5 Search Results for "Klein, Dominik"


Document
Track A: Algorithms, Complexity and Games
Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time

Authors: Nick Fischer and Leo Wennmann

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


Abstract
In this work we revisit the elementary scheduling problem 1||∑ p_j U_j. The goal is to select, among n jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence without violating their due dates. This problem is NP-hard, but a classical algorithm by Lawler and Moore from the 60s solves this problem in pseudo-polynomial time O(nP), where P is the total processing time of all jobs. With the aim to develop best-possible pseudo-polynomial-time algorithms, a recent wave of results has improved Lawler and Moore’s algorithm for 1||∑ p_j U_j: First to time Õ(P^{7/4}) [Bringmann, Fischer, Hermelin, Shabtay, Wellnitz; ICALP'20], then to time Õ(P^{5/3}) [Klein, Polak, Rohwedder; SODA'23], and finally to time Õ(P^{7/5}) [Schieber, Sitaraman; WADS'23]. It remained an exciting open question whether these works can be improved further. In this work we develop an algorithm in near-linear time Õ(P) for the 1||∑ p_j U_j problem. This running time not only significantly improves upon the previous results, but also matches conditional lower bounds based on the Strong Exponential Time Hypothesis or the Set Cover Hypothesis and is therefore likely optimal (up to subpolynomial factors). Our new algorithm also extends to the case of m machines in time Õ(P^m). In contrast to the previous improvements, we take a different, more direct approach inspired by the recent reductions from Modular Subset Sum to dynamic string problems. We thereby arrive at a satisfyingly simple algorithm.

Cite as

Nick Fischer and Leo Wennmann. Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 64:1-64:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{fischer_et_al:LIPIcs.ICALP.2024.64,
  author =	{Fischer, Nick and Wennmann, Leo},
  title =	{{Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{64:1--64:15},
  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.2024.64},
  URN =		{urn:nbn:de:0030-drops-202079},
  doi =		{10.4230/LIPIcs.ICALP.2024.64},
  annote =	{Keywords: Scheduling, Fine-Grained Complexity, Dynamic Strings}
}
Document
Track A: Algorithms, Complexity and Games
Testing Spreading Behavior in Networks with Arbitrary Topologies

Authors: Augusto Modanese and Yuichi Yoshida

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


Abstract
Given the full topology of a network, how hard is it to test if it is evolving according to a local rule or is far from doing so? Inspired by the works of Goldreich and Ron (J. ACM, 2017) and Nakar and Ron (ICALP, 2021), we initiate the study of property testing in dynamic environments with arbitrary topologies. Our focus is on the simplest non-trivial rule that can be tested, which corresponds to the 1-BP rule of bootstrap percolation and models a simple spreading behavior: Every "infected" node stays infected forever, and each "healthy" node becomes infected if and only if it has at least one infected neighbor. Our results are subdivided into two main groups: - If we are testing a single time step of evolution, then the query complexity is O(Δ/ε) or Õ(√n/ε) (whichever is smaller), where Δ and n are the maximum degree of a node and the number of vertices in the underlying graph, respectively. We also give lower bounds for both one- and two-sided error testers that match our upper bounds up to Δ = o(√n) and Δ = O(n^{1/3}), respectively. If ε is constant, then the first of these also holds against adaptive testers. - When testing the environment over T time steps, we have two algorithms that need O(Δ^{T-1}/εT) and Õ(|E|/εT) queries, respectively, where E is the set of edges of the underlying graph. All of our algorithms are one-sided error, and all of them are also non-adaptive, with the single exception of the more complex Õ(√n/ε)-query tester for the case T = 2.

Cite as

Augusto Modanese and Yuichi Yoshida. Testing Spreading Behavior in Networks with Arbitrary Topologies. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 112:1-112:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{modanese_et_al:LIPIcs.ICALP.2024.112,
  author =	{Modanese, Augusto and Yoshida, Yuichi},
  title =	{{Testing Spreading Behavior in Networks with Arbitrary Topologies}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{112:1--112:20},
  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.2024.112},
  URN =		{urn:nbn:de:0030-drops-202554},
  doi =		{10.4230/LIPIcs.ICALP.2024.112},
  annote =	{Keywords: Property testing, bootstrap percolation, local phenomena, expander graphs}
}
Document
Hamiltonian Paths and Cycles in NP-Complete Puzzles

Authors: Marnix Deurloo, Mitchell Donkers, Mieke Maarse, Benjamin G. Rin, and Karen Schutte

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)


Abstract
We show that several pen-and-paper puzzles are NP-complete by giving polynomial-time reductions from the Hamiltonian path and Hamiltonian cycle problems on grid graphs with maximum degree 3. The puzzles include Dotchi Loop, Chains, Linesweeper, Arukone{}₃ (also called Numberlink₃), and Araf. In addition, we show that this type of proof can still be used to prove the NP-completeness of Dotchi Loop even when the available puzzle instances are heavily restricted. Together, these results suggest that this approach holds promise in general for finding NP-completeness proofs of many pen-and-paper puzzles.

Cite as

Marnix Deurloo, Mitchell Donkers, Mieke Maarse, Benjamin G. Rin, and Karen Schutte. Hamiltonian Paths and Cycles in NP-Complete Puzzles. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 11:1-11:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{deurloo_et_al:LIPIcs.FUN.2024.11,
  author =	{Deurloo, Marnix and Donkers, Mitchell and Maarse, Mieke and Rin, Benjamin G. and Schutte, Karen},
  title =	{{Hamiltonian Paths and Cycles in NP-Complete Puzzles}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{11:1--11:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.11},
  URN =		{urn:nbn:de:0030-drops-199199},
  doi =		{10.4230/LIPIcs.FUN.2024.11},
  annote =	{Keywords: Hamiltonicity, NP-completeness, complexity theory, pen-and-paper puzzles}
}
Document
Arimaa Is PSPACE-Hard

Authors: Benjamin G. Rin and Atze Schipper

Published in: LIPIcs, Volume 291, 12th International Conference on Fun with Algorithms (FUN 2024)


Abstract
Arimaa is a strategy board game developed in 2003 by Omar Syed, designed to be hard for AI to win because of its large branching factor. In this paper, its theoretical complexity is considered. We prove that Arimaa (suitably generalized to an n × n board) is PSPACE-hard. This result is found by reducing a known PSPACE-hard variant of Generalized Geography to a variant of Arimaa that we call Arimaa^′, which in turn is then reduced to (n × n) Arimaa. Since the game is easily seen to be solvable in exponential time, it follows that its complexity lies somewhere between being PSPACE-complete and EXPTIME-complete.

Cite as

Benjamin G. Rin and Atze Schipper. Arimaa Is PSPACE-Hard. In 12th International Conference on Fun with Algorithms (FUN 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 291, pp. 27:1-27:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{rin_et_al:LIPIcs.FUN.2024.27,
  author =	{Rin, Benjamin G. and Schipper, Atze},
  title =	{{Arimaa Is PSPACE-Hard}},
  booktitle =	{12th International Conference on Fun with Algorithms (FUN 2024)},
  pages =	{27:1--27:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-314-0},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{291},
  editor =	{Broder, Andrei Z. and Tamir, Tami},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2024.27},
  URN =		{urn:nbn:de:0030-drops-199359},
  doi =		{10.4230/LIPIcs.FUN.2024.27},
  annote =	{Keywords: Arimaa, complexity theory, PSPACE-hardness, board games, Generalized Geography}
}
Document
Maximal Completion

Authors: Dominik Klein and Nao Hirokawa

Published in: LIPIcs, Volume 10, 22nd International Conference on Rewriting Techniques and Applications (RTA'11) (2011)


Abstract
Given an equational system, completion procedures compute an equivalent and complete (terminating and confluent) term rewrite system. We present a very simple and efficient completion procedure, which is based on MaxSAT solving. Experiments show that the procedure is comparable to recent powerful completion tools.

Cite as

Dominik Klein and Nao Hirokawa. Maximal Completion. In 22nd International Conference on Rewriting Techniques and Applications (RTA'11). Leibniz International Proceedings in Informatics (LIPIcs), Volume 10, pp. 71-80, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)


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@InProceedings{klein_et_al:LIPIcs.RTA.2011.71,
  author =	{Klein, Dominik and Hirokawa, Nao},
  title =	{{Maximal Completion}},
  booktitle =	{22nd International Conference on Rewriting Techniques and Applications (RTA'11)},
  pages =	{71--80},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-30-9},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{10},
  editor =	{Schmidt-Schauss, Manfred},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2011.71},
  URN =		{urn:nbn:de:0030-drops-31295},
  doi =		{10.4230/LIPIcs.RTA.2011.71},
  annote =	{Keywords: Term Rewriting, Knuth-Bendix Completion, Multi-completion}
}
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