non-Uniform Finite Automata

Authors: Pavol Ďuriš, Rastislav Královič, Richard Královič, Dana Pardubská, Martin Pašen, and Peter Rossmanith

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

Abstract
The non-uniform version of Turing machines with an extra advice input tape that depends on the length of the input but not the input itself is a well-studied model in complexity theory. We investigate the same notion of non-uniformity in weaker models, namely one-way finite automata. In particular, we are interested in the power of two-sided bounded-error randomization, and how it compares to determinism and non-determinism. We show that for unlimited advice, randomization is strictly stronger than determinism, and strictly weaker than non-determinism. However, when the advice is restricted to polynomial length, the landscape changes: the expressive power of determinism and randomization does not change, but the power of non-determinism is reduced to the extent that it becomes incomparable with randomization.
Cite as

Pavol Ďuriš, Rastislav Královič, Richard Královič, Dana Pardubská, Martin Pašen, and Peter Rossmanith. Randomization in Non-Uniform Finite Automata. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 30:1-30:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{duris_et_al:LIPIcs.MFCS.2020.30,
  author =	{\v{D}uri\v{s}, Pavol and Kr\'{a}lovi\v{c}, Rastislav and Kr\'{a}lovi\v{c}, Richard and Pardubsk\'{a}, Dana and Pa\v{s}en, Martin and Rossmanith, Peter},
  title =	{{Randomization in Non-Uniform Finite Automata}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{30:1--30:13},
  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.2020.30},
  URN =		{urn:nbn:de:0030-drops-126987},
  doi =		{10.4230/LIPIcs.MFCS.2020.30},
  annote =	{Keywords: finite automata, non-uniform computation, randomization}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2017.14
Treasure Hunt with Barely Communicating Agents

Authors: Stefan Dobrev, Rastislav Královic, and Dana Pardubská

Published in: LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017)

Abstract
We consider the problem of fault-tolerant parallel exhaustive search, a.k.a. “Treasure Hunt”, introduced by Fraigniaud, Korman and Rodeh in [13]: Imagine an infinite list of “boxes”, one of which contains a “treasure”. The ordering of the boxes reflects the importance of finding the treasure in a given box. There are k agents, whose goal is to locate the treasure in the least amount of time. The system is synchronous; at every step, an agent can ”open” a box and see whether the treasure is there. The hunt finishes when the first agent locates the treasure. The original paper [13] considers non-cooperating randomized agents, out of which at most f can fail, with the failure pattern determined by an adversary. In this paper, we consider deterministic agents and investigate two failure models: The failing-agents model from [13] and a “black hole” model: At most f boxes contain “black holes”, placed by the adversary. When an agent opens a box containing a black hole, the agent disappears without an observable trace. The crucial distinction, however, is that we consider “barely communicating” or “indirectly weakly communicating” agents: When an agent opens a box, it can tell whether the box has been previously opened. There are no other means of direct or indirect communication between the agents. We show that adding even such weak means of communication has very strong impact on the solvability and complexity of the Treasure Hunt problem. In particular, in the failing agents model it allows the agents to be 1-competitive w.r.t. an optimal algorithm which does not know the location of the treasure, but is instantly notified of agent failures. In the black holes model (where there is no deterministic solution for non-communicating agents even in the presence of a single black hole) we show a lower bound of 2f + 1 and an upper bound of 4f + 1 for the number of agents needed to solve Treasure Hunt in presence of up to f black holes, as well as partial results about the hunt time in the presence of few black holes.
Cite as

Stefan Dobrev, Rastislav Královic, and Dana Pardubská. Treasure Hunt with Barely Communicating Agents. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dobrev_et_al:LIPIcs.OPODIS.2017.14,
  author =	{Dobrev, Stefan and Kr\'{a}lovic, Rastislav and Pardubsk\'{a}, Dana},
  title =	{{Treasure Hunt with Barely Communicating Agents}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-061-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{95},
  editor =	{Aspnes, James and Bessani, Alysson and Felber, Pascal and Leit\~{a}o, Jo\~{a}o},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.14},
  URN =		{urn:nbn:de:0030-drops-86346},
  doi =		{10.4230/LIPIcs.OPODIS.2017.14},
  annote =	{Keywords: parallel exhaustive search, treasure hunt, fault-tolerant search, weak coordination, black holes}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2016.59
Advice Complexity of the Online Induced Subgraph Problem

Authors: Dennis Komm, Rastislav Královic, Richard Královic, and Christian Kudahl

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract
Several well-studied graph problems aim to select a largest (or smallest) induced subgraph with a given property of the input graph. Examples include maximum independent set, maximum planar graph, maximum clique, minimum feedback vertex set, and many others. In online versions of these problems, the vertices of the graph are presented in an adversarial order, and with each vertex, the online algorithm must irreversibly decide whether to include it into the constructed subgraph, based only on the subgraph induced by the vertices presented so far. We study the properties that are common to all these problems by investigating a generalized problem: for an arbitrary but fixed hereditary property pi, find some maximal induced subgraph having pi. We investigate this problem from the point of view of advice complexity, i.e., we ask how some additional information about the yet unrevealed parts of the input can influence the solution quality. We evaluate the information in a quantitative way by considering the best possible advice of given size that describes the unknown input. Using a result from Boyar et al. [STACS 2015, LIPIcs 30], we give a tight trade-off relationship stating that, for inputs of length n, roughly n/c bits of advice are both needed and sufficient to obtain a solution with competitive ratio c, regardless of the choice of pi, for any c (possibly a function of n). This complements the results from Bartal et al. [SIAM Journal on Computing 36(2), 2006] stating that, without any advice, even a randomized algorithm cannot achieve a competitive ratio better than Omega(n^{1-log_{4}3-o(1)}). Surprisingly, for a given cohereditary property pi and the objective to find a minimum subgraph having pi, the advice complexity varies significantly with the choice of pi. We also consider a preemptive online model, inspired by some applications mainly in networking and scheduling, where the decision of the algorithm is not completely irreversible. In particular, the algorithm may discard some vertices previously assigned to the constructed set, but discarded vertices cannot be reinserted into the set. We show that, for the maximum induced subgraph problem, preemption does not significantly help by giving a lower bound of Omega(n/(c^2log c)) on the bits of advice that are needed to obtain competitive ratio c, where c is any increasing function bounded from above by sqrt(n/log n). We also give a linear lower bound for c close to 1.
Cite as

Dennis Komm, Rastislav Královic, Richard Královic, and Christian Kudahl. Advice Complexity of the Online Induced Subgraph Problem. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 59:1-59:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{komm_et_al:LIPIcs.MFCS.2016.59,
  author =	{Komm, Dennis and Kr\'{a}lovic, Rastislav and Kr\'{a}lovic, Richard and Kudahl, Christian},
  title =	{{Advice Complexity of the Online Induced Subgraph Problem}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{59:1--59:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.59},
  URN =		{urn:nbn:de:0030-drops-64713},
  doi =		{10.4230/LIPIcs.MFCS.2016.59},
  annote =	{Keywords: online algorithms, advice complexity, induced subgraph problem}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.470
Randomized Online Algorithms with High Probability Guarantees

Authors: Dennis Komm, Rastislav Královic, Richard Královic, and Tobias Mömke

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

Abstract
We study the relationship between the competitive ratio and the tail distribution of randomized online problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like paging, k-server and metrical task systems on finite metrics, and show that for these problems it is possible to obtain, given an algorithm with constant expected competitive ratio, another algorithm that achieves the same solution quality up to an arbitrarily small constant error with high probability; the "high probability" statement is in terms of the optimal cost. Furthermore, we show that our assumptions are tight in the sense that removing any of them allows for a counterexample to the theorem.
Cite as

Dennis Komm, Rastislav Královic, Richard Královic, and Tobias Mömke. Randomized Online Algorithms with High Probability Guarantees. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 470-481, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{komm_et_al:LIPIcs.STACS.2014.470,
  author =	{Komm, Dennis and Kr\'{a}lovic, Rastislav and Kr\'{a}lovic, Richard and M\"{o}mke, Tobias},
  title =	{{Randomized Online Algorithms with High Probability Guarantees}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{470--481},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.470},
  URN =		{urn:nbn:de:0030-drops-44803},
  doi =		{10.4230/LIPIcs.STACS.2014.470},
  annote =	{Keywords: Online Algorithms, Randomization, High Probability}
}
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