Algorithmic and complexity aspects of simple coalitional games

Simple coalitional games are a fundamental class of cooperative games and voting games which are used to model coalition formation, resource allocation and decision making in computer science, artificial intelligence and multiagent systems. Although simple coalitional games are well studied in the domain of game theory and social choice, their algorithmic and computational complexity aspects have received less attention till recently. The computational aspects of simple coalitional games are of increased importance as these games are used by computer scientists to model distributed settings. This thesis fits in the wider setting of the interplay between economics and computer science which has led to the development of algorithmic game theory and computational social choice. A unified view of the computational aspects of simple coalitional games is presented here for the first time. Certain complexity results also apply to other coalitional games such as skill games and matching games. The following issues are given special consideration: influence of players, limit and complexity of manipulations in the coalitional games and complexity of resource allocation on networks. The complexity of comparison of influence between players in simple games is characterized. The simple games considered are represented by winning coalitions, minimal winning coalitions, weighted voting games or multiple weighted voting games. A comprehensive classification of weighted voting games which can be solved in polynomial time is presented. An efficient algorithm which uses generating functions and interpolation to compute an integer weight vector for target power indices is proposed. Voting theory, especially the Penrose Square Root Law, is used to investigate the fairness of a real life voting model. Computational complexity of manipulation in social choice protocols can determine whether manipulation is computationally feasible or not. The computational complexity and bounds of manipulation are considered from various angles including control, false-name manipulation and bribery. Moreover, the computational complexity of computing various cooperative game solutions of simple games in dierent representations is studied. Certain structural results regarding least core payos extend to the general monotone cooperative game. The thesis also studies a coalitional game called the spanning connectivity game. It is proved that whereas computing the Banzhaf values and Shapley-Shubik indices of such games is #P-complete, there is a polynomial time combinatorial algorithm to compute the nucleolus. The results have interesting significance for optimal strategies for the wiretapping game which is a noncooperative game defined on a network

Exploiting graph structures for computational efficiency

Coping with NP-hard graph problems by doing better than simply brute force is a field of significant practical importance, and which have also sparked wide theoretical interest. One route to cope with such hard graph problems is to exploit structures which can possibly be found in the input data or in the witness for a solution. In the framework of parameterized complexity, we attempt to quantify such structures by defining numbers which describe "how structured" the graph is. We then do a fine-grained classification of its computational complexity, where not only the input size, but also the structural measure in question come in to play. There is a number of structural measures called width parameters, which includes treewidth, clique-width, and mim-width. These width parameters can be compared by how many classes of graphs that have bounded width. In general there is a tradeoff; if more graph classes have bounded width, then fewer problems can be efficiently solved with the aid of a small width; and if a width is bounded for only a few graph classes, then it is easier to design algorithms which exploit the structure described by the width parameter. For each of the mentioned width parameters, there are known meta-theorems describing algorithmic results for a wide array of graph problems. Hence, showing that decompositions with bounded width can be found for a certain graph class yields algorithmic results for the given class. In the current thesis, we show that several graph classes have bounded width measures, which thus gives algorithmic consequences. Algorithms which are FPT or XP parameterized by width parameters are exploiting structure of the input graph. However, it is also possible to exploit structures that are required of a witness to the solution. We use this perspective to give a handful of polynomial-time algorithms for NP-hard problems whenever the witness belongs to certain graph classes. It is also possible to combine structures of the input graph with structures of the solution witnesses in order to obtain parameterized algorithms, when each structure individually is provably insufficient to provide so under standard complexity assumptions. We give an example of this in the final chapter of the thesis

Rapid Parallelization by Collaboration

The widespread adoption of Chip Multiprocessors has renewed the emphasis on the use of parallelism to improve performance. The present and growing diversity in hardware architectures and software environments, however, continues to pose difficulties in the effective use of parallelism thus delaying a quick and smooth transition to the concurrency era. In this document, we describe the research being conducted at the Computer Science Department at Columbia University on a system called COMPASS that aims to simplify this transition by providing advice to programmers considering parallelizing their code. The advice proffered to the programmer is based on the wisdom collected from programmers who have already parallelized some code. The utility of COMPASS rests, not only on its ability to collect the wisdom unintrusively but also on its ability to automatically seek, find and synthesize this wisdom into advice that is tailored to the code the user is considering parallelizing and to the environment in which the optimized program will execute in. COMPASS provides a platform and an extensible framework for sharing human expertise about code parallelization -- widely and on diverse hardware and software. By leveraging the "Wisdom of Crowds" model which has been conjunctured to scale exponentially and which has successfully worked for Wikis, COMPASS aims to enable rapid parallelization of code and thus continue to extend the benefits for Moore's law scaling to science and society

Graph Deep Learning: Methods and Applications

The past few years have seen the growing prevalence of deep neural networks on various application domains including image processing, computer vision, speech recognition, machine translation, self-driving cars, game playing, social networks, bioinformatics, and healthcare etc. Due to the broad applications and strong performance, deep learning, a subfield of machine learning and artificial intelligence, is changing everyone\u27s life.Graph learning has been another hot field among the machine learning and data mining communities, which learns knowledge from graph-structured data. Examples of graph learning range from social network analysis such as community detection and link prediction, to relational machine learning such as knowledge graph completion and recommender systems, to mutli-graph tasks such as graph classification and graph generation etc.An emerging new field, graph deep learning, aims at applying deep learning to graphs. To deal with graph-structured data, graph neural networks (GNNs) are invented in recent years which directly take graphs as input and output graph/node representations. Although GNNs have shown superior performance than traditional methods in tasks such as semi-supervised node classification, there still exist a wide range of other important graph learning problems where either GNNs\u27 applicabilities have not been explored or GNNs only have less satisfying performance.In this dissertation, we dive deeper into the field of graph deep learning. By developing new algorithms, architectures and theories, we push graph neural networks\u27 boundaries to a much wider range of graph learning problems. The problems we have explored include: 1) graph classification; 2) medical ontology embedding; 3) link prediction; 4) recommender systems; 5) graph generation; and 6) graph structure optimization.We first focus on two graph representation learning problems: graph classification and medical ontology embedding.For graph classification, we develop a novel deep GNN architecture which aggregates node features through a novel SortPooling layer that replaces the simple summing used in previous works. We demonstrate its state-of-the-art graph classification performance on benchmark datasets. For medical ontology embedding, we propose a novel hierarchical attention propagation model, which uses attention mechanism to learn embeddings of medical concepts from hierarchically-structured medical ontologies such as ICD-9 and CCS. We validate the learned embeddings on sequential procedure/diagnosis prediction tasks with real patient data.Then we investigate GNNs\u27 potential for predicting relations, specifically link prediction and recommender systems. For link prediction, we first develop a theory unifying various traditional link prediction heuristics, and then design a framework to automatically learn suitable heuristics from a given network based on GNNs. Our model shows unprecedented strong link prediction performance, significantly outperforming all traditional methods. For recommender systems, we propose a novel graph-based matrix completion model, which uses a GNN to learn graph structure features from the bipartite graph formed by user and item interactions. Our model not only outperforms various matrix completion baselines, but also demonstrates excellent transfer learning ability -- a model trained on MovieLens can be directly used to predict Douban movie ratings with high performance.Finally, we explore GNNs\u27 applicability to graph generation and graph structure optimization. We focus on a specific type of graphs which usually carry computations on them, namely directed acyclic graphs (DAGs). We develop a variational autoencoder (VAE) for DAGs and prove that it can injectively map computations into a latent space. This injectivity allows us to perform optimization in the continuous latent space instead of the original discrete structure space. We then apply our VAE to two types of DAGs, neural network architectures and Bayesian networks. Experiments show that our model not only generates novel and valid DAGs, but also finds high-quality neural architectures and Bayesian networks through performing Bayesian optimization in its latent space

Deterministic, Efficient Variation of Circuit Components to Improve Resistance to Reverse Engineering

This research proposes two alternative methods for generating semantically equivalent circuit variants which leave the circuit\u27s internal structure pseudo-randomly determined. Component fusion deterministically selects subcircuits using a component identification algorithm and replaces them using a deterministic algorithm that generates canonical logic forms. Component encryption seeks to alter the semantics of individual circuit components using an encoding function, but preserves the overall circuit semantics by decoding signal values later in the circuit. Experiments were conducted to examine the performance of component fusion and component encryption against representative trials of subcircuit selection-and-replacement and Boundary Blurring, two previously defined methods for circuit obfuscation. Overall, results support the conclusion that both component fusion and component encryption generate more secure variants than previous methods and that these variants are more efficient in terms of required circuit delay and the power and area required for their implementation

Power network and smart grids analysis from a graph theoretic perspective

The growing size and complexity of power systems has given raise to the use of complex network theory in their modelling, analysis, and synthesis. Though most of the previous studies in this area have focused on distributed control through well established protocols like synchronization and consensus, recently, a few fundamental concepts from graph theory have also been applied, for example in symmetry-based cluster synchronization. Among the existing notions of graph theory, graph symmetry is the focus of this proposal. However, there are other development around some concepts from complex network theory such as graph clustering in the study. In spite of the widespread applications of symmetry concepts in many real world complex networks, one can rarely find an article exploiting the symmetry in power systems. In addition, no study has been conducted in analysing controllability and robustness for a power network employing graph symmetry. It has been verified that graph symmetry promotes robustness but impedes controllability. A largely absent work, even in other fields outside power systems, is the simultaneous investigation of the symmetry effect on controllability and robustness. The thesis can be divided into two section. The first section, including Chapters 2-3, establishes the major theoretical development around the applications of graph symmetry in power networks. A few important topics in power systems and smart grids such as controllability and robustness are addressed using the symmetry concept. These topics are directed toward solving specific problems in complex power networks. The controllability analysis will lead to new algorithms elaborating current controllability benchmarks such as the maximum matching and the minimum dominant set. The resulting algorithms will optimize the number of required driver nodes indicated as FACTS devices in power networks. The second topic, robustness, will be tackled by the symmetry analysis of the network to investigate three aspects of network robustness: robustness of controllability, disturbance decoupling, and fault tolerance against failure in a network element. In the second section, including Chapters 4-8, in addition to theoretical development, a few novel applications are proposed for the theoretical development proposed in both sections one and two. In Chapter 4, an application for the proposed approaches is introduced and developed. The placement of flexible AC transmission systems (FACTS) is investigated where the cybersecurity of the associated data exchange under the wide area power networks is also considered. A new notion of security, i.e. moderated-k-symmetry, is introduced to leverage on the symmetry characteristics of the network to obscure the network data from the adversary perspective. In chapters 5-8, the use of graph theory, and in particular, graph symmetry and centrality, are adapted for the complex network of charging stations. In Chapter 5, the placement and sizing of charging stations (CSs) of the network of electric vehicles are addressed by proposing a novel complex network model of the charging stations. The problems of placement and sizing are then reformulated in a control framework and the impact of symmetry on the number and locations of charging stations is also investigated. These results are developed in Chapters 6-7 to robust placement and sizing of charging stations for the Tesla network of Sydney where the problem of extending the capacity having a set of pre-existing CSs are addressed. The role of centrality in placement of CSs is investigated in Chapter 8. Finally, concluding remarks and future works are presented in Chapter 9

Impact of Symmetries in Graph Clustering

Diese Dissertation beschäftigt sich mit der durch die Automorphismusgruppe definierten Symmetrie von Graphen und wie sich diese auf eine Knotenpartition, als Ergebnis von Graphenclustering, auswirkt. Durch eine Analyse von nahezu 1700 Graphen aus verschiedenen Anwendungsbereichen kann gezeigt werden, dass mehr als 70 % dieser Graphen Symmetrien enthalten. Dies bildet einen Gegensatz zum kombinatorischen Beweis, der besagt, dass die Wahrscheinlichkeit eines zufälligen Graphen symmetrisch zu sein bei zunehmender Größe gegen Null geht. Das Ergebnis rechtfertigt damit die Wichtigkeit weiterer Untersuchungen, die auf mögliche Auswirkungen der Symmetrie eingehen. Bei der Analyse werden sowohl sehr kleine Graphen (10 000 000 Knoten/>25 000 000 Kanten) berücksichtigt. Weiterhin wird ein theoretisches Rahmenwerk geschaffen, das zum einen die detaillierte Quantifizierung von Graphensymmetrie erlaubt und zum anderen Stabilität von Knotenpartitionen hinsichtlich dieser Symmetrie formalisiert. Eine Partition der Knotenmenge, die durch die Aufteilung in disjunkte Teilmengen definiert ist, wird dann als stabil angesehen, wenn keine Knoten symmetriebedingt von der einen in die andere Teilmenge abgebildet werden und dadurch die Partition verändert wird. Zudem wird definiert, wie eine mögliche Zerlegbarkeit der Automorphismusgruppe in unabhängige Untergruppen als lokale Symmetrie interpretiert werden kann, die dann nur Auswirkungen auf einen bestimmten Bereich des Graphen hat. Um die Auswirkungen der Symmetrie auf den gesamten Graphen und auf Partitionen zu quantifizieren, wird außerdem eine Entropiedefinition präsentiert, die sich an der Analyse dynamischer Systeme orientiert. Alle Definitionen sind allgemein und können daher für beliebige Graphen angewandt werden. Teilweise ist sogar eine Anwendbarkeit für beliebige Clusteranalysen gegeben, solange deren Ergebnis in einer Partition resultiert und sich eine Symmetrierelation auf den Datenpunkten als Permutationsgruppe angeben lässt. Um nun die tatsächliche Auswirkung von Symmetrie auf Graphenclustering zu untersuchen wird eine zweite Analyse durchgeführt. Diese kommt zum Ergebnis, dass von 629 untersuchten symmetrischen Graphen 72 eine instabile Partition haben. Für die Analyse werden die Definitionen des theoretischen Rahmenwerks verwendet. Es wird außerdem festgestellt, dass die Lokalität der Symmetrie eines Graphen maßgeblich beeinflusst, ob dessen Partition stabil ist oder nicht. Eine hohe Lokalität resultiert meist in einer stabilen Partition und eine stabile Partition impliziert meist eine hohe Lokalität. Bevor die obigen Ergebnisse beschrieben und definiert werden, wird eine umfassende Einführung in die verschiedenen benötigten Grundlagen gegeben. Diese umfasst die formalen Definitionen von Graphen und statistischen Graphmodellen, Partitionen, endlichen Permutationsgruppen, Graphenclustering und Algorithmen dafür, sowie von Entropie. Ein separates Kapitel widmet sich ausführlich der Graphensymmetrie, die durch eine endliche Permutationsgruppe, der Automorphismusgruppe, beschrieben wird. Außerdem werden Algorithmen vorgestellt, die die Symmetrie von Graphen ermitteln können und, teilweise, auch das damit eng verwandte Graphisomorphie Problem lösen. Am Beispiel von Graphenclustering gibt die Dissertation damit Einblicke in mögliche Auswirkungen von Symmetrie in der Datenanalyse, die so in der Literatur bisher wenig bis keine Beachtung fanden