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Philippe Jacquet

Publications and source records attributed to Philippe Jacquet.

At least 19 recordsLinked to original sources
arXiv2026

Asymptotics of Parking Search in Hyperfractal Networks

We study the asymptotic behaviour of the distance to the first available parking slot in a recursive Manhattan street network endowed with a hyperfractal intensity structure, where slot-release events occur according to Poisson processes along the streets. We establish, by analysing the associated self-similar harmonic sums via Mellin-transform asymptotics, a power-law decay of the expected distance as the total intensity grows, with exponent equal to the inverse of the hyperfractal dimension. In particular, the scaling exponent depends only on the large-scale geometry of the network. We further prove that this exponent is robust under random multiplicative modulations of the street intensities: mild stochastic heterogeneity affects only the multiplicative constant. Similar scaling behaviour holds for the variance, the number of turns before parking, and for a jump-over variant of the search strategy.

math.PR↗
arXiv2025

Generating Random Hyperfractal Cities

This paper focuses on the challenge of interactively modeling street networks. In this work, we extend the simple fractal model, which is particularly useful for describing small cities or individual districts, by constructing random cities based on a tiling structure over which hyperfractals are distributed. This approach enables the connection of multiple hyperfractal districts, providing a more comprehensive urban representation. Furthermore, we demonstrate how this decomposition can be used to segment a city into distinct districts through fractal analysis. Finally, we present tools for the numerical generation of random cities following this model.

cs.IT↗
arXiv2025

BUBBLE-BLUE a multihop private network based on Bluetooth

The BUBBLE-BLUE (BB) project aims to create private Bluetooth bubbles on top of smartphones and to create a kind of terrestrial STARLINK network based on users smartphones.. In each private bubble, participants will be able to communicate autonomously, without recourse to private operator networks, neither data nor cellular, relying solely on the Bluetooth technology of smartphones. The routing strategy is based on dynamic Connected Dominant Sets (CDS). We present the specific features of a BB network as well as some simulation results on their routing performance.

cs.NI↗
arXiv2022

Depth-First Search performance in a random digraph with geometric outdegree distribution

We present an analysis of the depth-first search algorithm in a random digraph model with independent outdegrees having a geometric distribution. The results include asymptotic results for the depth profile of vertices, the height (maximum depth) and average depth, the number of trees in the forest, the size of the largest and second-largest trees, and the numbers of arcs of different types in the depth-first jungle. Most results are first order. For the height we show an asymptotic normal distribution. This analysis proposed by Donald Knuth in his next to appear volume of The Art of Computer Programming gives interesting insight in one of the most elegant and efficient algorithm for graph analysis due to Tarjan.

cs.DS↗
arXiv2021

Connecting flying backhauls of UAVs to enhance vehicular networks with fixed 5G NR infrastructure

This paper investigates moving networks of Unmanned Aerial Vehicles (UAVs), such as drones, as one of the innovative opportunities brought by the 5G. With a main purpose to extend connectivity and guarantee data rates, the drones require hovering locations due to limitations such as flight time and coverage surface. We provide analytic bounds on the requirements in terms of connectivity extension for vehicular networks served by fixed Enhanced Mobile BroadBand (eMBB) infrastructure, where both vehicular networks and infrastructures are modeled using stochastic and fractal geometry as a model for urban environment. We prove that assuming $n$ mobile nodes (distributed according to a hyperfractal distribution of dimension $d_F$) and an average of $ρ$ Next Generation NodeB (gNBs), distributed like an hyperfractal of dimension $d_r$ if $ρ=n^θ$ with $θ>d_r/4$ and letting $n$ tending to infinity (to reflect megalopolis cities), then the average fraction of mobile nodes not covered by a gNB tends to zero like $O\left(n^{-\frac{(d_F-2)}{d_r}(2θ-\frac{d_r}{2})}\right)$. Interestingly, we then prove that the average number of drones, needed to connect each mobile node not covered by gNBs is comparable to the number of isolated mobile nodes. We complete the characterisation by proving that when $θ<d_r/4$ the proportion of covered mobile nodes tends to zero. We provide insights on the intelligent placement of the "garage of drones", the home location of these nomadic infrastructure nodes, such as to minimize what we call the "flight-to-coverage time". We provide a fast procedure to select the relays that will be garages (and store drones) in order to minimize the number of garages and minimize the delay. Finally we confirm our analytical results using simulations carried out in Matlab.

cs.DC↗
arXiv2021

Characterizing the Energy Trade-Offs of End-to-End Vehicular Communications using an Hyperfractal Urban Modelling

We characterize trade-offs between the end-to-end communication delay and the energy in urban vehicular communications with infrastructure assistance. Our study exploits the self-similarity of the location of communication entities in cities by modeling them with an innovative model called "hyperfractal". We show that the hyperfractal model can be extended to incorporate road-side infrastructure and provide stochastic geometry tools to allow a rigorous analysis. We compute theoretical bounds for the end-to-end communication hop count considering two different energy-minimizing goals: either total accumulated energy or maximum energy per node. We prove that the hop count for an end-to-end transmission is bounded by $O(n^{1-α/(d_F-1)})$ where $α<1$ and $d_F>2$ is the fractal dimension of the mobile nodes process. This proves that for both constraints the energy decreases as we allow choosing routing paths of higher length. The asymptotic limit of the energy becomes significantly small when the number of nodes becomes asymptotically large. A lower bound on the network throughput capacity with constraints on path energy is also given. We show that our model fits real deployments where open data sets are available. The results are confirmed through simulations using different fractal dimensions in a Matlab simulator.

cs.DC↗
arXiv2020

On Feature Selection Using Anisotropic General Regression Neural Network

The presence of irrelevant features in the input dataset tends to reduce the interpretability and predictive quality of machine learning models. Therefore, the development of feature selection methods to recognize irrelevant features is a crucial topic in machine learning. Here we show how the General Regression Neural Network used with an anisotropic Gaussian Kernel can be used to perform feature selection. A number of numerical experiments are conducted using simulated data to study the robustness of the proposed methodology and its sensitivity to sample size. Finally, a comparison with four other feature selection methods is performed on several real world datasets.

stat.ML↗
arXiv2019

Blockchain moderated by empty blocks to reduce the energetic impact of crypto-moneys

While cryptocurrencies and blockchain applications continue to gain popularity, their energy cost is evidently becoming unsustainable. In most instances, the main cost comes from the required amount of energy for the Proof-of-Work, and this cost is inherent to the design. In addition, useless costs from discarded work (e.g., the so-called Forks) and lack of scalability (in number of users and in rapid transactions) limit their practical effectiveness. In this paper, we present an innovative scheme which eliminates the nonce and thus the burden of the Proof-of-Work which is the main cause of the energy waste in cryptocurrencies such as Bitcoin. We prove that our scheme guarantees a tunable and bounded average number of simultaneous mining whatever the size of the population in competition, thus by making the use of nonce-based techniques unnecessary, achieves scalability without the cost of consuming a large volume of energy. The technique used in the proof of our scheme is based on the analogy of the analysis of a green leader election. The additional difference with Proof-of-Work schemes (beyond the suppression of the nonce field that is triggering most of the waste), is the introduction of (what we denote as) "empty blocks" which aim are to call regular blocks following a staircase set of values. Our scheme reduces the risk of Forks and provides tunable scalability for the number of users and the speed of block generation. We also prove using game theoretical analysis that our scheme is resilient to unfair competitive investments (e.g., "51 percent" attack) and block nursing.

cs.CR↗
arXiv2019

Information Dissemination Speed in Delay Tolerant Urban Vehicular Networks in a Hyperfractal Setting

This paper studies the fundamental communication properties of urban vehicle networks by exploiting the self-similarity and hierarchical organization of modern cities. We use an innovative model called "hyperfractal" that captures the self-similarities of both the traffic and vehicle locations but avoids the extremes of regularity and randomness. We use analytical tools to derive theoretical upper and lower bounds for the information propagation speed in an urban delay tolerant network (i.e., a network that is disconnected at all time, and thus uses a store-carry-and-forward routing model). We prove that the average broadcast time behaves as $n^{1-δ}$ times a slowly varying function, where $δ$ depends on the precise fractal dimension. Furthermore, we show that the broadcast speedup is due in part to an interesting self-similar phenomenon, that we denote as {\em information teleportation}. This phenomenon arises as a consequence of the topology of the vehicle traffic, and triggers an acceleration of the broadcast time. We show that our model fits real cities where open traffic data sets are available. We present simulations confirming the validity of the bounds in multiple realistic settings, including scenarios with variable speed, using both QualNet and a discrete-event simulator in Matlab.

cs.NI↗
arXiv2018

Joint String Complexity for Markov Sources: Small Data Matters

String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings. String complexity finds a number of applications from capturing the richness of a language to finding similarities between two genome sequences. In this paper we analyze the joint string complexity when both strings are generated by Markov sources. We prove that the joint string complexity grows linearly (in terms of the string lengths) when both sources are statistically indistinguishable and sublinearly when sources are statistically not the same. Precise analysis of the joint string complexity turns out to be quite challenging requiring subtle singularity analysis and saddle point method over infinity many saddle points leading to novel oscillatory phenomena with single and double periodicities. To overcome these challenges, we apply powerful analytic techniques such as multivariate generating functions, multivariate depoissonization and Mellin transform, spectral matrix analysis, and complex asymptotic methods.

cs.IT↗
arXiv2017

Hamiltonian System Approach to Distributed Spectral Decomposition in Networks

Because of the significant increase in size and complexity of the networks, the distributed computation of eigenvalues and eigenvectors of graph matrices has become very challenging and yet it remains as important as before. In this paper we develop efficient distributed algorithms to detect, with higher resolution, closely situated eigenvalues and corresponding eigenvectors of symmetric graph matrices. We model the system of graph spectral computation as physical systems with Lagrangian and Hamiltonian dynamics. The spectrum of Laplacian matrix, in particular, is framed as a classical spring-mass system with Lagrangian dynamics. The spectrum of any general symmetric graph matrix turns out to have a simple connection with quantum systems and it can be thus formulated as a solution to a Schr\"odinger-type differential equation. Taking into account the higher resolution requirement in the spectrum computation and the related stability issues in the numerical solution of the underlying differential equation, we propose the application of symplectic integrators to the calculation of eigenspectrum. The effectiveness of the proposed techniques is demonstrated with numerical simulations on real-world networks of different sizes and complexities.

math.NA↗
arXiv2016

Average Size of a Suffix Tree for Markov Sources

We study a suffix tree built from a sequence generated by a Markovian source. Such sources are more realistic probabilistic models for text generation, data compression, molecular applications, and so forth. We prove that the average size of such a suffix tree is asymptotically equivalent to the average size of a trie built over $n$ independent sequences from the same Markovian source. This equivalence is only known for memoryless sources. We then derive a formula for the size of a trie under Markovian model to complete the analysis for suffix trees. We accomplish our goal by applying some novel techniques of analytic combinatorics on words also known as analytic pattern matching.

cs.DS↗
arXiv2012

Optimizing the Medium Access Control in Multi-hop Wireless Networks

We study the problem of geometric optimization of medium access control in multi-hop wireless network. We discuss the optimal placements of simultaneous transmitters in the network and our general framework allows us to evaluate the performance gains of highly managed medium access control schemes that would be required to implement these placements. In a wireless network consisting of randomly distributed nodes, our performance metrics are the optimum transmission range that achieves the most optimal tradeoff between the progress of packets in desired directions towards their respective destinations and the total number of transmissions required to transport packets to their destinations. We evaluate ALOHA based scheme where simultaneous transmitters are dispatched according to a uniform Poisson distribution and compare it with various grid pattern based schemes where simultaneous transmitters are positioned in specific regular patterns. Our results show that optimizing the medium access control in multi-hop network should take into account the parameters like signal-to-interference ratio threshold and attenuation coefficient. For instance, at typical values of signal-to-interference ratio threshold and attenuation coefficient, the most optimal scheme is based on triangular grid pattern and, under no fading channel model, the most optimal transmission range and network capacity are higher than the optimum transmission range and capacity achievable with ALOHA based scheme by factors of two and three respectively. Later on, we also identify the optimal medium access control schemes when signal-to-interference ratio threshold and attenuation coefficient approach the extreme values and discuss how fading impacts the performance of all schemes we evaluate in this article.

cs.IT↗
arXiv2012

An Overview of Local Capacity in Wireless Networks

This article introduces a metric for performance evaluation of medium access schemes in wireless ad hoc networks known as local capacity. Although deriving the end-to-end capacity of wireless ad hoc networks is a difficult problem, the local capacity framework allows us to quantify the average information rate received by a receiver node randomly located in the network. In this article, the basic network model and analytical tools are first discussed and applied to a simple network to derive the local capacity of various medium access schemes. Our goal is to identify the most optimal scheme and also to see how does it compare with more practical medium access schemes. We analyzed grid pattern schemes where simultaneous transmitters are positioned in a regular grid pattern, ALOHA schemes where simultaneous transmitters are dispatched according to a uniform Poisson distribution and exclusion schemes where simultaneous transmitters are dispatched according to an exclusion rule such as node coloring and carrier sense schemes. Our analysis shows that local capacity is optimal when simultaneous transmitters are positioned in a grid pattern based on equilateral triangles and our results show that this optimal local capacity is at most double the local capacity of ALOHA based scheme. Our results also show that node coloring and carrier sense schemes approach the optimal local capacity by an almost negligible difference. At the end, we also discuss the shortcomings in our model as well as future research directions.

cs.IT↗
arXiv2011

On the Throughput Capacity of Wireless Multi-hop Networks with ALOHA, Node Coloring and CSMA

We quantify the throughput capacity of wireless multi-hop networks with several medium access schemes. We analyze pure ALOHA scheme where simultaneous transmitters are dispatched according to a uniform Poisson distribution and exclusion schemes where simultaneous transmitters are dispatched according to an exclusion rule such as node coloring and carrier sense based schemes. We consider both no-fading and standard Rayleigh fading channel models. Our results show that, under no-fading, slotted ALOHA can achieve at least one-third (or half under Rayleigh fading) of the throughput capacity of node coloring scheme whereas carrier sense based scheme can achieve almost the same throughput capacity as node coloring.

cs.NI↗
arXiv2011

On the Optimal Transmission Scheme to Maximize Local Capacity in Wireless Networks

We study the optimal transmission scheme that maximizes the local capacity in two-dimensional (2D) wireless networks. Local capacity is defined as the average information rate received by a node randomly located in the network. Using analysis based on analytical and numerical methods, we show that maximum local capacity can be obtained if simultaneous emitters are positioned in a grid pattern based on equilateral triangles. We also compare this maximum local capacity with the local capacity of slotted ALOHA scheme and our results show that slotted ALOHA can achieve at least half of the maximum local capacity in wireless networks.

cs.NI↗
arXiv2011

Optimizing Local Capacity of Wireless Ad Hoc Networks

In this work, we evaluate local capacity of wireless ad hoc networks with several medium access protocols and identify the most optimal protocol. We define local capacity as the average information rate received by a receiver randomly located in the network. We analyzed grid pattern protocols where simultaneous transmitters are positioned in a regular grid pattern, pure ALOHA protocols where simultaneous transmitters are dispatched according to a uniform Poisson distribution and exclusion protocols where simultaneous transmitters are dispatched according to an exclusion rule such as node coloring and carrier sense protocols. Our analysis allows us to conjecture that local capacity is optimal when simultaneous transmitters are positioned in a grid pattern based on equilateral triangles and our results show that this optimal local capacity is at most double the local capacity of simple ALOHA protocol. Our results also show that node coloring and carrier sense protocols approach the optimal local capacity by an almost negligible difference.

cs.NI↗