5 Search Results for "Auger, Nicolas"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.31
Delaunay Triangulations with Predictions

Authors: Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set P of n points in the plane and a triangulation G that serves as a "prediction" of the Delaunay triangulation, we would like to use G to compute the correct Delaunay triangulation DT(P) more quickly when G is "close" to DT(P). We obtain a variety of results of this type, under different deterministic and probabilistic settings, including the following: 1) Define D to be the number of edges in G that are not in DT(P). We present a deterministic algorithm to compute DT(P) from G in O(n + Dlog³ n) time, and a randomized algorithm in O(n+Dlog n) expected time, the latter of which is optimal in terms of D. 2) Let R be a random subset of the edges of DT(P), where each edge is chosen independently with probability ρ. Suppose G is any triangulation of P that contains R. We present an algorithm to compute DT(P) from G in O(nlog log n + nlog(1/ρ)) time with high probability. 3) Define d_{vio} to be the maximum number of points of P strictly inside the circumcircle of a triangle in G (the number is 0 if G is equal to DT(P)). We present a deterministic algorithm to compute DT(P) from G in O(nlog^*n + nlog d_{vio}) time. We also obtain results in similar settings for related problems such as 2D Euclidean minimum spanning trees, and hope that our work will open up a fruitful line of future research.
Cite as

Sergio Cabello, Timothy M. Chan, and Panos Giannopoulos. Delaunay Triangulations with Predictions. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 31:1-31:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cabello_et_al:LIPIcs.ITCS.2026.31,
  author =	{Cabello, Sergio and Chan, Timothy M. and Giannopoulos, Panos},
  title =	{{Delaunay Triangulations with Predictions}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{31:1--31:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.31},
  URN =		{urn:nbn:de:0030-drops-253186},
  doi =		{10.4230/LIPIcs.ITCS.2026.31},
  annote =	{Keywords: Delaunay Triangulation, Minimum Spanning Tree, Algorithms with Predictions}
}
Document
DOI: 10.4230/LIPIcs.CPM.2025.8
Branch Prediction Analysis of Morris-Pratt and Knuth-Morris-Pratt Algorithms

Authors: Cyril Nicaud, Carine Pivoteau, and Stéphane Vialette

Published in: LIPIcs, Volume 331, 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)

Abstract
We investigate the classical Morris-Pratt and Knuth-Morris-Pratt pattern matching algorithms from the perspective of computer architecture, focusing on the effects of incorporating a simple branch prediction mechanism into the computational model. Assuming a fixed pattern and a random text, we derive precise estimates for the number of branch mispredictions incurred by these algorithms when using local predictors. Our analysis relies on tools from automata theory and Markov chains, offering a theoretical framework that can be extended to other text processing algorithms and more sophisticated branch prediction strategies.
Cite as

Cyril Nicaud, Carine Pivoteau, and Stéphane Vialette. Branch Prediction Analysis of Morris-Pratt and Knuth-Morris-Pratt Algorithms. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nicaud_et_al:LIPIcs.CPM.2025.8,
  author =	{Nicaud, Cyril and Pivoteau, Carine and Vialette, St\'{e}phane},
  title =	{{Branch Prediction Analysis of Morris-Pratt and Knuth-Morris-Pratt Algorithms}},
  booktitle =	{36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-369-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{331},
  editor =	{Bonizzoni, Paola and M\"{a}kinen, Veli},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2025.8},
  URN =		{urn:nbn:de:0030-drops-231027},
  doi =		{10.4230/LIPIcs.CPM.2025.8},
  annote =	{Keywords: Pattern matching, branch prediction, transducers, average case complexity, Markov chains}
}
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.
Cite as

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.STACS.2016.12
Good Predictions Are Worth a Few Comparisons

Authors: Nicolas Auger, Cyril Nicaud, and Carine Pivoteau

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
Most modern processors are heavily parallelized and use predictors to guess the outcome of conditional branches, in order to avoid costly stalls in their pipelines. We propose predictor-friendly versions of two classical algorithms: exponentiation by squaring and binary search in a sorted array. These variants result in less mispredictions on average, at the cost of an increased number of operations. These theoretical results are supported by experimentations that show that our algorithms perform significantly better than the standard ones, for primitive data types.
Cite as

Nicolas Auger, Cyril Nicaud, and Carine Pivoteau. Good Predictions Are Worth a Few Comparisons. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{auger_et_al:LIPIcs.STACS.2016.12,
  author =	{Auger, Nicolas and Nicaud, Cyril and Pivoteau, Carine},
  title =	{{Good Predictions Are Worth a Few Comparisons}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.12},
  URN =		{urn:nbn:de:0030-drops-57135},
  doi =		{10.4230/LIPIcs.STACS.2016.12},
  annote =	{Keywords: branch misses, binary search, exponentiation by squaring, Markov chains}
}
Document
DOI: 10.4230/LITES-v002-i002-a001
From Dataflow Specification to Multiprocessor Partitioned Time-triggered Real-time Implementation

Authors: Thomas Carle, Dumitru Potop-Butucaru, Yves Sorel, and David Lesens

Published in: LITES, Volume 2, Issue 2 (2015). Leibniz Transactions on Embedded Systems, Volume 2, Issue 2

Abstract
Our objective is to facilitate the development of complex time-triggered systems by automating the allocation and scheduling steps. We show that full automation is possible while taking into account the elements of complexity needed by a complex embedded control system. More precisely, we consider deterministic functional specifications provided (as often in an industrial setting) by means of synchronous data-flow models with multiple modes and multiple relative periods. We first extend this functional model with an original real-time characterization that takes advantage of our time-triggered framework to provide a simpler representation of complex end-to-end flow requirements. We also extend our specifications with additional non-functional properties specifying partitioning, allocation, and preemptability constraints. Then, we provide novel algorithms for the off-line scheduling of these extended specifications onto partitioned time-triggered architectures à la ARINC 653. The main originality of our work is that it takes into account at the same time multiple complexity elements: various types of non-functional properties (real-time, partitioning, allocation, preemptability) and functional specifications with conditional execution and multiple modes. Allocation of time slots/windows to partitions can be fully or partially provided, or synthesized by our tool. Our algorithms allow the automatic allocation and scheduling onto multi-processor (distributed) systems with a global time base, taking into account communication costs. We demonstrate our technique on a model of space flight software system with strong real-time determinism requirements.
Cite as

Thomas Carle, Dumitru Potop-Butucaru, Yves Sorel, and David Lesens. From Dataflow Specification to Multiprocessor Partitioned Time-triggered Real-time Implementation. In LITES, Volume 2, Issue 2 (2015). Leibniz Transactions on Embedded Systems, Volume 2, Issue 2, pp. 01:1-01:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@Article{carle_et_al:LITES-v002-i002-a001,
  author =	{Carle, Thomas and Potop-Butucaru, Dumitru and Sorel, Yves and Lesens, David},
  title =	{{From Dataflow Specification to Multiprocessor Partitioned Time-triggered Real-time Implementation}},
  journal =	{Leibniz Transactions on Embedded Systems},
  pages =	{01:1--01:30},
  ISSN =	{2199-2002},
  year =	{2015},
  volume =	{2},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LITES-v002-i002-a001},
  URN =		{urn:nbn:de:0030-drops-192540},
  doi =		{10.4230/LITES-v002-i002-a001},
  annote =	{Keywords: Time-triggered, Off-line real-time scheduling, Temporal partitioning}
}
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