Schnyder woods for higher genus triangulated surfaces, with applications to encoding

Schnyder woods are a well-known combinatorial structure for plane triangulations, which yields a decomposition into 3 spanning trees. We extend here definitions and algorithms for Schnyder woods to closed orientable surfaces of arbitrary genus. In particular, we describe a method to traverse a triangulation of genus $g$ and compute a so-called $g$-Schnyder wood on the way. As an application, we give a procedure to encode a triangulation of genus $g$ and $n$ vertices in $4n+O(g \log(n))$ bits. This matches the worst-case encoding rate of Edgebreaker in positive genus. All the algorithms presented here have execution time $O((n+g)g)$, hence are linear when the genus is fixed.Comment: 27 pages, to appear in a special issue of Discrete and Computational Geometr

Canonical ordering for graphs on the cylinder, with applications to periodic straight-line drawings on the flat cylinder and torus

We extend the notion of canonical ordering (initially developed for planar triangulations and 3-connected planar maps) to cylindric (essentially simple) triangulations and more generally to cylindric (essentially internally) $3$-connected maps. This allows us to extend the incremental straight-line drawing algorithm of de Fraysseix, Pach and Pollack (in the triangulated case) and of Kant (in the $3$-connected case) to this setting. Precisely, for any cylindric essentially internally $3$-connected map $G$ with $n$ vertices, we can obtain in linear time a periodic (in $x$) straight-line drawing of $G$ that is crossing-free and internally (weakly) convex, on a regular grid $\mathbb{Z}/w\mathbb{Z}\times[0..h]$, with $w\leq 2n$ and $h\leq n(2d+1)$, where $d$ is the face-distance between the two boundaries. This also yields an efficient periodic drawing algorithm for graphs on the torus. Precisely, for any essentially $3$-connected map $G$ on the torus (i.e., $3$-connected in the periodic representation) with $n$ vertices, we can compute in linear time a periodic straight-line drawing of $G$ that is crossing-free and (weakly) convex, on a periodic regular grid $\mathbb{Z}/w\mathbb{Z}\times\mathbb{Z}/h\mathbb{Z}$, with $w\leq 2n$ and $h\leq 1+2n(c+1)$, where $c$ is the face-width of $G$. Since $c\leq\sqrt{2n}$, the grid area is $O(n^{5/2})$.Comment: 37 page

Periodic planar straight-frame drawings with polynomial resolution

International audienceWe present a new algorithm to compute periodic (planar) straight-line drawings of toroidal graphs. Our algorithm is the first to achieve two important aesthetic criteria: the drawing fits in a straight rectangular frame, and the grid area is polynomial, precisely the grid size is O(n 4 × n 4). This solves one of the main open problems in a recent paper by Duncan et al. [3]

Schnyder woods for higher genus triangulated surfaces

The final version of this extended abstract has been published in "Discrete and Computational Geometry (2009)"International audienceSchnyder woods are a well known combinatorial structure for planar graphs, which yields a decomposition into 3 vertex-spanning trees. Our goal is to extend definitions and algorithms for Schnyder woods designed for planar graphs (corresponding to combinatorial surfaces with the topology of the sphere, i.e., of genus 0) to the more general case of graphs embedded on surfaces of arbitrary genus. First, we define a new traversal order of the vertices of a triangulated surface of genus g together with an orientation and coloration of the edges that extends the one proposed by Schnyder for the planar case. As a by-product we show how some recent schemes for compression and compact encoding of graphs can be extended to higher genus. All the algorithms presented here have linear time complexity

Canonical Ordering for Triangulations on the Cylinder, with Applications to Periodic Straight-line Drawings

International audienceWe extend the notion of canonical orderings to cylindric triangulations. This allows us to extend the incremental straight-line drawing algorithm of de Fraysseix, Pach and Pollack to this setting. Our algorithm yields in linear time a crossing-free straight-line drawing of a cylindric triangulation $G$ with $n$ vertices on a regular grid \mZ/w\mZ\times[0..h], with $w\leq 2n$ and $h\leq n(2d+1)$, where $d$ is the (graph-) distance between the two boundaries. As a by-product, we can also obtain in linear time a crossing-free straight-line drawing of a toroidal triangulation with $n$ vertices on a periodic regular grid \mZ/w\mZ\times\mZ/h\mZ, with $w\leq 2n$ and $h\leq 1+n(2c+1)$, where $c$ is the length of a shortest non-contractible cycle. Since $c\leq\sqrt{2n}$, the grid area is $O(n^{5/2})$. Our algorithms apply to any triangulation (whether on the cylinder or on the torus) that have no loops nor multiple edges in the periodic representation

Towards the automatic processing of Yongning Na (Sino-Tibetan): developing a 'light' acoustic model of the target language and testing 'heavyweight' models from five national languages

International audienceAutomatic speech processing technologies hold great potential to facilitate the urgent task of documenting the world's languages. The present research aims to explore the application of speech recognition tools to a little-documented language, with a view to facilitating processes of annotation, transcription and linguistic analysis. The target language is Yongning Na (a.k.a. Mosuo), an unwritten Sino-Tibetan language with less than 50,000 speakers. An acoustic model of Na was built using CMU Sphinx. In addition to this 'light' model, trained on a small data set (only 4 hours of speech from 1 speaker), 'heavyweight' models from five national languages (English, French, Chinese, Vietnamese and Khmer) were also applied to the same data. Preliminary results are reported, and perspectives for the long road ahead are outlined

Smartphone-based User Location Tracking in Indoor Environment

International audienceThis paper introduces our work in the framework of Track 3 of the IPIN 2016 Indoor Localization Competition, which addresses the smartphone-based tracking problem in an offline manner.Our approach splits the path-reconstruction into several smaller tasks, including building identification, floor identification, user direction and speed inference.For each task, a specific set of data from the provided log data is used.Evaluation is carried out using a cross validation scheme.To produce the robustness again noisy data, we combine several approaches into one on the basis of their testing results.By testing on the provided training data, we have a good accuracy on building and floor identification. For the task of tracking the user's position within the floor, the result is 10m at 3rd-quarter distance error after 3 minutes of walking

Smartphone-based user positioning in a multiple-user context with Wi-Fi and Bluetooth

In a multiuser context, the Bluetooth data from the smartphone could give an approximation of the distance between users. Meanwhile, the Wi-Fi data can be used to calculate the user's position directly. However, both the Wi-Fi-based position outputs and Bluetooth-based distances are affected by some degree of noise. In our work, we propose several approaches to combine the two types of outputs for improving the tracking accuracy in the context of collaborative positioning. The two proposed approaches attempt to build a model for measuring the errors of the Bluetooth output and Wi-Fi output. In a non-temporal approach, the model establishes the relationship in a specific interval of the Bluetooth output and Wi-Fi output. In a temporal approach, the error measurement model is expanded to include the time component between users' movement. To evaluate the performance of the two approaches, we collected the data from several multiuser scenarios in indoor environment. The results show that the proposed approaches could reach a distance error around 3.0m for 75 percent of time, which outperforms the positioning results of the standard Wi-Fi fingerprinting model.Comment: International Conference on Indoor Positioning and Indoor Navigation (IPIN), Sep 2018, Nantes, Franc

The Grenoble System for the Social Touch Challenge at ICMI 2015

International audienceNew technologies and especially robotics is going towards more natural user interfaces. Works have been done in different modality of interaction such as sight (visual computing), and audio (speech and audio recognition) but some other modalities are still less researched. The touch modality is one of the less studied in HRI but could be valuable for naturalistic interaction. However touch signals can vary in semantics. It is therefore necessary to be able to recognize touch gestures in order to make human-robot interaction even more natural.We propose a method to recognize touch gestures. This method was developed on the CoST corpus and then directly applied on the HAART dataset as a participation of the Social Touch Challenge at ICMI 2015.Our touch gesture recognition process is detailed in this article to make it reproducible by other research teams.Besides features set description, we manually filtered the training corpus to produce 2 datasets.For the challenge, we submitted 6 different systems.A Support Vector Machine and a Random Forest classifiers for the HAART dataset.For the CoST dataset, the same classifiers are tested in two conditions: using all or filtered training datasets.As reported by organizers, our systems have the best correct rate in this year's challenge (70.91% on HAART, 61.34% on CoST).Our performances are slightly better that other participants but stay under previous reported state-of-the-art results