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Documents authored by Jugé, Vincent

Document
DOI: 10.4230/LIPIcs.AofA.2024.23
The Alternating Normal Form of Braids and Its Minimal Automaton

Authors: Vincent Jugé and June Roupin

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
The alternating normal form of braids is a well-known normal form on standard braid monoids. This normal form is regular: the language it identifies with is regular. We give a characterisation of the minimal automaton of this language and compute its size, both in terms of number of states and of transitions, depending on the number of generators of the monoid.
Cite as

Vincent Jugé and June Roupin. The Alternating Normal Form of Braids and Its Minimal Automaton. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 23:1-23:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{juge_et_al:LIPIcs.AofA.2024.23,
  author =	{Jug\'{e}, Vincent and Roupin, June},
  title =	{{The Alternating Normal Form of Braids and Its Minimal Automaton}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{23:1--23:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.23},
  URN =		{urn:nbn:de:0030-drops-204587},
  doi =		{10.4230/LIPIcs.AofA.2024.23},
  annote =	{Keywords: Automata, braids, enumeration, normal forms}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.68
Galloping in Fast-Growth Natural Merge Sorts

Authors: Elahe Ghasemi, Vincent Jugé, and Ghazal Khalighinejad

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

Abstract
We study the impact of sub-array merging routines on merge-based sorting algorithms. More precisely, we focus on the galloping sub-routine that TimSort uses to merge monotonic (non-decreasing) sub-arrays, hereafter called runs, and on the impact on the number of element comparisons performed if one uses this sub-routine instead of a naive merging routine. The efficiency of TimSort and of similar sorting algorithms has often been explained by using the notion of runs and the associated run-length entropy. Here, we focus on the related notion of dual runs, which was introduced in the 1990s, and the associated dual run-length entropy. We prove, for this complexity measure, results that are similar to those already known when considering standard run-induced measures: in particular, TimSort requires only 𝒪(n + n log(σ)) element comparisons to sort arrays of length n with σ distinct values. In order to do so, we introduce new notions of fast- and middle-growth for natural merge sorts (i.e., algorithms based on merging runs). By using these notions, we prove that several merge sorting algorithms, provided that they use TimSort’s galloping sub-routine for merging runs, are as efficient as TimSort at sorting arrays with low run-induced or dual-run-induced complexities.
Cite as

Elahe Ghasemi, Vincent Jugé, and Ghazal Khalighinejad. Galloping in Fast-Growth Natural Merge Sorts. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 68:1-68:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ghasemi_et_al:LIPIcs.ICALP.2022.68,
  author =	{Ghasemi, Elahe and Jug\'{e}, Vincent and Khalighinejad, Ghazal},
  title =	{{Galloping in Fast-Growth Natural Merge Sorts}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{68:1--68:19},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.68},
  URN =		{urn:nbn:de:0030-drops-164098},
  doi =		{10.4230/LIPIcs.ICALP.2022.68},
  annote =	{Keywords: Sorting algorithms, Merge sorting algorithms, Analysis of algorithms}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.8
Reduction Ratio of the IS-Algorithm: Worst and Random Cases

Authors: Vincent Jugé

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
We study the IS-algorithm, a well-known linear-time algorithm for computing the suffix array of a word. This algorithm relies on transforming the input word w into another word, called the reduced word of w, that will be at least twice shorter; then, the algorithm recursively computes the suffix array of the reduced word. In this article, we study the reduction ratio of the IS-algorithm, i.e., the ratio between the lengths of the input word and the word obtained after reducing k times the input word. We investigate both worst cases, in which we find precise results, and random cases, where we prove some strong convergence phenomena. Finally, we prove that, if the input word is a randomly chosen word of length n, we should not expect much more than log(log(n)) recursive function calls.
Cite as

Vincent Jugé. Reduction Ratio of the IS-Algorithm: Worst and Random Cases. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{juge:LIPIcs.CPM.2022.8,
  author =	{Jug\'{e}, Vincent},
  title =	{{Reduction Ratio of the IS-Algorithm: Worst and Random Cases}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.8},
  URN =		{urn:nbn:de:0030-drops-161357},
  doi =		{10.4230/LIPIcs.CPM.2022.8},
  annote =	{Keywords: Word combinatorics, Suffix array, IS algorithm}
}
Document
DOI: 10.4230/LIPIcs.CPM.2022.21
Permutation Pattern Matching for Doubly Partially Ordered Patterns

Authors: Laurent Bulteau, Guillaume Fertin, Vincent Jugé, and Stéphane Vialette

Published in: LIPIcs, Volume 223, 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)

Abstract
We study in this paper the Doubly Partially Ordered Pattern Matching (or DPOP Matching) problem, a natural extension of the Permutation Pattern Matching problem. Permutation Pattern Matching takes as input two permutations σ and π, and asks whether there exists an occurrence of σ in π; whereas DPOP Matching takes two partial orders P_v and P_p defined on the same set X and a permutation π, and asks whether there exist |X| elements in π whose values (resp., positions) are in accordance with P_v (resp., P_p). Posets P_v and P_p aim at relaxing the conditions formerly imposed by the permutation σ, since σ yields a total order on both positions and values. Our problem being NP-hard in general (as Permutation Pattern Matching is), we consider restrictions on several parameters/properties of the input, e.g., bounding the size of the pattern, assuming symmetry of the posets (i.e., P_v and P_p are identical), assuming that one partial order is a total (resp., weak) order, bounding the length of the longest chain/anti-chain in the posets, or forbidding specific patterns in π. For each such restriction, we provide results which together give a(n almost) complete landscape for the algorithmic complexity of the problem.
Cite as

Laurent Bulteau, Guillaume Fertin, Vincent Jugé, and Stéphane Vialette. Permutation Pattern Matching for Doubly Partially Ordered Patterns. In 33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 223, pp. 21:1-21:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bulteau_et_al:LIPIcs.CPM.2022.21,
  author =	{Bulteau, Laurent and Fertin, Guillaume and Jug\'{e}, Vincent and Vialette, St\'{e}phane},
  title =	{{Permutation Pattern Matching for Doubly Partially Ordered Patterns}},
  booktitle =	{33rd Annual Symposium on Combinatorial Pattern Matching (CPM 2022)},
  pages =	{21:1--21:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-234-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{223},
  editor =	{Bannai, Hideo and Holub, Jan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2022.21},
  URN =		{urn:nbn:de:0030-drops-161481},
  doi =		{10.4230/LIPIcs.CPM.2022.21},
  annote =	{Keywords: Partial orders, Permutations, Pattern Matching, Algorithmic Complexity, Parameterized Complexity}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.26
Finite Bisimulations for Dynamical Systems with Overlapping Trajectories

Authors: Béatrice Bérard, Patricia Bouyer, and Vincent Jugé

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Having a finite bisimulation is a good feature for a dynamical system, since it can lead to the decidability of the verification of reachability properties. We investigate a new class of o-minimal dynamical systems with very general flows, where the classical restrictions on trajectory intersections are partly lifted. We identify conditions, that we call Finite and Uniform Crossing: When Finite Crossing holds, the time-abstract bisimulation is computable and, under the stronger Uniform Crossing assumption, this bisimulation is finite and definable.
Cite as

Béatrice Bérard, Patricia Bouyer, and Vincent Jugé. Finite Bisimulations for Dynamical Systems with Overlapping Trajectories. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{berard_et_al:LIPIcs.CSL.2018.26,
  author =	{B\'{e}rard, B\'{e}atrice and Bouyer, Patricia and Jug\'{e}, Vincent},
  title =	{{Finite Bisimulations for Dynamical Systems with Overlapping Trajectories}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.26},
  URN =		{urn:nbn:de:0030-drops-96932},
  doi =		{10.4230/LIPIcs.CSL.2018.26},
  annote =	{Keywords: Reachability properties, dynamical systems, o-minimal structures, intersecting trajectories, finite bisimulations}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.4
On the Worst-Case Complexity of TimSort

Authors: Nicolas Auger, Vincent Jugé, Cyril Nicaud, and Carine Pivoteau

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
TimSort is an intriguing sorting algorithm designed in 2002 for Python, whose worst-case complexity was announced, but not proved until our recent preprint. In fact, there are two slightly different versions of TimSort that are currently implemented in Python and in Java respectively. We propose a pedagogical and insightful proof that the Python version runs in O(n log n). The approach we use in the analysis also applies to the Java version, although not without very involved technical details. As a byproduct of our study, we uncover a bug in the Java implementation that can cause the sorting method to fail during the execution. We also give a proof that Python's TimSort running time is in O(n + n log rho), where rho is the number of runs (i.e. maximal monotonic sequences), which is quite a natural parameter here and part of the explanation for the good behavior of TimSort on partially sorted inputs.
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Nicolas Auger, Vincent Jugé, Cyril Nicaud, and Carine Pivoteau. On the Worst-Case Complexity of TimSort. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{auger_et_al:LIPIcs.ESA.2018.4,
  author =	{Auger, Nicolas and Jug\'{e}, Vincent and Nicaud, Cyril and Pivoteau, Carine},
  title =	{{On the Worst-Case Complexity of TimSort}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.4},
  URN =		{urn:nbn:de:0030-drops-94678},
  doi =		{10.4230/LIPIcs.ESA.2018.4},
  annote =	{Keywords: Sorting algorithms, Merge sorting algorithms, TimSort, Analysis of algorithms}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2017.31
Unbounded Product-Form Petri Nets

Authors: Patricia Bouyer, Serge Haddad, and Vincent Jugé

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract
Computing steady-state distributions in infinite-state stochastic systems is in general a very difficult task. Product-form Petri nets are those Petri nets for which the steady-state distribution can be described as a natural product corresponding, up to a normalising constant, to an exponentiation of the markings. However, even though some classes of nets are known to have a product-form distribution, computing the normalising constant can be hard. The class of (closed) \Pi^3-nets has been proposed in an earlier work, for which it is shown that one can compute the steady-state distribution efficiently. However these nets are bounded. In this paper, we generalise queuing Markovian networks and closed \Pi^3-nets to obtain the class of open \Pi^3-nets, that generate infinite-state systems. We show interesting properties of these nets: (1) we prove that liveness can be decided in polynomial time, and that reachability in live \Pi^3-nets can be decided in polynomial time; (2) we show that we can decide ergodicity of such nets in polynomial time as well; (3) we provide a pseudo-polynomial time algorithm to compute the normalising constant.
Cite as

Patricia Bouyer, Serge Haddad, and Vincent Jugé. Unbounded Product-Form Petri Nets. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{bouyer_et_al:LIPIcs.CONCUR.2017.31,
  author =	{Bouyer, Patricia and Haddad, Serge and Jug\'{e}, Vincent},
  title =	{{Unbounded Product-Form Petri Nets}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.31},
  URN =		{urn:nbn:de:0030-drops-77957},
  doi =		{10.4230/LIPIcs.CONCUR.2017.31},
  annote =	{Keywords: Performance evaluation, infinite-state systems, Petri nets, steady-state distribution}
}
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