5 Search Results for "Folwarczný, Lukáš"


Document
Track A: Algorithms, Complexity and Games
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)


Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.

Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
One-Way Functions vs. TFNP: Simpler and Improved

Authors: Lukáš Folwarczný, Mika Göös, Pavel Hubáček, Gilbert Maystre, and Weiqiang Yuan

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
Simon (1998) proved that it is impossible to construct collision-resistant hash functions from one-way functions using a black-box reduction. It is conjectured more generally that one-way functions do not imply, via a black-box reduction, the hardness of any total NP search problem (collision-resistant hash functions being just one such example). We make progress towards this conjecture by ruling out a large class of "single-query" reductions. In particular, we improve over the prior work of Hubáček et al. (2020) in two ways: our result is established via a novel simpler combinatorial technique and applies to a broader class of semi black-box reductions.

Cite as

Lukáš Folwarczný, Mika Göös, Pavel Hubáček, Gilbert Maystre, and Weiqiang Yuan. One-Way Functions vs. TFNP: Simpler and Improved. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{folwarczny_et_al:LIPIcs.ITCS.2024.50,
  author =	{Folwarczn\'{y}, Luk\'{a}\v{s} and G\"{o}\"{o}s, Mika and Hub\'{a}\v{c}ek, Pavel and Maystre, Gilbert and Yuan, Weiqiang},
  title =	{{One-Way Functions vs. TFNP: Simpler and Improved}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.50},
  URN =		{urn:nbn:de:0030-drops-195788},
  doi =		{10.4230/LIPIcs.ITCS.2024.50},
  annote =	{Keywords: TFNP, One-Way Functions, Oracle, Separation, Black-Box}
}
Document
TFNP Intersections Through the Lens of Feasible Disjunction

Authors: Pavel Hubáček, Erfan Khaniki, and Neil Thapen

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
The complexity class CLS was introduced by Daskalakis and Papadimitriou (SODA 2010) to capture the computational complexity of important TFNP problems solvable by local search over continuous domains and, thus, lying in both PLS and PPAD. It was later shown that, e.g., the problem of computing fixed points guaranteed by Banach’s fixed point theorem is CLS-complete by Daskalakis et al. (STOC 2018). Recently, Fearnley et al. (J. ACM 2023) disproved the plausible conjecture of Daskalakis and Papadimitriou that CLS is a proper subclass of PLS∩PPAD by proving that CLS = PLS∩PPAD. To study the possibility of other collapses in TFNP, we connect classes formed as the intersection of existing subclasses of TFNP with the phenomenon of feasible disjunction in propositional proof complexity; where a proof system has the feasible disjunction property if, whenever a disjunction F ∨ G has a small proof, and F and G have no variables in common, then either F or G has a small proof. Based on some known and some new results about feasible disjunction, we separate the classes formed by intersecting the classical subclasses PLS, PPA, PPAD, PPADS, PPP and CLS. We also give the first examples of proof systems which have the feasible interpolation property, but not the feasible disjunction property.

Cite as

Pavel Hubáček, Erfan Khaniki, and Neil Thapen. TFNP Intersections Through the Lens of Feasible Disjunction. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 63:1-63:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{hubacek_et_al:LIPIcs.ITCS.2024.63,
  author =	{Hub\'{a}\v{c}ek, Pavel and Khaniki, Erfan and Thapen, Neil},
  title =	{{TFNP Intersections Through the Lens of Feasible Disjunction}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{63:1--63:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.63},
  URN =		{urn:nbn:de:0030-drops-195917},
  doi =		{10.4230/LIPIcs.ITCS.2024.63},
  annote =	{Keywords: TFNP, feasible disjunction, proof complexity, TFNP intersection classes}
}
Document
PPP-Completeness and Extremal Combinatorics

Authors: Romain Bourneuf, Lukáš Folwarczný, Pavel Hubáček, Alon Rosen, and Nikolaj I. Schwartzbach

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
Many classical theorems in combinatorics establish the emergence of substructures within sufficiently large collections of objects. Well-known examples are Ramsey’s theorem on monochromatic subgraphs and the Erdős-Rado sunflower lemma. Implicit versions of the corresponding total search problems are known to be PWPP-hard under randomized reductions in the case of Ramsey’s theorem and PWPP-hard in the case of the sunflower lemma; here "implicit” means that the collection is represented by a poly-sized circuit inducing an exponentially large number of objects. We show that several other well-known theorems from extremal combinatorics - including Erdős-Ko-Rado, Sperner, and Cayley’s formula – give rise to complete problems for PWPP and PPP. This is in contrast to the Ramsey and Erdős-Rado problems, for which establishing inclusion in PWPP has remained elusive. Besides significantly expanding the set of problems that are complete for PWPP and PPP, our work identifies some key properties of combinatorial proofs of existence that can give rise to completeness for these classes. Our completeness results rely on efficient encodings for which finding collisions allows extracting the desired substructure. These encodings are made possible by the tightness of the bounds for the problems at hand (tighter than what is known for Ramsey’s theorem and the sunflower lemma). Previous techniques for proving bounds in TFNP invariably made use of structured algorithms. Such algorithms are not known to exist for the theorems considered in this work, as their proofs "from the book" are non-constructive.

Cite as

Romain Bourneuf, Lukáš Folwarczný, Pavel Hubáček, Alon Rosen, and Nikolaj I. Schwartzbach. PPP-Completeness and Extremal Combinatorics. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{bourneuf_et_al:LIPIcs.ITCS.2023.22,
  author =	{Bourneuf, Romain and Folwarczn\'{y}, Luk\'{a}\v{s} and Hub\'{a}\v{c}ek, Pavel and Rosen, Alon and Schwartzbach, Nikolaj I.},
  title =	{{PPP-Completeness and Extremal Combinatorics}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{22:1--22:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.22},
  URN =		{urn:nbn:de:0030-drops-175255},
  doi =		{10.4230/LIPIcs.ITCS.2023.22},
  annote =	{Keywords: total search problems, extremal combinatorics, PPP-completeness}
}
Document
Online Algorithms for Multi-Level Aggregation

Authors: Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, Marek Chrobak, Christoph Dürr, Lukas Folwarczny, Lukasz Jez, Jiri Sgall, Nguyen Kim Thang, and Pavel Vesely

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)


Abstract
In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and in supply-chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant competitive online algorithm for networks of arbitrary (fixed) number of levels. The competitive ratio is O(D^4*2^D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines. We include several additional results in the paper. We show that a standard lower-bound technique for MLAP, based on so-called Single-Phase instances, cannot give super-constant lower bounds (as a function of the tree depth). This result is established by giving an online algorithm with optimal competitive ratio 4 for such instances on arbitrary trees. We also study the MLAP variant when the tree is a path, for which we give a lower bound of 4 on the competitive ratio, improving the lower bound known for general MLAP. We complement this with a matching upper bound for the deadline setting.

Cite as

Marcin Bienkowski, Martin Böhm, Jaroslaw Byrka, Marek Chrobak, Christoph Dürr, Lukas Folwarczny, Lukasz Jez, Jiri Sgall, Nguyen Kim Thang, and Pavel Vesely. Online Algorithms for Multi-Level Aggregation. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bienkowski_et_al:LIPIcs.ESA.2016.12,
  author =	{Bienkowski, Marcin and B\"{o}hm, Martin and Byrka, Jaroslaw and Chrobak, Marek and D\"{u}rr, Christoph and Folwarczny, Lukas and Jez, Lukasz and Sgall, Jiri and Kim Thang, Nguyen and Vesely, Pavel},
  title =	{{Online Algorithms for Multi-Level Aggregation}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{12:1--12:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.12},
  URN =		{urn:nbn:de:0030-drops-63637},
  doi =		{10.4230/LIPIcs.ESA.2016.12},
  annote =	{Keywords: algorithmic aspects of networks, online algorithms, scheduling and resource allocation}
}
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