3,848 research outputs found
Dynamic Connectivity in Disk Graphs
Let S ⊆ R2 be a set of n sites in the plane, so that every site s ∈ S has an associated
radius rs > 0. Let D(S) be the disk intersection graph defined by S, i.e., the graph
with vertex set S and an edge between two distinct sites s, t ∈ S if and only if the
disks with centers s, t and radii rs , rt intersect. Our goal is to design data structures
that maintain the connectivity structure of D(S) as sites are inserted and/or deleted
in S. First, we consider unit disk graphs, i.e., we fix rs = 1, for all sites s ∈ S.
For this case, we describe a data structure that has O(log2 n) amortized update time
and O(log n/ log log n) query time. Second, we look at disk graphs with bounded
radius ratio Ψ, i.e., for all s ∈ S, we have 1 ≤ rs ≤ Ψ, for a parameter Ψ that is
known in advance. Here, we not only investigate the fully dynamic case, but also the
incremental and the decremental scenario, where only insertions or only deletions of
sites are allowed. In the fully dynamic case, we achieve amortized expected update
time O(Ψ log4 n) and query time O(log n/ log log n). This improves the currently
best update time by a factor of Ψ. In the incremental case, we achieve logarithmic
dependency on Ψ, with a data structure that has O(α(n)) amortized query time and
O(log Ψ log4 n) amortized expected update time, where α(n) denotes the inverse Ackermann
function. For the decremental setting, we first develop an efficient decremental
disk revealing data structure: given two sets R and B of disks in the plane, we can delete
disks from B, and upon each deletion, we receive a list of all disks in R that no longer
intersect the union of B. Using this data structure, we get decremental data structures
with a query time of O(log n/ log log n) that supports deletions in O(n log Ψ log4 n)
overall expected time for disk graphs with bounded radius ratio Ψ and O(n log5 n)
overall expected time for disk graphs with arbitrary radii, assuming that the deletion
sequence is oblivious of the internal random choices of the data structures
Algorithms and complexity for approximately counting hypergraph colourings and related problems
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 Lovász local lemma when Δ ≲ qᵏ. In prior, however, fast approximate counting algorithms exist when Δ ≲ qᵏ/³, 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·qᵏ/², approximating the number of hypergraph colourings is NP-hard.
• When the input hypergraph is linear and Δ ≲ qᵏ/², a fast approximate counting algorithm does exist
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Dynamic scene understanding: Pedestrian tracking from aerial devices.
Multiple Object Tracking (MOT) is the problem that involves following the trajectory of multiple objects in a sequence, generally a video. Pedestrians are among the most interesting subjects to track and recognize for many purposes such as surveillance, and safety. In the recent years, Unmanned Aerial Vehicles (UAV’s) have been viewed as a viable option for monitoring public areas, as they provide a low-cost method of data collection while covering large and difficult-to-reach areas. In this thesis, we present an online pedestrian tracking and re-identification from aerial devices framework. This framework is based on learning a compact directional statistic distribution (von-Mises-Fisher distribution) for each person ID using a deep convolutional neural network. The distribution characteristics are trained to be invariant to clothes appearances and to transformations. In real world scenarios, during deployment, new pedestrian and objects can appear in the scene and the model should detect them as Out Of Distribution (OOD). Thus, our frameworks also includes an OOD detection adopted from [16] called Virtual Outlier Synthetic (VOS), that detects OOD based on synthesising virtual outlier in the embedding space in an online manner. To validate, analyze and compare our approach, we use a large real benchmark data that contain detection tracking and identity annotations. These targets are captured at different viewing angles, different places, and different times by a ”DJI Phantom 4” drone. We validate the effectiveness of the proposed framework by evaluating their detection, tracking and long term identification performance as well as classification performance between In Distribution (ID) and OOD. We show that the the proposed methods in the framework can learn models that achieve their objectives
Mining Butterflies in Streaming Graphs
This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection.
sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals
Multi-objective resource optimization in space-aerial-ground-sea integrated networks
Space-air-ground-sea integrated (SAGSI) networks are envisioned to connect satellite, aerial, ground,
and sea networks to provide connectivity everywhere and all the time in sixth-generation (6G) networks. However, the success of SAGSI networks is constrained by several challenges including
resource optimization when the users have diverse requirements and applications. We present a
comprehensive review of SAGSI networks from a resource optimization perspective. We discuss
use case scenarios and possible applications of SAGSI networks. The resource optimization discussion considers the challenges associated with SAGSI networks. In our review, we categorized
resource optimization techniques based on throughput and capacity maximization, delay minimization, energy consumption, task offloading, task scheduling, resource allocation or utilization,
network operation cost, outage probability, and the average age of information, joint optimization (data rate difference, storage or caching, CPU cycle frequency), the overall performance of
network and performance degradation, software-defined networking, and intelligent surveillance
and relay communication. We then formulate a mathematical framework for maximizing energy
efficiency, resource utilization, and user association. We optimize user association while satisfying
the constraints of transmit power, data rate, and user association with priority. The binary decision
variable is used to associate users with system resources. Since the decision variable is binary and
constraints are linear, the formulated problem is a binary linear programming problem. Based on
our formulated framework, we simulate and analyze the performance of three different algorithms
(branch and bound algorithm, interior point method, and barrier simplex algorithm) and compare
the results. Simulation results show that the branch and bound algorithm shows the best results,
so this is our benchmark algorithm. The complexity of branch and bound increases exponentially
as the number of users and stations increases in the SAGSI network. We got comparable results
for the interior point method and barrier simplex algorithm to the benchmark algorithm with low
complexity. Finally, we discuss future research directions and challenges of resource optimization
in SAGSI networks
Searching for Dead Sea Scribes:a study on using Artificial Intelligence and palaeography for writer identification in correlation with spelling and scribal practices, codicology, handwriting quality, and literary classification systems for Dead Sea Scrolls
My study explores the Dead Sea Scrolls through the lens of individual scribes. Specifically, the practices of individual scribes responsible for penningtwo or more of the Oumran manuscripts. It utilises innovative digital palaeographic methods alongside traditional palaeographic approaches for scribalidentification. It gathers previously un-gathered data on the handwriting, spelling practices, codicological features and literary content of individual scribes. The study explores how this data on scribes both supports and challenges various aspects of theories in the field of Dead Sea Scroll studies, which accept a a sectarian origin for the Qumran manuscripts
Towards the reduction of greenhouse gas emissions : models and algorithms for ridesharing and carbon capture and storage
Avec la ratification de l'Accord de Paris, les pays se sont engagés à limiter le réchauffement climatique bien en dessous de 2, de préférence à 1,5 degrés Celsius, par rapport aux niveaux préindustriels. À cette fin, les émissions anthropiques de gaz à effet de serre (GES, tels que CO2) doivent être réduites pour atteindre des émissions nettes de carbone nulles d'ici 2050. Cet objectif ambitieux peut être atteint grâce à différentes stratégies d'atténuation des GES, telles que l'électrification, les changements de comportement des consommateurs, l'amélioration de l'efficacité énergétique des procédés, l'utilisation de substituts aux combustibles fossiles (tels que la bioénergie ou l'hydrogène), le captage et le stockage du carbone (CSC), entre autres. Cette thèse vise à contribuer à deux de ces stratégies : le covoiturage (qui appartient à la catégorie des changements de comportement du consommateur) et la capture et le stockage du carbone. Cette thèse fournit des modèles mathématiques et d'optimisation et des algorithmes pour la planification opérationnelle et tactique des systèmes de covoiturage, et des heuristiques pour la planification stratégique d'un réseau de captage et de stockage du carbone.
Dans le covoiturage, les émissions sont réduites lorsque les individus voyagent ensemble au lieu de conduire seuls. Dans ce contexte, cette thèse fournit de nouveaux modèles mathématiques pour représenter les systèmes de covoiturage, allant des problèmes d'affectation stochastique à deux étapes aux problèmes d'empaquetage d'ensembles stochastiques à deux étapes qui peuvent représenter un large éventail de systèmes de covoiturage. Ces modèles aident les décideurs dans leur planification opérationnelle des covoiturages, où les conducteurs et les passagers doivent être jumelés pour le covoiturage à court terme. De plus, cette thèse explore la planification tactique des systèmes de covoiturage en comparant différents modes de fonctionnement du covoiturage et les paramètres de la plateforme (par exemple, le partage des revenus et les pénalités). De nouvelles caractéristiques de problèmes sont étudiées, telles que l'incertitude du conducteur et du passager, la flexibilité de réappariement et la réservation de l'offre de conducteur via les frais de réservation et les pénalités. En particulier, la flexibilité de réappariement peut augmenter l'efficacité d'une plateforme de covoiturage, et la réservation de l'offre de conducteurs via les frais de réservation et les pénalités peut augmenter la satisfaction des utilisateurs grâce à une compensation garantie si un covoiturage n'est pas fourni. Des expériences computationnelles détaillées sont menées et des informations managériales sont fournies.
Malgré la possibilité de réduction des émissions grâce au covoiturage et à d'autres stratégies d'atténuation, des études macroéconomiques mondiales montrent que même si plusieurs stratégies d'atténuation des GES sont utilisées simultanément, il ne sera probablement pas possible d'atteindre des émissions nettes nulles d'ici 2050 sans le CSC. Ici, le CO2 est capturé à partir des sites émetteurs et transporté vers des réservoirs géologiques, où il est injecté pour un stockage à long terme. Cette thèse considère un problème de planification stratégique multipériode pour l'optimisation d'une chaîne de valeur CSC. Ce problème est un problème combiné de localisation des installations et de conception du réseau où une infrastructure CSC est prévue pour les prochaines décennies. En raison des défis informatiques associés à ce problème, une heuristique est introduite, qui est capable de trouver de meilleures solutions qu'un solveur commercial de programmation mathématique, pour une fraction du temps de calcul. Cette heuristique comporte des phases d'intensification et de diversification, une génération améliorée de solutions réalisables par programmation dynamique, et une étape finale de raffinement basée sur un modèle restreint. Dans l'ensemble, les contributions de cette thèse sur le covoiturage et le CSC fournissent des modèles de programmation mathématique, des algorithmes et des informations managériales qui peuvent aider les praticiens et les parties prenantes à planifier des émissions nettes nulles.With the ratification of the Paris Agreement, countries committed to limiting global warming to well below 2, preferably to 1.5 degrees Celsius, compared to pre-industrial levels. To this end, anthropogenic greenhouse gas (GHG) emissions (such as CO2) must be reduced to reach net-zero carbon emissions by 2050. This ambitious target may be met by means of different GHG mitigation strategies, such as electrification, changes in consumer behavior, improving the energy efficiency of processes, using substitutes for fossil fuels (such as bioenergy or hydrogen), and carbon capture and storage (CCS). This thesis aims at contributing to two of these strategies: ridesharing (which belongs to the category of changes in consumer behavior) and carbon capture and storage. This thesis provides mathematical and optimization models and algorithms for the operational and tactical planning of ridesharing systems, and heuristics for the strategic planning of a carbon capture and storage network.
In ridesharing, emissions are reduced when individuals travel together instead of driving alone. In this context, this thesis provides novel mathematical models to represent ridesharing systems, ranging from two-stage stochastic assignment problems to two-stage stochastic set packing problems that can represent a wide variety of ridesharing systems. These models aid decision makers in their operational planning of rideshares, where drivers and riders have to be matched for ridesharing on the short-term. Additionally, this thesis explores the tactical planning of ridesharing systems by comparing different modes of ridesharing operation and platform parameters (e.g., revenue share and penalties). Novel problem characteristics are studied, such as driver and rider uncertainty, rematching flexibility, and reservation of driver supply through booking fees and penalties. In particular, rematching flexibility may increase the efficiency of a ridesharing platform, and the reservation of driver supply through booking fees and penalties may increase user satisfaction through guaranteed compensation if a rideshare is not provided. Extensive computational experiments are conducted and managerial insights are given.
Despite the opportunity to reduce emissions through ridesharing and other mitigation strategies, global macroeconomic studies show that even if several GHG mitigation strategies are used simultaneously, achieving net-zero emissions by 2050 will likely not be possible without CCS. Here, CO2 is captured from emitter sites and transported to geological reservoirs, where it is injected for long-term storage. This thesis considers a multiperiod strategic planning problem for the optimization of a CCS value chain. This problem is a combined facility location and network design problem where a CCS infrastructure is planned for the next decades. Due to the computational challenges associated with that problem, a slope scaling heuristic is introduced, which is capable of finding better solutions than a state-of-the-art general-purpose mathematical programming solver, at a fraction of the computational time. This heuristic has intensification and diversification phases, improved generation of feasible solutions through dynamic programming, and a final refining step based on a restricted model. Overall, the contributions of this thesis on ridesharing and CCS provide mathematical programming models, algorithms, and managerial insights that may help practitioners and stakeholders plan for net-zero emissions
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