Network robustness describes a network's ability to provide and maintain an acceptable level of service in the face of failures and challenges to normal operation. Unfortunately, failures of networks, such as power outages in power systems, congestions in transportation networks, failures of routers on the Internet, happen frequently in our daily life and introduce a tremendous cascading effect on our society. We naturally expect that these networks have high robustness to maintain their performance in face of failures or attacks. As the first step, it is vital to investigate and analyze the robustness of networks so as to propose effective methods to improve network robustness. The first part of the thesis mainly focuses on the robustness of network controllability in face of topological perturbations. In Chapter 2, we propose closed-form analytic approximations for the minimum number of driver nodes which denotes the controllability of the network. Inspired by the concept of critical links, we deduce and validate our approximations on both real-world and synthetic networks. We show that when the fraction of removed links is small, our approximations perform well. Besides, we also find that the critical link attack is the most effective among 4 considered attacks, as long as the fraction of removed links is smaller than the fraction of critical links. In Chapter 3, we focus on the controllability of swarm signalling networks with regular out-degree and bi-modal out-degree distribution. We deduce the generating functions in random failure process and then estimate the fraction of driver nodes with simulations. Results show that our estimations have high accuracy in predicting the fraction of driver nodes in case of random link failures. In order to further improve the accuracy of our proposed approximations in Chapter 4, we use a machine learning method to decrease the gap between our analytical approximations and the simulation results. We compare our approximations obtained by machine learning with existing analytical approximations and show that our approximations significantly outperform the existing closed-form analytical approximations in both synthetic and real-world networks. Apart from targeted attacks based upon the removal of critical links, we also propose analytical approximations for out-in degree-based attacks. In Chapter 5, we investigate the reachability-based robustness of controllability considering link-based random attack, targeted attack, as well as random attack under the protection of critical links. We validate our approximations using 200 real-world communication networks and some synthetic networks and find that our approximations perform well in most cases. In the second part of the thesis, we work on the recoverability of networks. The recoverability of networks refers to the ability of a network to return to a desired performance level after suffering topological perturbations such as link failures. In Chapter 6, we propose a general topological approach and two recoverability indicators to measure the network recoverability for optical networks for two recovery scenarios. Furthermore, we employ the proposed approach to assess 20 real-world optical networks. Numerical results show that the network recoverability is coupled to the network topology, the robustness metric and the recovery strategy. We also find that assortativity, which denotes the tendency of network nodes to connect preferentially to other nodes with similar degree, has the strongest correlation with both recoverability indicators. In Chapter 7, we adopted the framework of network recoverability and investigate the recoverability of network controllability for two recovery scenarios. We employ the proposed approach to assess swarm signalling networks with regular out-degree, and networks with bi-modal out-degree distributions. Besides, we also deduced the analytical results of the recoverability indicators by generating functions, which are close to the results based on simulations. In Chapter 8, we conclude this thesis and come up with some future work.@en

In this article, we propose closed-form analytical expressions to determine the minimum number of driver nodes that is needed to control a specific class of networks. We consider swarm signalling networks with regular out-degree distribution where a fraction $p$ of the links is unavailable. We further apply our method to networks with bi-modal out-degree distributions. Our approximations are validated through intensive simulations. Results show that our approximations have high accuracy when compared with simulation results for both types of out-degree distribution.

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Optical networks are vulnerable to failures due to targeted attacks or large-scale disasters. The recoverability of optical networks refers to the ability of an optical network to return to a desired performance level after suffering topological perturbations such as link failures. This paper proposes a general topological approach and recoverability indicators to measure the network recoverability for optical networks for two recovery scenarios: 1) only the links which are damaged in the failure process can be recovered and 2) links can be established between any pair of nodes that have no link between them after the failure process. We use the robustness envelopes of realizations and the histograms of two recoverability indicators to illustrate the impact of the random failure and recovery processes on the network performance. By applying the average two-terminal reliability and the network efficiency as robustness metrics, we employ the proposed approach to assess 20 real-world optical networks. Numerical results validate that the network recoverability is coupled to the network topology, the robustness metric and the recovery strategy. We further show that a greedy recovery strategy could provide a near-optimal recovery performance for the robustness metrics. We investigate the sensitivity of network recoverability and find that the sensitivity of the recoverability indicators varies according to different robustness metrics and scenarios. We also find that assortativity has the strongest correlation with both recoverability indicators.@en

This paper presents machine learning based approximations for the minimum number of driver nodes needed for structural controllability of networks under link-based random and targeted attacks. We compare our approximations with existing analytical approximations and show that our machine learning based approximations significantly outperform the existing closed-form analytical approximations in case of both synthetic and real-world networks. Apart from targeted attacks based upon the removal of so-called critical links, we also propose analytical approximations for out-in degree-based attacks.

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In this paper, we propose closed-form analytic approximations for the number of controllable nodes in sparse communication networks from the aspect of network controllability, considering link-based random attack, targeted attack, as well as random attack under the protection of critical links. We compare our approximations with simulation results on communication networks. Results show that our approximations perform well for all three attack strategies as long as the fraction of removed links is small. Only when the fraction of removed links is large, our approximation for targeted attacks does not fit well with simulation results. Finally, we validate our approximations using 200 communication networks and some synthetic networks. Results show that our approximations perform well in most cases.

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Network recoverability refers to the ability of a network to recover to a desired performance level after suffering topological perturbations such as link failures. The minimum number of driver nodes is a typical metric to denote the network controllability. In this paper, we propose closed-form analytic approximations for the minimum number of driver nodes to investigate the recoverability of network controllability under link-based perturbations in two scenarios: 1) only the links which are damaged in the failure process can be recovered and 2) links can be established between any pair of nodes that have no link between them after the failure process. Results show that our approximations fit well with simulation results both in synthetic networks and real-world networks, such as swarm signaling networks and some communication networks.@en

In this paper, we propose closed-form analytic approximations for the minimum number of driver nodes needed to fully control networks, where links are removed according to both random and targeted attacks. Our approximations rely on the concept of critical links. A link is called critical if its removal increases the required number of driver nodes. We validate our approximation on both real-world and synthetic networks. For random attacks, the approximation is always very good, as long as the fraction of removed links is smaller than the fraction of critical links. For some cases, the approximation is still accurate for larger fractions of removed links. The approximation for an attack, where first the critical links are removed, is also accurate, as long as the fraction of removed links is sufficiently small. Finally, we show that the critical link attack is the most effective among 4 considered attacks, as long as the fraction of removed links is smaller than the fraction of critical links. @en

Network recoverability refers to the ability of a network to return to a desired performance level after suffering malicious attacks or random failures. This paper proposes a general topological approach and recoverability indicators to measure the network recoverability in two scenarios: 1) recovery of damaged connections and 2) any disconnected pair of nodes can be connected to each other. Our approach presents the effect of the random attack and recovery processes on the network performance by the robustness envelopes of realizations and the histograms of two recoverability indicators. By applying the effective graph resistance and the network efficiency as robustness metrics, we employ the proposed approach to assess 10 realworld communication networks. Numerical results verify that the network recoverability is coupled to the network topology, the robustness metric and the recovery strategy. We also show that a greedy recovery strategy could provide a near-optimal recovery performance for the investigated robustness metrics.

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The diversified system requirements have been continuously growing to drive the development of a variety of new package styles. Wafer-Level Packaging (WLP) technology has drawn attention with its thinner package due to the removal of substrate and thus higher performance. With the greater design flexibility in having more I/Os, Fan-out Wafer Level Packaging (FOWLP) technology has proven to be a more optimal and promising solution. Infineon's eWLB was introduced as the first generation FOWLP technology. In the eWLB technology, die shift is the processing defect that the die moves from its default position result in the wire disconnection. Placing the dies at the preset pitch can compensate the die shift before die attach process. In this paper, the key factors to controlling die shift will be discussed, and the complex process capability index (Cpk) of process is 2.06 which represents the die shift can be well minimized after compensation.

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