5 Search Results for "Vesel�, Pavel"


Document
Approximation Guarantees for Shortest Superstrings: Simpler and Better

Authors: Matthias Englert, Nicolaos Matsakis, and Pavel Veselý

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)


Abstract
The Shortest Superstring problem is an NP-hard problem, in which given as input a set of strings, we are looking for a string of minimum length that contains all input strings as substrings. The Greedy Conjecture (Tarhio and Ukkonen, 1988) states that the GREEDY algorithm, which repeatedly merges the two strings of maximum overlap, is 2-approximate. We have recently shown (STOC 2022) that the approximation guarantee of GREEDY is at most (13+√{57})/6 ≈ 3.425. Before that, the best established upper bound for this was 3.5 by Kaplan and Shafrir (IPL 2005), which improved upon the upper bound of 4 by Blum et al. (STOC 1991). To derive our previous result, we established two incomparable upper bounds on the overlap sum of all cycle-closing edges in an optimal cycle cover and utilized lemmas of Blum et al. We improve the more involved one of the two bounds and, at the same time, make its proof more straightforward. This results in an improved approximation guarantee of (√{67}+2)/3 ≈ 3.396 for GREEDY. Additionally, our result implies an algorithm for the Shortest Superstring problem having an approximation guarantee of (√{67}+14)/9 ≈ 2.466, improving slightly upon the previously best guarantee of (√{57}+37)/18 ≈ 2.475 (STOC 2022).

Cite as

Matthias Englert, Nicolaos Matsakis, and Pavel Veselý. Approximation Guarantees for Shortest Superstrings: Simpler and Better. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 29:1-29:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{englert_et_al:LIPIcs.ISAAC.2023.29,
  author =	{Englert, Matthias and Matsakis, Nicolaos and Vesel\'{y}, Pavel},
  title =	{{Approximation Guarantees for Shortest Superstrings: Simpler and Better}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{29:1--29:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.29},
  URN =		{urn:nbn:de:0030-drops-193319},
  doi =		{10.4230/LIPIcs.ISAAC.2023.29},
  annote =	{Keywords: Shortest Superstring problem, Approximation Algorithms}
}
Document
Track A: Algorithms, Complexity and Games
Streaming Algorithms for Geometric Steiner Forest

Authors: Artur Czumaj, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý

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


Abstract
We consider an important generalization of the Steiner tree problem, the Steiner forest problem, in the Euclidean plane: the input is a multiset X ⊆ ℝ², partitioned into k color classes C₁, C₂, …, Cₖ ⊆ X. The goal is to find a minimum-cost Euclidean graph G such that every color class Cᵢ is connected in G. We study this Steiner forest problem in the streaming setting, where the stream consists of insertions and deletions of points to X. Each input point x ∈ X arrives with its color color(x) ∈ [k], and as usual for dynamic geometric streams, the input is restricted to the discrete grid {0, …, Δ}². We design a single-pass streaming algorithm that uses poly(k ⋅ log Δ) space and time, and estimates the cost of an optimal Steiner forest solution within ratio arbitrarily close to the famous Euclidean Steiner ratio α₂ (currently 1.1547 ≤ α₂ ≤ 1.214). This approximation guarantee matches the state of the art bound for streaming Steiner tree, i.e., when k = 1. Our approach relies on a novel combination of streaming techniques, like sampling and linear sketching, with the classical Arora-style dynamic-programming framework for geometric optimization problems, which usually requires large memory and has so far not been applied in the streaming setting. We complement our streaming algorithm for the Steiner forest problem with simple arguments showing that any finite approximation requires Ω(k) bits of space.

Cite as

Artur Czumaj, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý. Streaming Algorithms for Geometric Steiner Forest. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 47:1-47:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2022.47,
  author =	{Czumaj, Artur and Jiang, Shaofeng H.-C. and Krauthgamer, Robert and Vesel\'{y}, Pavel},
  title =	{{Streaming Algorithms for Geometric Steiner Forest}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{47:1--47:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.47},
  URN =		{urn:nbn:de:0030-drops-163880},
  doi =		{10.4230/LIPIcs.ICALP.2022.47},
  annote =	{Keywords: Steiner forest, streaming, sublinear algorithms, dynamic programming}
}
Document
Track A: Algorithms, Complexity and Games
Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop

Authors: Antonios Antoniadis, Matthias Englert, Nicolaos Matsakis, and Pavel Veselý

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


Abstract
We consider the problem of managing the buffer of a shared-memory switch that transmits packets of unit value. A shared-memory switch consists of an input port, a number of output ports, and a buffer with a specific capacity. In each time step, an arbitrary number of packets arrive at the input port, each packet designated for one output port. Each packet is added to the queue of the respective output port. If the total number of packets exceeds the capacity of the buffer, some packets have to be irrevocably rejected. At the end of each time step, each output port transmits a packet in its queue and the goal is to maximize the number of transmitted packets. The Longest Queue Drop (LQD) online algorithm accepts any arriving packet to the buffer. However, if this results in the buffer exceeding its memory capacity, then LQD drops a packet from the back of whichever queue is currently the longest, breaking ties arbitrarily. The LQD algorithm was first introduced in 1991, and is known to be 2-competitive since 2001. Although LQD remains the best known online algorithm for the problem and is of practical interest, determining its true competitiveness is a long-standing open problem. We show that LQD is 1.707-competitive, establishing the first (2-ε) upper bound for the competitive ratio of LQD, for a constant ε > 0.

Cite as

Antonios Antoniadis, Matthias Englert, Nicolaos Matsakis, and Pavel Veselý. Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 17:1-17:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{antoniadis_et_al:LIPIcs.ICALP.2021.17,
  author =	{Antoniadis, Antonios and Englert, Matthias and Matsakis, Nicolaos and Vesel\'{y}, Pavel},
  title =	{{Breaking the Barrier Of 2 for the Competitiveness of Longest Queue Drop}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{17:1--17:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.17},
  URN =		{urn:nbn:de:0030-drops-140864},
  doi =		{10.4230/LIPIcs.ICALP.2021.17},
  annote =	{Keywords: buffer management, online scheduling, online algorithms, longest queue drop}
}
Document
Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices

Authors: Pavel Dvorák, Andreas Emil Feldmann, Dušan Knop, Tomáš Masarík, Tomáš Toufar, and Pavel Veselý

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)


Abstract
We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This problem has been extensively studied from the viewpoint of approximation and also parametrization. In particular, on one hand Steiner Tree is known to be APX-hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (Steiner vertices) in the optimum solution. In contrast to this we give an efficient parameterized approximation scheme (EPAS), which circumvents both hardness results. Moreover, our methods imply the existence of a polynomial size approximate kernelization scheme (PSAKS) for the considered parameter. We further study the parameterized approximability of other variants of Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of these an EPAS is likely to exist for the studied parameter: for Steiner Forest an easy observation shows that the problem is APX-hard, even if the input graph contains no Steiner vertices. For Directed Steiner Tree we prove that computing a constant approximation for this parameter is W[1]-hard. Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree. Also we prove that there is an EPAS and a PSAKS for Steiner Forest if in addition to the number of Steiner vertices, the number of connected components of an optimal solution is considered to be a parameter.

Cite as

Pavel Dvorák, Andreas Emil Feldmann, Dušan Knop, Tomáš Masarík, Tomáš Toufar, and Pavel Veselý. Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{dvorak_et_al:LIPIcs.STACS.2018.26,
  author =	{Dvor\'{a}k, Pavel and Feldmann, Andreas Emil and Knop, Du\v{s}an and Masar{\'\i}k, Tom\'{a}\v{s} and Toufar, Tom\'{a}\v{s} and Vesel\'{y}, Pavel},
  title =	{{Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{26:1--26:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.26},
  URN =		{urn:nbn:de:0030-drops-85158},
  doi =		{10.4230/LIPIcs.STACS.2018.26},
  annote =	{Keywords: Steiner Tree, Steiner Forest, Approximation Algorithms, Parameterized Algorithms, Lossy Kernelization}
}
Document
Online Packet Scheduling with Bounded Delay and Lookahead

Authors: Martin Böhm, Marek Chrobak, Lukasz Jez, Fei Li, Jirí Sgall, and Pavel Veselý

Published in: LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)


Abstract
We study the online bounded-delay packet scheduling problem (PacketScheduling), where packets of unit size arrive at a router over time and need to be transmitted over a network link. Each packet has two attributes: a non-negative weight and a deadline for its transmission. The objective is to maximize the total weight of the transmitted packets. This problem has been well studied in the literature, yet its optimal competitive ratio remains unknown: the best upper bound is 1.828 [Englert and Westermann, SODA 2007], still quite far from the best lower bound of phi approx 1.618 [Hajek, CISS 2001; Andelman et al, SODA 2003; Chin and Fung, Algorithmica, 2003]. In the variant of PacketScheduling with s-bounded instances, each packet can be scheduled in at most s consecutive slots, starting at its release time. The lower bound of phi applies even to the special case of 2-bounded instances, and a phi-competitive algorithm for 3-bounded instances was given in [Chin et al, JDA, 2006]. Improving that result, and addressing a question posed by Goldwasser [SIGACT News, 2010], we present a phi-competitive algorithm for 4-bounded instances. We also study a variant of PacketScheduling where an online algorithm has the additional power of 1-lookahead, knowing at time t which packets will arrive at time t+1. For PacketScheduling with 1-lookahead restricted to 2-bounded instances, we present an online algorithm with competitive ratio frac{1}{2}(sqrt{13} - 1) approx 1.303 and we prove a nearly tight lower bound of frac{1}{4}(1 + sqrt{17}) approx 1.281.

Cite as

Martin Böhm, Marek Chrobak, Lukasz Jez, Fei Li, Jirí Sgall, and Pavel Veselý. Online Packet Scheduling with Bounded Delay and Lookahead. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bohm_et_al:LIPIcs.ISAAC.2016.21,
  author =	{B\"{o}hm, Martin and Chrobak, Marek and Jez, Lukasz and Li, Fei and Sgall, Jir{\'\i} and Vesel\'{y}, Pavel},
  title =	{{Online Packet Scheduling with Bounded Delay and Lookahead}},
  booktitle =	{27th International Symposium on Algorithms and Computation (ISAAC 2016)},
  pages =	{21:1--21:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-026-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{64},
  editor =	{Hong, Seok-Hee},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.21},
  URN =		{urn:nbn:de:0030-drops-67901},
  doi =		{10.4230/LIPIcs.ISAAC.2016.21},
  annote =	{Keywords: buffer management, online scheduling, online algorithm, lookahead}
}
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