2,145 research outputs found

    Intrusion Response Systems for the 5G Networks and Beyond: A New Joint Security-vs-QoS Optimization Approach

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    Network connectivity exposes the network infrastructure and assets to vulnerabilities that attackers can exploit. Protecting network assets against attacks requires the application of security countermeasures. Nevertheless, employing countermeasures incurs costs, such as monetary costs, along with time and energy to prepare and deploy the countermeasures. Thus, an Intrusion Response System (IRS) shall consider security and QoS costs when dynamically selecting the countermeasures to address the detected attacks. This has motivated us to formulate a joint Security-vs-QoS optimization problem to select the best countermeasures in an IRS. The problem is then transformed into a matching game-theoretical model. Considering the monetary costs and attack coverage constraints, we first derive the theoretical upper bound for the problem and later propose stable matching-based solutions to address the trade-off. The performance of the proposed solution, considering different settings, is validated over a series of simulations

    Classical and quantum algorithms for scaling problems

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    This thesis is concerned with scaling problems, which have a plethora of connections to different areas of mathematics, physics and computer science. Although many structural aspects of these problems are understood by now, we only know how to solve them efficiently in special cases.We give new algorithms for non-commutative scaling problems with complexity guarantees that match the prior state of the art. To this end, we extend the well-known (self-concordance based) interior-point method (IPM) framework to Riemannian manifolds, motivated by its success in the commutative setting. Moreover, the IPM framework does not obviously suffer from the same obstructions to efficiency as previous methods. It also yields the first high-precision algorithms for other natural geometric problems in non-positive curvature.For the (commutative) problems of matrix scaling and balancing, we show that quantum algorithms can outperform the (already very efficient) state-of-the-art classical algorithms. Their time complexity can be sublinear in the input size; in certain parameter regimes they are also optimal, whereas in others we show no quantum speedup over the classical methods is possible. Along the way, we provide improvements over the long-standing state of the art for searching for all marked elements in a list, and computing the sum of a list of numbers.We identify a new application in the context of tensor networks for quantum many-body physics. We define a computable canonical form for uniform projected entangled pair states (as the solution to a scaling problem), circumventing previously known undecidability results. We also show, by characterizing the invariant polynomials, that the canonical form is determined by evaluating the tensor network contractions on networks of bounded size

    Algorithms and complexity for approximately counting hypergraph colourings and related problems

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    The past decade has witnessed advancements in designing efficient algorithms for approximating the number of solutions to constraint satisfaction problems (CSPs), especially in the local lemma regime. However, the phase transition for the computational tractability is not known. This thesis is dedicated to the prototypical problem of this kind of CSPs, the hypergraph colouring. Parameterised by the number of colours q, the arity of each hyperedge k, and the vertex maximum degree Δ, this problem falls into the regime of LovĂĄsz local lemma when Δ â‰Č qᔏ. In prior, however, fast approximate counting algorithms exist when Δ â‰Č qᔏ/Âł, and there is no known inapproximability result. In pursuit of this, our contribution is two-folded, stated as follows. ‱ When q, k ≄ 4 are evens and Δ ≄ 5·qᔏ/ÂČ, approximating the number of hypergraph colourings is NP-hard. ‱ When the input hypergraph is linear and Δ â‰Č qᔏ/ÂČ, a fast approximate counting algorithm does exist

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Faster Discrete Convex Function Minimization with Predictions: The M-Convex Case

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    Recent years have seen a growing interest in accelerating optimization algorithms with machine-learned predictions. Sakaue and Oki (NeurIPS 2022) have developed a general framework that warm-starts the L-convex function minimization method with predictions, revealing the idea's usefulness for various discrete optimization problems. In this paper, we present a framework for using predictions to accelerate M-convex function minimization, thus complementing previous research and extending the range of discrete optimization algorithms that can benefit from predictions. Our framework is particularly effective for an important subclass called laminar convex minimization, which appears in many operations research applications. Our methods can improve time complexity bounds upon the best worst-case results by using predictions and even have potential to go beyond a lower-bound result

    Exploration autonome et efficiente de chantiers miniers souterrains inconnus avec un drone filaire

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    Abstract: Underground mining stopes are often mapped using a sensor located at the end of a pole that the operator introduces into the stope from a secure area. The sensor emits laser beams that provide the distance to a detected wall, thus creating a 3D map. This produces shadow zones and a low point density on the distant walls. To address these challenges, a research team from the UniversitĂ© de Sherbrooke is designing a tethered drone equipped with a rotating LiDAR for this mission, thus benefiting from several points of view. The wired transmission allows for unlimited flight time, shared computing, and real-time communication. For compatibility with the movement of the drone after tether entanglements, the excess length is integrated into an onboard spool, contributing to the drone payload. During manual piloting, the human factor causes problems in the perception and comprehension of a virtual 3D environment, as well as the execution of an optimal mission. This thesis focuses on autonomous navigation in two aspects: path planning and exploration. The system must compute a trajectory that maps the entire environment, minimizing the mission time and respecting the maximum onboard tether length. Path planning using a Rapidly-exploring Random Tree (RRT) quickly finds a feasible path, but the optimization is computationally expensive and the performance is variable and unpredictable. Exploration by the frontier method is representative of the space to be explored and the path can be optimized by solving a Traveling Salesman Problem (TSP) but existing techniques for a tethered drone only consider the 2D case and do not optimize the global path. To meet these challenges, this thesis presents two new algorithms. The first one, RRT-Rope, produces an equal or shorter path than existing algorithms in a significantly shorter computation time, up to 70% faster than the next best algorithm in a representative environment. A modified version of RRT-connect computes a feasible path, shortened with a deterministic technique that takes advantage of previously added intermediate nodes. The second algorithm, TAPE, is the first 3D cavity exploration method that focuses on minimizing mission time and unwound tether length. On average, the overall path is 4% longer than the method that solves the TSP, but the tether remains under the allowed length in 100% of the simulated cases, compared to 53% with the initial method. The approach uses a 2-level hierarchical architecture: global planning solves a TSP after frontier extraction, and local planning minimizes the path cost and tether length via a decision function. The integration of these two tools in the NetherDrone produces an intelligent system for autonomous exploration, with semi-autonomous features for operator interaction. This work opens the door to new navigation approaches in the field of inspection, mapping, and Search and Rescue missions.La cartographie des chantiers miniers souterrains est souvent rĂ©alisĂ©e Ă  l’aide d’un capteur situĂ© au bout d’une perche que l’opĂ©rateur introduit dans le chantier, depuis une zone sĂ©curisĂ©e. Le capteur Ă©met des faisceaux laser qui fournissent la distance Ă  un mur dĂ©tectĂ©, crĂ©ant ainsi une carte en 3D. Ceci produit des zones d’ombres et une faible densitĂ© de points sur les parois Ă©loignĂ©es. Pour relever ces dĂ©fis, une Ă©quipe de recherche de l’UniversitĂ© de Sherbrooke conçoit un drone filaire Ă©quipĂ© d’un LiDAR rotatif pour cette mission, bĂ©nĂ©ficiant ainsi de plusieurs points de vue. La transmission filaire permet un temps de vol illimitĂ©, un partage de calcul et une communication en temps rĂ©el. Pour une compatibilitĂ© avec le mouvement du drone lors des coincements du fil, la longueur excĂ©dante est intĂ©grĂ©e dans une bobine embarquĂ©e, qui contribue Ă  la charge utile du drone. Lors d’un pilotage manuel, le facteur humain entraĂźne des problĂšmes de perception et comprĂ©hension d’un environnement 3D virtuel, et d’exĂ©cution d’une mission optimale. Cette thĂšse se concentre sur la navigation autonome sous deux aspects : la planification de trajectoire et l’exploration. Le systĂšme doit calculer une trajectoire qui cartographie l’environnement complet, en minimisant le temps de mission et en respectant la longueur maximale de fil embarquĂ©e. La planification de trajectoire Ă  l’aide d’un Rapidly-exploring Random Tree (RRT) trouve rapidement un chemin rĂ©alisable, mais l’optimisation est coĂ»teuse en calcul et la performance est variable et imprĂ©visible. L’exploration par la mĂ©thode des frontiĂšres est reprĂ©sentative de l’espace Ă  explorer et le chemin peut ĂȘtre optimisĂ© en rĂ©solvant un Traveling Salesman Problem (TSP), mais les techniques existantes pour un drone filaire ne considĂšrent que le cas 2D et n’optimisent pas le chemin global. Pour relever ces dĂ©fis, cette thĂšse prĂ©sente deux nouveaux algorithmes. Le premier, RRT-Rope, produit un chemin Ă©gal ou plus court que les algorithmes existants en un temps de calcul jusqu’à 70% plus court que le deuxiĂšme meilleur algorithme dans un environnement reprĂ©sentatif. Une version modifiĂ©e de RRT-connect calcule un chemin rĂ©alisable, raccourci avec une technique dĂ©terministe qui tire profit des noeuds intermĂ©diaires prĂ©alablement ajoutĂ©s. Le deuxiĂšme algorithme, TAPE, est la premiĂšre mĂ©thode d’exploration de cavitĂ©s en 3D qui minimise le temps de mission et la longueur du fil dĂ©roulĂ©. En moyenne, le trajet global est 4% plus long que la mĂ©thode qui rĂ©sout le TSP, mais le fil reste sous la longueur autorisĂ©e dans 100% des cas simulĂ©s, contre 53% avec la mĂ©thode initiale. L’approche utilise une architecture hiĂ©rarchique Ă  2 niveaux : la planification globale rĂ©sout un TSP aprĂšs extraction des frontiĂšres, et la planification locale minimise le coĂ»t du chemin et la longueur de fil via une fonction de dĂ©cision. L’intĂ©gration de ces deux outils dans le NetherDrone produit un systĂšme intelligent pour l’exploration autonome, dotĂ© de fonctionnalitĂ©s semi-autonomes pour une interaction avec l’opĂ©rateur. Les travaux rĂ©alisĂ©s ouvrent la porte Ă  de nouvelles approches de navigation dans le domaine des missions d’inspection, de cartographie et de recherche et sauvetage

    Engineering Fast Algorithms for the Bottleneck Matching Problem

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    Algebraic combinatorial optimization on the degree of determinants of noncommutative symbolic matrices

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    We address the computation of the degrees of minors of a noncommutative symbolic matrix of form A[c]:=∑k=1mAktckxk, A[c] := \sum_{k=1}^m A_k t^{c_k} x_k, where AkA_k are matrices over a field K\mathbb{K}, xix_i are noncommutative variables, ckc_k are integer weights, and tt is a commuting variable specifying the degree. This problem extends noncommutative Edmonds' problem (Ivanyos et al. 2017), and can formulate various combinatorial optimization problems. Extending the study by Hirai 2018, and Hirai, Ikeda 2022, we provide novel duality theorems and polyhedral characterization for the maximum degrees of minors of A[c]A[c] of all sizes, and develop a strongly polynomial-time algorithm for computing them. This algorithm is viewed as a unified algebraization of the classical Hungarian method for bipartite matching and the weight-splitting algorithm for linear matroid intersection. As applications, we provide polynomial-time algorithms for weighted fractional linear matroid matching and linear optimization over rank-2 Brascamp-Lieb polytopes

    Approximating Min-Diameter: Standard and Bichromatic

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    The min-diameter of a directed graph GG is a measure of the largest distance between nodes. It is equal to the maximum min-distance dmin(u,v)d_{min}(u,v) across all pairs u,v∈V(G)u,v \in V(G), where dmin(u,v)=min⁥(d(u,v),d(v,u))d_{min}(u,v) = \min(d(u,v), d(v,u)). Our work provides a O(m1.426n0.288)O(m^{1.426}n^{0.288})-time 3/23/2-approximation algorithm for min-diameter in DAGs, and a faster O(m0.713n)O(m^{0.713}n)-time almost-3/23/2-approximation variant. (An almost-α\alpha-approximation algorithm determines the min-diameter to within a multiplicative factor of α\alpha plus constant additive error.) By a conditional lower bound result of [Abboud et al, SODA 2016], a better than 3/23/2-approximation can't be achieved in truly subquadratic time under the Strong Exponential Time Hypothesis (SETH), so our result is conditionally tight. We additionally obtain a new conditional lower bound for min-diameter approximation in general directed graphs, showing that under SETH, one cannot achieve an approximation factor below 2 in truly subquadratic time. We also present the first study of approximating bichromatic min-diameter, which is the maximum min-distance between oppositely colored vertices in a 2-colored graph.Comment: ESA 202

    Spatial-temporal domain charging optimization and charging scenario iteration for EV

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    Environmental problems have become increasingly serious around the world. With lower carbon emissions, Electric Vehicles (EVs) have been utilized on a large scale over the past few years. However, EVs are limited by battery capacity and require frequent charging. Currently, EVs suffer from long charging time and charging congestion. Therefore, EV charging optimization is vital to ensure drivers’ mobility. This study first presents a literature analysis of the current charging modes taxonomy to elucidate the advantages and disadvantages of different charging modes. In specific optimization, under plug-in charging mode, an Urgency First Charging (UFC) scheduling policy is proposed with collaborative optimization of the spatialtemporal domain. The UFC policy allows those EVs with charging urgency to get preempted charging services. As conventional plug-in charging mode is limited by the deployment of Charging Stations (CSs), this study further introduces and optimizes Vehicle-to-Vehicle (V2V) charging. This is aim to maximize the utilization of charging infrastructures and to balance the grid load. This proposed reservation-based V2V charging scheme optimizes pair matching of EVs based on minimized distance. Meanwhile, this V2V scheme allows more EVs get fully charged via minimized waiting time based parking lot allocation. Constrained by shortcomings (rigid location of CSs and slow charging power under V2V converters), a single charging mode can hardly meet a large number of parallel charging requests. Thus, this study further proposes a hybrid charging mode. This mode is to utilize the advantages of plug-in and V2V modes to alleviate the pressure on the grid. Finally, this study addresses the potential problems of EV charging with a view to further optimizing EV charging in subsequent studies
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