Fully-Dynamic Bin Packing with Little Repacking

We study the classic bin packing problem in a fully-dynamic setting, where new items can arrive and old items may depart. We want algorithms with low asymptotic competitive ratio while repacking items sparingly between updates. Formally, each item i has a movement cost c_i >= 0, and we want to use alpha * OPT bins and incur a movement cost gamma * c_i, either in the worst case, or in an amortized sense, for alpha, gamma as small as possible. We call gamma the recourse of the algorithm. This is motivated by cloud storage applications, where fully-dynamic bin packing models the problem of data backup to minimize the number of disks used, as well as communication incurred in moving file backups between disks. Since the set of files changes over time, we could recompute a solution periodically from scratch, but this would give a high number of disk rewrites, incurring a high energy cost and possible wear and tear of the disks. In this work, we present optimal tradeoffs between number of bins used and number of items repacked, as well as natural extensions of the latter measure

Advanced Topics on State Complexity of Combined Operations

State complexity is a fundamental topic in formal languages and automata theory. The study of state complexity is also strongly motivated by applications of finite automata in software engineering, programming languages, natural language and speech processing and other practical areas. Since many of these applications use automata of large sizes, it is important to know the number of states of the automata. In this thesis, we firstly discuss the state complexities of individual operations on regular languages, including union, intersection, star, catenation, reversal and so on. The state complexity of an operation on unary languages is usually different from that of the same operation on languages over a larger alphabet. Both kinds of state complexities are reviewed in the thesis. Secondly, we study the exact state complexities of twelve combined operations on regular languages. The state complexities of most of these combined operations are not equal to the compositions of the state complexities of the individual operations which make up these combined operations. We also explore the reason for this difference. Finally, we introduce the concept of estimation and approximation of state complexity. We show close estimates and approximations of the state complexities of six combined operations on regular languages which are good enough to use in practice

Optical Technologies and Control Methods for Scalable Data Centre Networks

Attributing to the increasing adoption of cloud services, video services and associated machine learning applications, the traffic demand inside data centers is increasing exponentially, which necessitates an innovated networking infrastructure with high scalability and cost-efficiency. As a promising candidate to provide high capacity, low latency, cost-effective and scalable interconnections, optical technologies have been introduced to data center networks (DCNs) for approximately a decade. To further improve the DCN performance to meet the increasing traffic demand by using photonic technologies, two current trends are a)increasing the bandwidth density of the transmission links and b) maximizing IT and network resources utilization through disaggregated topologies and architectures. Therefore, this PhD thesis focuses on introducing and applying advanced and efficient technologies in these two fields to DCNs to improve their performance. On the one hand, at the link level, since the traditional single-mode fiber (SMF) solutions based on wavelength division multiplexing (WDM) over C+L band may fall short in satisfying the capacity, front panel density, power consumption, and cost requirements of high-performance DCNs, a space division multiplexing (SDM) based DCN using homogeneous multi-core fibers (MCFs) is proposed.With the exploited bi-directional model and proposed spectrum allocation algorithms, the proposed DCN shows great benefits over the SMF solution in terms of network capacity and spatial efficiency. In the meanwhile, it is found that the inter-core crosstalk (IC-XT) between the adjacent cores inside the MCF is dynamic rather than static, therefore, the behaviour of the IC-XT is experimentally investigated under different transmission conditions. On the other hand, an optically disaggregated DCN is developed and to ensure the performance of it, different architectures, topologies, resource routing and allocation algorithms are proposed and compared. Compared to the traditional server-based DCN, the resource utilization, scalability and the cost-efficiency are significantly improved

Minimisation du nombre de tâches d'un système temps réel par regroupement

Embedded systems dedicated to aeronautics or automotive interact permanently with their environment. They get information from their sensors, process the data and react with their actuators. Such systems have to execute the functionalities correctly, but also to process them within the allocated time. This feature classifies those systems in the category of real-time systems. In the cited domains, those functionalities are originally defined accordingly to the dynamics of the system and their number can reach several thousand. The real-time operating systems, software which handles the processing of those functionalities on the hardware, generally limit the number of functionalities, due to the overhead caused by their management. In this work, we are interested in techniques that reduce the number of those functionalities so to overstep those restrictions. We propose clustering algorithms that ensure that timing constraints are respected. These methods are applied to monoprocessor and multiprocessor architecture with communicating processes.Les systèmes embarqués des domaines de l'aéronautique ou de l'automobile sont en interaction permanente avec leur environnement. Ils récupèrent de l'information depuis leurs capteurs, traitent les données et réagissent par le biais de leurs actionneurs. Ces systèmes critiques se doivent non seulement de produire des résultats corrects du point de vue logique mais aussi de les réaliser dans le temps imparti. Cette particularité les classe dans la famille des systèmes temps réel. Dans les domaines cités, les fonctionnalités sont à l'origine définies au regard de la dynamique du système et leur nombre peut atteindre plusieurs milliers. Les systèmes d'exploitation temps réel, logiciels responsables du traitement de ces fonctionnalités sur le matériel, limitent généralement le nombre de traitements implantables, en raison des surcoûts engendrés par leur gestion. Dans ce travail, nous nous intéressons donc à des techniques de réduction du nombre de ces traitements, de manière à passer outre les limitations des systèmes d'exploitation temps réel. Nous proposons des algorithmes de regroupement qui assurent que les contraintes de temps soient respectées. Ces méthodes visent des architectures monoprocesseurs et multiprocesseurs pour des traitements communicants