Nondeterministic Graph Searching: From Pathwidth to Treewidth

We introduce nondeterministic graph searching with a controlled amount of nondeterminism and show how this new tool can be used in algorithm design and combinatorial analysis applying to both pathwidth and treewidth. We prove equivalence between this game-theoretic approach and graph decompositions called q -branched tree decompositions, which can be interpreted as a parameterized version of tree decompositions. Path decomposition and (standard) tree decomposition are two extreme cases of q-branched tree decompositions. The equivalence between nondeterministic graph searching and q-branched tree decomposition enables us to design an exact (exponential time) algorithm computing q-branched treewidth for all q≥0, which is thus valid for both treewidth and pathwidth. This algorithm performs as fast as the best known exact algorithm for pathwidth. Conversely, this equivalence also enables us to design a lower bound on the amount of nondeterminism required to search a graph with the minimum number of searchers. Additional support of F.V. Fomin by the Research Council of Norway. Additional supports of P. Fraigniaud from the INRIA Project “Grand Large”, and from the Project PairAPair of the ACI “Masse de Données”. Additional supports of N. Nisse from the Project Fragile of the ACI “Sécurité & Informatique”.     

Labeling Schemes for Tree Representation

This paper deals with compact label-based representations for trees. Consider an n-node undirected connected graph G with a predefined numbering on the ports of each node. The all-ports tree labeling ℒ _all gives each node v of G a label containing the port numbers of all the tree edges incident to v. The upward tree labeling ℒ _up labels each node v by the number of the port leading from v to its parent in the tree. Our measure of interest is the worst case and total length of the labels used by the scheme, denoted M _up (T) and S _up (T) for ℒ _up and M _all (T) and S _all (T) for ℒ _all . The problem studied in this paper is the following: Given a graph G and a predefined port labeling for it, with the ports of each node v numbered by 0,…,deg (v)−1, select a rooted spanning tree for G minimizing (one of) these measures. We show that the problem is polynomial for M _up (T), S _up (T) and S _all (T) but NP-hard for M _all (T) (even for 3-regular planar graphs). We show that for every graph G and port labeling there exists a spanning tree T for which S _up (T)=O(nlog log n). We give a tight bound of O(n) in the cases of complete graphs with arbitrary labeling and arbitrary graphs with symmetric port labeling. We conclude by discussing some applications for our tree representation schemes. A preliminary version of this paper has appeared in the proceedings of the 7th International Workshop on Distributed Computing (IWDC), Kharagpur, India, December 27–30, 2005, as part of Cohen, R. et al.: Labeling schemes for tree representation. In: Proceedings of 7th International Workshop on Distributed Computing (IWDC), Lecture Notes of Computer Science, vol. 3741, pp. 13–24 (2005). R. Cohen supported by the Pacific Theaters Foundation. P. Fraigniaud and D. Ilcinkas supported by the project “PairAPair” of the ACI Masses de Données, the project “Fragile” of the ACI Sécurité et Informatique, and by the project “Grand Large” of INRIA. A. Korman supported in part by an Aly Kaufman fellowship. D. Peleg supported in part by a grant from the Israel Science Foundation.     

Assessment of Digital Elevation Model (DEM) aggregation methods for hydrological modeling: Lake Chad basin,Africa

Digital Elevation Models (DEMs) are used to compute the hydro-geomorphological variables required by distributed hydrological models. However, the resolution of the most precise DEMs is too fine to run these models over regional watersheds. DEMs therefore need to be aggregated to coarser resolutions, affecting both the representation of the land surface and the hydrological simulations. In the present paper, six algorithms (mean, median, mode, nearest neighbour, maximum and minimum) are used to aggregate the Shuttle Radar Topography Mission (SRTM) DEM from 3″ (90 m) to 5′ (10 km) in order to simulate the water balance of the Lake Chad basin (2.5 Mkm²). Each of these methods is assessed with respect to selected hydro-geomorphological properties that influence Terrestrial Hydrology Model with Biogeochemistry (THMB) simulations, namely the drainage network, the Lake Chad bottom topography and the floodplain extent.The results show that mean and median methods produce a smoother representation of the topography. This smoothing involves the removing of the depressions governing the floodplain dynamics (floodplain area<5000 km²) but it eliminates the spikes and wells responsible for deviations regarding the drainage network. By contrast, using other aggregation methods, a rougher relief representation enables the simulation of a higher floodplain area (>14,000 km² with the maximum or nearest neighbour) but results in anomalies concerning the drainage network. An aggregation procedure based on a variographic analysis of the SRTM data is therefore suggested. This consists of preliminary filtering of the 3″ DEM in order to smooth spikes and wells, then resampling to 5′ via the nearest neighbour method so as to preserve the representation of depressions. With the resulting DEM, the drainage network, the Lake Chad bathymetric curves and the simulated floodplain hydrology are consistent with the observations (3% underestimation for simulated evaporation volumes).     

Action Recognition Using a Bio-Inspired Feedforward Spiking Network

We propose a bio-inspired feedforward spiking network modeling two brain areas dedicated to motion (V1 and MT), and we show how the spiking output can be exploited in a computer vision application: action recognition. In order to analyze spike trains, we consider two characteristics of the neural code: mean firing rate of each neuron and synchrony between neurons. Interestingly, we show that they carry some relevant information for the action recognition application. We compare our results to Jhuang et al. (Proceedings of the 11th international conference on computer vision, pp. 1–8, 2007) on the Weizmann database. As a conclusion, we are convinced that spiking networks represent a powerful alternative framework for real vision applications that will benefit from recent advances in computational neuroscience.     

Investigating the usability of real-time scheduling theory with the Cheddar project

This article deals with real-time critical systems modelling and verification. Real-time scheduling theory provides algebraic methods and algorithms in order to make timing constraints verifications of these systems. Nevertheless, many industrial projects do not perform analysis with real-time scheduling theory even if demand for use of this theory is large and the industrial application field is wide (avionics, aerospace, automotive, autonomous systems, …). The Cheddar project investigates why real-time scheduling theory is not used and how its usability can be increased. The project was launched at the University of Brest in 2002. In Lecture Notes on Computer Sciences, vol. 5026, pp. 240–253, 2008, we have presented a short overview of this project. This article is an extended presentation of the Cheddar project, its contributions and also its ongoing works.     

Using online simulation in Holonic manufacturing systems

This paper deals with the use of online simulation on Holonic manufacturing systems. Concepts needed for the use of online simulation in a classical hierarchical system were already defined, the observer being the central one. The behavior's differences between both classes of systems are studied to determine the best way to adapt these concepts to this new environment. In the product resource order staff approach (PROSA) reference architecture, staff holons were chosen to welcome the simulation models and the observer. An application on an industrial sized Holonic manufacturing system is described to demonstrate the validity of the approach.     

Formal Proofs of Rounding Error Bounds

Floating-point arithmetic is a very efficient solution to perform computations in the real field. However, it induces rounding errors making results computed in floating-point differ from what would be computed with reals. Although numerical analysis gives tools to bound such differences, the proofs involved can be painful, hence error prone. We thus investigate the ability of a proof assistant like Coq to mechanically check such proofs. We demonstrate two different results involving matrices, which are pervasive among numerical algorithms, and show that a large part of the development effort can be shared between them.     

Multi-contact vertical ladder climbing with an HRP-2 humanoid

We describe the research and the integration methods we developed to make the HRP-2 humanoid robot climb vertical industrial-norm ladders. We use our multi-contact planner and multi-objective closed-loop control formulated as a QP (quadratic program). First, a set of contacts to climb the ladder is planned off-line (automatically or by the user). These contacts are provided as an input for a finite state machine. The latter builds supplementary tasks that account for geometric uncertainties and specific grasps procedures to be added to the QP controller. The latter provides instant desired states in terms of joint accelerations and contact forces to be tracked by the embedded low-level motor controllers. Our trials revealed that hardware changes are necessary, and parts of software must be made more robust. Yet, we confirmed that HRP-2 has the kinematic and power capabilities to climb real industrial ladders, such as those found in nuclear power plants and large scale manufacturing factories (e.g. aircraft, shipyard) and construction sites.     

Periodic event‐triggered observation and control for nonlinear Lipschitz systems using impulsive observers

In this paper, we investigate the observation and stabilization problems for a class of nonlinear Lipschitz systems, subject to network constraints, and partial state knowledge. In order to address these problems, an impulsive observer is designed, making use of the event‐triggered technique in order to diminish the network communications. Sufficient conditions are given to ensure a milder version of the separation principle for these systems, controlled via an event‐triggered controller. The proposed observer ensures practical state estimation, while the corresponding dynamic controller ensures practical stabilization. The sampling and the data transmission are carried out asynchronously. The dynamic controller is tested in simulation on a flexible joint. Copyright © 2017 John Wiley & Sons, Ltd.     

A Declarative Approach to Network Device Configuration Correctness

Configuration Logic (CL) is a formal language that allows a network engineer to express constraints in terms of the actual parameters found in the configuration of network devices. We present an efficient algorithm that can automatically check a pool of devices for conformance to a set of CL constraints; moreover, this algorithm can point to the part of the configuration responsible for the error when a constraint is violated. Contrary to other validation approaches that require dumping the configuration of the whole network to a central location in order to be verified, we also present an algorithm that analyzes the correct formulas and greatly helps reduce the amount of data that need to be transferred to that central location, pushing as much of the evaluation of the formula locally on each device. The procedure is also backwards-compatible, in such a way that a device that does not (or only partially) supports a local evaluation may simply return a subset or all of its configuration. These capabilities have been integrated into a network management tool called ValidMaker.