QoS-aware architectures, technologies, and middleware for the cloud continuum

The recent trend of moving Cloud Computing capabilities to the Edge of the network is reshaping how applications and their middleware supports are designed, deployed, and operated. This new model envisions a continuum of virtual resources between the traditional cloud and the network edge, which is potentially more suitable to meet the heterogeneous Quality of Service (QoS) requirements of diverse application domains and next-generation applications. Several classes of advanced Internet of Things (IoT) applications, e.g., in the industrial manufacturing domain, are expected to serve a wide range of applications with heterogeneous QoS requirements and call for QoS management systems to guarantee/control performance indicators, even in the presence of real-world factors such as limited bandwidth and concurrent virtual resource utilization. The present dissertation proposes a comprehensive QoS-aware architecture that addresses the challenges of integrating cloud infrastructure with edge nodes in IoT applications. The architecture provides end-to-end QoS support by incorporating several components for managing physical and virtual resources. The proposed architecture features: i) a multilevel middleware for resolving the convergence between Operational Technology (OT) and Information Technology (IT), ii) an end-to-end QoS management approach compliant with the Time-Sensitive Networking (TSN) standard, iii) new approaches for virtualized network environments, such as running TSN-based applications under Ultra-low Latency (ULL) constraints in virtual and 5G environments, and iv) an accelerated and deterministic container overlay network architecture. Additionally, the QoS-aware architecture includes two novel middlewares: i) a middleware that transparently integrates multiple acceleration technologies in heterogeneous Edge contexts and ii) a QoS-aware middleware for Serverless platforms that leverages coordination of various QoS mechanisms and virtualized Function-as-a-Service (FaaS) invocation stack to manage end-to-end QoS metrics. Finally, all architecture components were tested and evaluated by leveraging realistic testbeds, demonstrating the efficacy of the proposed solutions.

Support infrastructures for multimedia services with guaranteed continuity and QoS

Advances in wireless networking and content delivery systems are enabling new challenging provisioning scenarios where a growing number of users access multimedia services, e.g., audio/video streaming, while moving among different points of attachment to the Internet, possibly with different connectivity technologies, e.g., Wi-Fi, Bluetooth, and cellular 3G. That calls for novel middlewares capable of dynamically personalizing service provisioning to the characteristics of client environments, in particular to discontinuities in wireless resource availability due to handoffs. This dissertation proposes a novel middleware solution, called MUM, that performs effective and context-aware handoff management to transparently avoid service interruptions during both horizontal and vertical handoffs. To achieve the goal, MUM exploits the full visibility of wireless connections available in client localities and their handoff implementations (handoff awareness), of service quality requirements and handoff-related quality degradations (QoS awareness), and of network topology and resources available in current/future localities (location awareness). The design and implementation of the all main MUM components along with extensive on the field trials of the realized middleware architecture confirmed the validity of the proposed full context-aware handoff management approach. In particular, the reported experimental results demonstrate that MUM can effectively maintain service continuity for a wide range of different multimedia services by exploiting handoff prediction mechanisms, adaptive buffering and pre-fetching techniques, and proactive re-addressing/re-binding.

Formulations and Algorithms for Routing Problems

Combinatorial Optimization is a branch of optimization that deals with the problems where the set of feasible solutions is discrete. Routing problem is a well studied branch of Combinatorial Optimization that concerns the process of deciding the best way of visiting the nodes (customers) in a network. Routing problems appear in many real world applications including: Transportation, Telephone or Electronic data Networks. During the years, many solution procedures have been introduced for the solution of different Routing problems. Some of them are based on exact approaches to solve the problems to optimality and some others are based on heuristic or metaheuristic search to find optimal or near optimal solutions. There is also a less studied method, which combines both heuristic and exact approaches to face different problems including those in the Combinatorial Optimization area. The aim of this dissertation is to develop some solution procedures based on the combination of heuristic and Integer Linear Programming (ILP) techniques for some important problems in Routing Optimization. In this approach, given an initial feasible solution to be possibly improved, the method follows a destruct-and-repair paradigm, where the given solution is randomly destroyed (i.e., customers are removed in a random way) and repaired by solving an ILP model, in an attempt to find a new improved solution.

Cross-layer optimizations in multi-hop ad hoc networks

Unlike traditional wireless networks, characterized by the presence of last-mile, static and reliable infrastructures, Mobile ad Hoc Networks (MANETs) are dynamically formed by collections of mobile and static terminals that exchange data by enabling each other's communication. Supporting multi-hop communication in a MANET is a challenging research area because it requires cooperation between different protocol layers (MAC, routing, transport). In particular, MAC and routing protocols could be considered mutually cooperative protocol layers. When a route is established, the exposed and hidden terminal problems at MAC layer may decrease the end-to-end performance proportionally with the length of each route. Conversely, the contention at MAC layer may cause a routing protocol to respond by initiating new routes queries and routing table updates. Multi-hop communication may also benefit the presence of pseudo-centralized virtual infrastructures obtained by grouping nodes into clusters. Clustering structures may facilitate the spatial reuse of resources by increasing the system capacity: at the same time, the clustering hierarchy may be used to coordinate transmissions events inside the network and to support intra-cluster routing schemes. Again, MAC and clustering protocols could be considered mutually cooperative protocol layers: the clustering scheme could support MAC layer coordination among nodes, by shifting the distributed MAC paradigm towards a pseudo-centralized MAC paradigm. On the other hand, the system benefits of the clustering scheme could be emphasized by the pseudo-centralized MAC layer with the support for differentiated access priorities and controlled contention. In this thesis, we propose cross-layer solutions involving joint design of MAC, clustering and routing protocols in MANETs. As main contribution, we study and analyze the integration of MAC and clustering schemes to support multi-hop communication in large-scale ad hoc networks. A novel clustering protocol, named Availability Clustering (AC), is defined under general nodes' heterogeneity assumptions in terms of connectivity, available energy and relative mobility. On this basis, we design and analyze a distributed and adaptive MAC protocol, named Differentiated Distributed Coordination Function (DDCF), whose focus is to implement adaptive access differentiation based on the node roles, which have been assigned by the upper-layer's clustering scheme. We extensively simulate the proposed clustering scheme by showing its effectiveness in dominating the network dynamics, under some stressing mobility models and different mobility rates. Based on these results, we propose a possible application of the cross-layer MAC+Clustering scheme to support the fast propagation of alert messages in a vehicular environment. At the same time, we investigate the integration of MAC and routing protocols in large scale multi-hop ad-hoc networks. A novel multipath routing scheme is proposed, by extending the AOMDV protocol with a novel load-balancing approach to concurrently distribute the traffic among the multiple paths. We also study the composition effect of a IEEE 802.11-based enhanced MAC forwarding mechanism called Fast Forward (FF), used to reduce the effects of self-contention among frames at the MAC layer. The protocol framework is modelled and extensively simulated for a large set of metrics and scenarios. For both the schemes, the simulation results reveal the benefits of the cross-layer MAC+routing and MAC+clustering approaches over single-layer solutions.

Comparing Different Approaches for Clustering Categorical Data

There are different ways to do cluster analysis of categorical data in the literature and the choice among them is strongly related to the aim of the researcher, if we do not take into account time and economical constraints. Main approaches for clustering are usually distinguished into model-based and distance-based methods: the former assume that objects belonging to the same class are similar in the sense that their observed values come from the same probability distribution, whose parameters are unknown and need to be estimated; the latter evaluate distances among objects by a defined dissimilarity measure and, basing on it, allocate units to the closest group. In clustering, one may be interested in the classification of similar objects into groups, and one may be interested in finding observations that come from the same true homogeneous distribution. But do both of these aims lead to the same clustering? And how good are clustering methods designed to fulfil one of these aims in terms of the other? In order to answer, two approaches, namely a latent class model (mixture of multinomial distributions) and a partition around medoids one, are evaluated and compared by Adjusted Rand Index, Average Silhouette Width and Pearson-Gamma indexes in a fairly wide simulation study. Simulation outcomes are plotted in bi-dimensional graphs via Multidimensional Scaling; size of points is proportional to the number of points that overlap and different colours are used according to the cluster membership.

Essays on the Empirical Analysis of Economic and Political Development in Sub-Saharan Africa

In Sub-Saharan Africa, non-democratic events, like civil wars and coup d'etat, destroy economic development. This study investigates both domestic and spatial effects on the likelihood of civil wars and coup d'etat. To civil wars, an increase of income growth is one of common research conclusions to stop wars. This study adds a concern on ethnic fractionalization. IV-2SLS is applied to overcome causality problem. The findings document that income growth is significant to reduce number and degree of violence in high ethnic fractionalized countries, otherwise they are trade-off. Income growth reduces amount of wars, but increases its violent level, in the countries with few large ethnic groups. Promoting growth should consider ethnic composition. This study also investigates the clustering and contagion of civil wars using spatial panel data models. Onset, incidence and end of civil conflicts spread across the network of neighboring countries while peace, the end of conflicts, diffuse only with the nearest neighbor. There is an evidence of indirect links from neighboring income growth, without too much inequality, to reduce the likelihood of civil wars. To coup d'etat, this study revisits its diffusion for both all types of coups and only successful ones. The results find an existence of both domestic and spatial determinants in different periods. Domestic income growth plays major role to reduce the likelihood of coup before cold war ends, while spatial effects do negative afterward. Results on probability to succeed coup are similar. After cold war ends, international organisations seriously promote democracy with pressure against coup d'etat, and it seems to be effective. In sum, this study indicates the role of domestic ethnic fractionalization and the spread of neighboring effects to the likelihood of non-democratic events in a country. Policy implementation should concern these factors.

Spatial Disparity and Dynamic Trajectory of Convergence in China: Construction and Application of a Composite Index of Regional Development

China is a large country characterized by remarkable growth and distinct regional diversity. Spatial disparity has always been a hot issue since China has been struggling to follow a balanced growth path but still confronting with unprecedented pressures and challenges. To better understand the inequality level benchmarking spatial distributions of Chinese provinces and municipalities and estimate dynamic trajectory of sustainable development in China, I constructed the Composite Index of Regional Development (CIRD) with five sub pillars/dimensions involving Macroeconomic Index (MEI), Science and Innovation Index (SCI), Environmental Sustainability Index (ESI), Human Capital Index (HCI) and Public Facilities Index (PFI), endeavoring to cover various fields of regional socioeconomic development. Ranking reports on the five sub dimensions and aggregated CIRD were provided in order to better measure the developmental degrees of 31 or 30 Chinese provinces and municipalities over 13 years from 1998 to 2010 as the time interval of three “Five-year Plans”. Further empirical applications of this CIRD focused on clustering and convergence estimation, attempting to fill up the gap in quantifying the developmental levels of regional comprehensive socioeconomics and estimating the dynamic convergence trajectory of regional sustainable development in a long run. Four clusters were benchmarked geographically-oriented in the map on the basis of cluster analysis, and club-convergence was observed in the Chinese provinces and municipalities based on stochastic kernel density estimation.

Distributed Large-scale Mixed-Integer Optimization with Application to Energy and Multi-robot Networks

Several decision and control tasks in cyber-physical networks can be formulated as large- scale optimization problems with coupling constraints. In these "constraint-coupled" problems, each agent is associated to a local decision variable, subject to individual constraints. This thesis explores the use of primal decomposition techniques to develop tailored distributed algorithms for this challenging set-up over graphs. We first develop a distributed scheme for convex problems over random time-varying graphs with non-uniform edge probabilities. The approach is then extended to unknown cost functions estimated online. Subsequently, we consider Mixed-Integer Linear Programs (MILPs), which are of great interest in smart grid control and cooperative robotics. We propose a distributed methodological framework to compute a feasible solution to the original MILP, with guaranteed suboptimality bounds, and extend it to general nonconvex problems. Monte Carlo simulations highlight that the approach represents a substantial breakthrough with respect to the state of the art, thus representing a valuable solution for new toolboxes addressing large-scale MILPs. We then propose a distributed Benders decomposition algorithm for asynchronous unreliable networks. The framework has been then used as starting point to develop distributed methodologies for a microgrid optimal control scenario. We develop an ad-hoc distributed strategy for a stochastic set-up with renewable energy sources, and show a case study with samples generated using Generative Adversarial Networks (GANs). We then introduce a software toolbox named ChoiRbot, based on the novel Robot Operating System 2, and show how it facilitates simulations and experiments in distributed multi-robot scenarios. Finally, we consider a Pickup-and-Delivery Vehicle Routing Problem for which we design a distributed method inspired to the approach of general MILPs, and show the efficacy through simulations and experiments in ChoiRbot with ground and aerial robots.

Characterization of DNA sequence properties through network and statistical approaches

In this thesis we will see that the DNA sequence is constantly shaped by the interactions with its environment at multiple levels, showing footprints of DNA methylation, of its 3D organization and, in the case of bacteria, of the interaction with the host organisms. In the first chapter, we will see that analyzing the distribution of distances between consecutive dinucleotides of the same type along the sequence, we can detect epigenetic and structural footprints. In particular, we will see that CG distance distribution allows to distinguish among organisms of different biological complexity, depending on how much CG sites are involved in DNA methylation. Moreover, we will see that CG and TA can be described by the same fitting function, suggesting a relationship between the two. We will also provide an interpretation of the observed trend, simulating a positioning process guided by the presence and absence of memory. In the end, we will focus on TA distance distribution, characterizing deviations from the trend predicted by the best fitting function, and identifying specific patterns that might be related to peculiar mechanical properties of the DNA and also to epigenetic and structural processes. In the second chapter, we will see how we can map the 3D structure of the DNA onto its sequence. In particular, we devised a network-based algorithm that produces a genome assembly starting from its 3D configuration, using as inputs Hi-C contact maps. Specifically, we will see how we can identify the different chromosomes and reconstruct their sequences by exploiting the spectral properties of the Laplacian operator of a network. In the third chapter, we will see a novel method for source clustering and source attribution, based on a network approach, that allows to identify host-bacteria interaction starting from the detection of Single-Nucleotide Polymorphisms along the sequence of bacterial genomes.

Hybrid ground-aerial mesh networks for IoT monitoring applications: network design and software platform development

The Internet of Things (IoT) has grown rapidly in recent years, leading to an increased need for efficient and secure communication between connected devices. Wireless Sensor Networks (WSNs) are composed of small, low-power devices that are capable of sensing and exchanging data, and are often used in IoT applications. In addition, Mesh WSNs involve intermediate nodes forwarding data to ensure more robust communication. The integration of Unmanned Aerial Vehicles (UAVs) in Mesh WSNs has emerged as a promising solution for increasing the effectiveness of data collection, as UAVs can act as mobile relays, providing extended communication range and reducing energy consumption. However, the integration of UAVs and Mesh WSNs still poses new challenges, such as the design of efficient control and communication strategies. This thesis explores the networking capabilities of WSNs and investigates how the integration of UAVs can enhance their performance. The research focuses on three main objectives: (1) Ground Wireless Mesh Sensor Networks, (2) Aerial Wireless Mesh Sensor Networks, and (3) Ground/Aerial WMSN integration. For the first objective, we investigate the use of the Bluetooth Mesh standard for IoT monitoring in different environments. The second objective focuses on deploying aerial nodes to maximize data collection effectiveness and QoS of UAV-to-UAV links while maintaining the aerial mesh connectivity. The third objective investigates hybrid WMSN scenarios with air-to-ground communication links. One of the main contribution of the thesis consists in the design and implementation of a software framework called "Uhura", which enables the creation of Hybrid Wireless Mesh Sensor Networks and abstracts and handles multiple M2M communication stacks on both ground and aerial links. The operations of Uhura have been validated through simulations and small-scale testbeds involving ground and aerial devices.

Data Mining in Clinical Practice for the Quantification of Motor Impairment in Parkinson's Disease

Advances in biomedical signal acquisition systems for motion analysis have led to lowcost and ubiquitous wearable sensors which can be used to record movement data in different settings. This implies the potential availability of large amounts of quantitative data. It is then crucial to identify and to extract the information of clinical relevance from the large amount of available data. This quantitative and objective information can be an important aid for clinical decision making. Data mining is the process of discovering such information in databases through data processing, selection of informative data, and identification of relevant patterns. The databases considered in this thesis store motion data from wearable sensors (specifically accelerometers) and clinical information (clinical data, scores, tests). The main goal of this thesis is to develop data mining tools which can provide quantitative information to the clinician in the field of movement disorders. This thesis will focus on motor impairment in Parkinson's disease (PD). Different databases related to Parkinson subjects in different stages of the disease were considered for this thesis. Each database is characterized by the data recorded during a specific motor task performed by different groups of subjects. The data mining techniques that were used in this thesis are feature selection (a technique which was used to find relevant information and to discard useless or redundant data), classification, clustering, and regression. The aims were to identify high risk subjects for PD, characterize the differences between early PD subjects and healthy ones, characterize PD subtypes and automatically assess the severity of symptoms in the home setting.

Attenuation of Eph Receptor Kinase Activation in Cancer Cells by Coexpressed Ephrin Ligands

The Eph receptor tyrosine kinases mediate juxtacrine signals by interacting “in trans” with ligands anchored to the surface of neighboring cells via a GPI-anchor (ephrin-As) or a transmembrane segment (ephrin-Bs), which leads to receptor clustering and increased kinase activity. Additionally, soluble forms of the ephrin-A ligands released from the cell surface by matrix metalloproteases can also activate EphA receptor signaling. Besides these trans interactions, recent studies have revealed that Eph receptors and ephrins coexpressed in neurons can also engage in lateral “cis” associations that attenuate receptor activation by ephrins in trans with critical functional consequences. Despite the importance of the Eph/ephrin system in tumorigenesis, Eph receptor-ephrin cis interactions have not been previously investigated in cancer cells. Here we show that in cancer cells, coexpressed ephrin-A3 can inhibit the ability of EphA2 and EphA3 to bind ephrins in trans and become activated, while ephrin-B2 can inhibit not only EphB4 but also EphA3. The cis-inhibition of EphA3 by ephrin-B2 implies that in some cases ephrins that cannot activate a particular Eph receptor in trans can nevertheless inhibit its signaling ability through cis association. We also found that an EphA3 mutation identified in lung cancer enhances cis interaction with ephrin-A3. These results suggest a novel mechanism that may contribute to cancer pathogenesis by attenuating the tumor suppressing effects of Eph receptor signaling pathways activated by ephrins in trans (Falivelli et al. 2013).

Management and routing algorithms for ad-hoc and sensor networks

Large scale wireless adhoc networks of computers, sensors, PDAs etc. (i.e. nodes) are revolutionizing connectivity and leading to a paradigm shift from centralized systems to highly distributed and dynamic environments. An example of adhoc networks are sensor networks, which are usually composed by small units able to sense and transmit to a sink elementary data which are successively processed by an external machine. Recent improvements in the memory and computational power of sensors, together with the reduction of energy consumptions, are rapidly changing the potential of such systems, moving the attention towards datacentric sensor networks. A plethora of routing and data management algorithms have been proposed for the network path discovery ranging from broadcasting/floodingbased approaches to those using global positioning systems (GPS). We studied WGrid, a novel decentralized infrastructure that organizes wireless devices in an adhoc manner, where each node has one or more virtual coordinates through which both message routing and data management occur without reliance on either flooding/broadcasting operations or GPS. The resulting adhoc network does not suffer from the deadend problem, which happens in geographicbased routing when a node is unable to locate a neighbor closer to the destination than itself. WGrid allow multidimensional data management capability since nodes' virtual coordinates can act as a distributed database without needing neither special implementation or reorganization. Any kind of data (both single and multidimensional) can be distributed, stored and managed. We will show how a location service can be easily implemented so that any search is reduced to a simple query, like for any other data type. WGrid has then been extended by adopting a replication methodology. We called the resulting algorithm WRGrid. Just like WGrid, WRGrid acts as a distributed database without needing neither special implementation nor reorganization and any kind of data can be distributed, stored and managed. We have evaluated the benefits of replication on data management, finding out, from experimental results, that it can halve the average number of hops in the network. The direct consequence of this fact are a significant improvement on energy consumption and a workload balancing among sensors (number of messages routed by each node). Finally, thanks to the replications, whose number can be arbitrarily chosen, the resulting sensor network can face sensors disconnections/connections, due to failures of sensors, without data loss. Another extension to {WGrid} is {W*Grid} which extends it by strongly improving network recovery performance from link and/or device failures that may happen due to crashes or battery exhaustion of devices or to temporary obstacles. W*Grid guarantees, by construction, at least two disjoint paths between each couple of nodes. This implies that the recovery in W*Grid occurs without broadcasting transmissions and guaranteeing robustness while drastically reducing the energy consumption. An extensive number of simulations shows the efficiency, robustness and traffic road of resulting networks under several scenarios of device density and of number of coordinates. Performance analysis have been compared to existent algorithms in order to validate the results.

Measure of Global Specialization and Spatial Clustering for the Identification of "Specialized" Agglomeration

The intensity of regional specialization in specific activities, and conversely, the level of industrial concentration in specific locations, has been used as a complementary evidence for the existence and significance of externalities. Additionally, economists have mainly focused the debate on disentangling the sources of specialization and concentration processes according to three vectors: natural advantages, internal, and external scale economies. The arbitrariness of partitions plays a key role in capturing these effects, while the selection of the partition would have to reflect the actual characteristics of the economy. Thus, the identification of spatial boundaries to measure specialization becomes critical, since most likely the model will be adapted to different scales of distance, and be influenced by different types of externalities or economies of agglomeration, which are based on the mechanisms of interaction with particular requirements of spatial proximity. This work is based on the analysis of the spatial aspect of economic specialization supported by the manufacturing industry case. The main objective is to propose, for discrete and continuous space: i) a measure of global specialization; ii) a local disaggregation of the global measure; and iii) a spatial clustering method for the identification of specialized agglomerations.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.