8 Search Results for "Královič, Rastislav"


Document
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
Finding Optimal Solutions With Neighborly Help

Authors: Elisabet Burjons, Fabian Frei, Edith Hemaspaandra, Dennis Komm, and David Wehner

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
Can we efficiently compute optimal solutions to instances of a hard problem from optimal solutions to neighboring (i.e., locally modified) instances? For example, can we efficiently compute an optimal coloring for a graph from optimal colorings for all one-edge-deleted subgraphs? Studying such questions not only gives detailed insight into the structure of the problem itself, but also into the complexity of related problems; most notably graph theory’s core notion of critical graphs (e.g., graphs whose chromatic number decreases under deletion of an arbitrary edge) and the complexity-theoretic notion of minimality problems (also called criticality problems, e.g., recognizing graphs that become 3-colorable when an arbitrary edge is deleted). We focus on two prototypical graph problems, Colorability and Vertex Cover. For example, we show that it is NP-hard to compute an optimal coloring for a graph from optimal colorings for all its one-vertex-deleted subgraphs, and that this remains true even when optimal solutions for all one-edge-deleted subgraphs are given. In contrast, computing an optimal coloring from all (or even just two) one-edge-added supergraphs is in P. We observe that Vertex Cover exhibits a remarkably different behavior, demonstrating the power of our model to delineate problems from each other more precisely on a structural level. Moreover, we provide a number of new complexity results for minimality and criticality problems. For example, we prove that Minimal-3-UnColorability is complete for DP (differences of NP sets), which was previously known only for the more amenable case of deleting vertices rather than edges. For Vertex Cover, we show that recognizing beta-vertex-critical graphs is complete for Theta_2^p (parallel access to NP), obtaining the first completeness result for a criticality problem for this class.

Cite as

Elisabet Burjons, Fabian Frei, Edith Hemaspaandra, Dennis Komm, and David Wehner. Finding Optimal Solutions With Neighborly Help. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 78:1-78:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{burjons_et_al:LIPIcs.MFCS.2019.78,
  author =	{Burjons, Elisabet and Frei, Fabian and Hemaspaandra, Edith and Komm, Dennis and Wehner, David},
  title =	{{Finding Optimal Solutions With Neighborly Help}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{78:1--78:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.78},
  URN =		{urn:nbn:de:0030-drops-110221},
  doi =		{10.4230/LIPIcs.MFCS.2019.78},
  annote =	{Keywords: Critical Graphs, Computational Complexity, Structural Self-Reducibility, Minimality Problems, Colorability, Vertex Cover, Satisfiability, Reoptimization, Advice}
}
Document
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
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
Complexity and Approximability of Parameterized MAX-CSPs

Authors: Holger Dell, Eun Jung Kim, Michael Lampis, Valia Mitsou, and Tobias Mömke

Published in: LIPIcs, Volume 43, 10th International Symposium on Parameterized and Exact Computation (IPEC 2015)


Abstract
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard CSPs, we want to decide whether this fraction equals one. The parameters we investigate are structural measures, such as the treewidth or the clique-width of the variable–constraint incidence graph of the CSP instance. We consider Max-CSPs with the constraint types AND, OR, PARITY, and MAJORITY, and with various parameters k. We attempt to fully classify them into the following three cases: 1. The exact optimum can be computed in FPT-time. 2. It is W[1]-hard to compute the exact optimum, but there is a randomized FPT approximation scheme (FPT-AS), which computes a (1-epsilon)-approximation in time f(k,epsilon) * poly(n). 3. There is no FPT-AS unless FPT=W[1]. For the corresponding standard CSPs, we establish FPT vs. W[1]-hardness results.

Cite as

Holger Dell, Eun Jung Kim, Michael Lampis, Valia Mitsou, and Tobias Mömke. Complexity and Approximability of Parameterized MAX-CSPs. In 10th International Symposium on Parameterized and Exact Computation (IPEC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 43, pp. 294-306, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{dell_et_al:LIPIcs.IPEC.2015.294,
  author =	{Dell, Holger and Kim, Eun Jung and Lampis, Michael and Mitsou, Valia and M\"{o}mke, Tobias},
  title =	{{Complexity and Approximability of Parameterized MAX-CSPs}},
  booktitle =	{10th International Symposium on Parameterized and Exact Computation (IPEC 2015)},
  pages =	{294--306},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-92-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{43},
  editor =	{Husfeldt, Thore and Kanj, Iyad},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2015.294},
  URN =		{urn:nbn:de:0030-drops-55910},
  doi =		{10.4230/LIPIcs.IPEC.2015.294},
  annote =	{Keywords: Approximation, Structural Parameters, Constraint Satisfaction}
}
Document
Games for Active XML Revisited

Authors: Martin Schuster and Thomas Schwentick

Published in: LIPIcs, Volume 31, 18th International Conference on Database Theory (ICDT 2015)


Abstract
The paper studies the rewriting mechanisms for intensional documents in the Active XML framework, abstracted in the form of active context-free games. The safe rewriting problem studied in this paper is to decide whether the first player, Juliet, has a winning strategy for a given game and (nested) word; this corresponds to a successful rewriting strategy for a given intensional document. The paper examines several extensions to active context-free games. The primary extension allows more expressive schemas (namely XML schemas and regular nested word languages) for both target and replacement languages and has the effect that games are played on nested words instead of (flat) words as in previous studies. Other extensions consider validation of input parameters of web services, and an alternative semantics based on insertion of service call results. In general, the complexity of the safe rewriting problem is highly intractable (doubly exponential time), but the paper identifies interesting tractable cases.

Cite as

Martin Schuster and Thomas Schwentick. Games for Active XML Revisited. In 18th International Conference on Database Theory (ICDT 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 31, pp. 60-75, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{schuster_et_al:LIPIcs.ICDT.2015.60,
  author =	{Schuster, Martin and Schwentick, Thomas},
  title =	{{Games for Active XML Revisited}},
  booktitle =	{18th International Conference on Database Theory (ICDT 2015)},
  pages =	{60--75},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-79-8},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{31},
  editor =	{Arenas, Marcelo and Ugarte, Mart{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2015.60},
  URN =		{urn:nbn:de:0030-drops-49773},
  doi =		{10.4230/LIPIcs.ICDT.2015.60},
  annote =	{Keywords: Active XML, Computational Complexity, Nested Words, Rewriting Games, Semistructured Data}
}
Document
Advice Complexity for a Class of Online Problems

Authors: Joan Boyar, Lene M. Favrholdt, Christian Kudahl, and Jesper W. Mikkelsen

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


Abstract
The advice complexity of an online problem is a measure of how much knowledge of the future an online algorithm needs in order to achieve a certain competitive ratio. We determine the advice complexity of a number of hard online problems including independent set, vertex cover, dominating set and several others. These problems are hard, since a single wrong answer by the online algorithm can have devastating consequences. For each of these problems, we show that \log\left(1+\frac{(c-1)^{c-1}}{c^{c}}\right)n=\Theta (n/c) bits of advice are necessary and sufficient (up to an additive term of O(\log n)) to achieve a competitive ratio of c. This is done by introducing a new string guessing problem related to those of Emek et al. (TCS 2011) and Böckenhauer et al. (TCS 2014). It turns out that this gives a powerful but easy-to-use method for providing both upper and lower bounds on the advice complexity of an entire class of online problems. Previous results of Halldórsson et al. (TCS 2002) on online independent set, in a related model, imply that the advice complexity of the problem is \Theta (n/c). Our results improve on this by providing an exact formula for the higher-order term. Böckenhauer et al. (ISAAC 2009) gave a lower bound of \Omega (n/c) and an upper bound of O((n\log c)/c) on the advice complexity of online disjoint path allocation. We improve on the upper bound by a factor of $\log c$. For the remaining problems, no bounds on their advice complexity were previously known.

Cite as

Joan Boyar, Lene M. Favrholdt, Christian Kudahl, and Jesper W. Mikkelsen. Advice Complexity for a Class of Online Problems. In 32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 30, pp. 116-129, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{boyar_et_al:LIPIcs.STACS.2015.116,
  author =	{Boyar, Joan and Favrholdt, Lene M. and Kudahl, Christian and Mikkelsen, Jesper W.},
  title =	{{Advice Complexity for a Class of Online Problems}},
  booktitle =	{32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)},
  pages =	{116--129},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.116},
  URN =		{urn:nbn:de:0030-drops-49086},
  doi =		{10.4230/LIPIcs.STACS.2015.116},
  annote =	{Keywords: online algorithms, advice complexity, asymmetric string guessing, advice complexity class AOC, covering designs}
}
Document
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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