1. Main Contributions made by the supplicant: This thesis proposes an Open Computing Language (OpenCL) framework to address the challenges of implementation of graph algorithms on parallel architectures and large scale graph processing. The proposed framework uses the front-end of the existing Falcon DSL compiler, andso, programmers enjoy conventional, imperative and shared memory programming style. The back-end of the framework generates implementations of graph algorithms in OpenCL to target single device architectures. The generated OpenCL code is portable across various platforms, e.g., CPU and GPU, and also vendors, e.g., NVIDIA, Intel and AMD. The framework automatically generates code for thread management and memory management for the devices. It hides all the lower level programming details from the programmers. A few optimizations are applied to reduce the execution time. The large graph processing challenge is tackled through graph partitioning over multiple devices of a single node and multiple nodes of a distributed cluster. The programmer codes a graph algorithm in Falcon assuming that the graph fits into single machine memory and the framework handles graph partitioning without any intervention by the programmer. The framework analyses the Abstract Syntax Tree (AST) generated by Falcon to find all the necessary information about communication and synchronization. It automatically generates code for message passing to hide the complexity of programming in a distributed environment. The framework also applies a set of optimizations to minimize the communication latency. The thesis reports results of several experiments conducted on widely used graph algorithms: single source shortest path, pagerank and minimum spanning tree to name a few. Experimental evaluations show that the reported results are comparable to the state-of-art non-portable graph DSLs and frameworks on a single node. Experiments in a distributed environment to show the scalability and efficiency of the framework are also described. 2. Summary of the Referees' Written Comments: Extracts from the referees' reports are provided below. A copy of the written replies to the clarifications sought by the external examiner is appended to this report. Referee 1: This thesis extends the Falcon framework with OpenCL for parallel graph processing on multi-device and multi-node architectures. The thesis makes important contributions. Processing large graphs in short time is very important, and making use of multiple nodes and devices is perhaps the only way to achieve this. Towards this, the thesis makes good contributions for easy programming, compiler transformations and efficient runtime systems. One of the commendable aspects of the thesis that it demonstrates with graphs that cannot be accommodated In the memory of a single device. The thesis is generally written well. The related work coverage is very good. The magnitude of thesis excellent for a Masters work. The experimental setup is very comprehensive with good set of graphs, good experimental comparisons with state-of-art works and good platforms. Particularly. the demonstration with a GPU cluster with multiple GPU nodes (Chapter 5) is excellent. The attempt to demonstrate scalability with 2, 4 and 8 nodes is also noteworthy. However, the contributions on optimizations are weak. Most of the optimizations and compiler transformations are straight-forward. There should be summary observations on the results in Chapter 3, especially given that the results are mixed and don't quite clearly convey the clear advantages of their work. The same is the case with multi-device results in chapter 4, where the results are once again mixed. Similarly, the speedups and scalability achieved with multiple nodes are not great. The problem size justification in the multi-node results is not clear. (Referee 1 also indicates a couple of minor changes to the thesis). Referee 2: The thesis uses the OpenCL framework to address the problem of programming graph algorithms on distributed systems. The use of OpenCL ensures that the generated code is platform-agnoistic and vendor-agnoistic. Sufficient experimentation with large scale graphs and reasonable size clusters have been conducted to demonstrate the scalability and portability of the code generated by the framework. The automatically generated code is almost as efficient as manually written code. The thesis is well written and is of high quality. The related work section is well organized and displays a good knowledge of the subject matter under consideration. The author has made important contributions to a good publication as well. 3. An Account of the Open Oral Examination: The oral examination of Ms. Parita Patel took place during 10 AM and 11AM on 27th November 2017, in the Seminar Hall of the Department of Computer Science and Automation. The members of the Oral Examination Board present were, Prof. Sathish Vadhiyar, external examiner and Prof. Y. N. Srikant, research supervisor. The candidate presented the work in an open defense seminar highlighting the problem domain, the methodology used, the investigations carried out by her, and the resulting contributions documented in the thesis before an audience consisting of the examiners, some faculty members, and students. Some of the questions posed by the examiners and the members of the audience during the oral examination are listed below. 1. How much is the overlap between Falcon work and this thesis? Response: We have used the Falcon front end in our work. Further, the existing Falcon compiler was useful to us to test our own implementation of algorithms in Falcon. 2. Why are speedup and scalability not very high with multiple nodes? Response: For the multi-node architecture, we were not able to achieve linear scalability because, with the increase in number of nodes, communication cost increases significantly. Unless the computation cost in the nodes is significant and is much more than the communication cost, this is bound to happen. 3. Do you have plans of making the code available for use by the community? Response: The code includes some part of Falcon implementation (front-end parsing/grammar) also. After discussion with the author of Falcon, the code can be made available to the community. 4. How can a graph that does not fit into a single device fit into a single node in the case of multiple nodes? Response: Single node machine used in the experiments of “multi-device architecture” contains multiple devices while each node used in experiments of “multi-node architecture” contains only a single device. So, the graph which does not fit into single-node-single-device memory can fit into single-node-multi-device after partitioning. 5. Is there a way to permit morph algorithms to be coded in your framework? Response: Currently, our framework does not translate morph algorithms. Supporting morph algorithms will require some kind of runtime system to manage memory on GPU since morph algorithms add and remove the vertices and edges to the graph dynamically. This can be further explored in future work. 6. Is it possible to accommodate FPGA devices in your framework? Response: Yes, we can support FPGA devices (or any other device that is compatible for OpenCL) just by specifying the device type in the command line argument. We did not work with other devices because CPU and GPU are generally used to process graph algorithms. The candidate provided satisfactory answers to all the questions posed and the clarifications sought by the audience and the examiners during the presentation. The candidate's overall performance during the open defense and the oral examination was very satisfactory to the oral examination board. 4. Certificate of Corrections and Changes: All the necessary corrections and changes suggested by the examiners have been made in the thesis and these have been verified by the members of the oral examination board. The thesis has been recommended for acceptance in its revised form. 5. Final Recommendation: In view of the recommendations of the referees and the satisfactory performance of the candidate in the oral examination, the oral examination board recommends that the thesis of Ms. ParitaPatel be accepted for the award of the M.Sc(Engg.) Degree of the Institute. Response to the comments by the external examiner on the M.Sc(Engg.) thesis “Compilation of Graph Algorithms for Hybrid, Cross-Platform, and Distributed Architectures” by Parita Patel 1. Comment: The contributions on optimizations are weak. Response: The novelty of this thesis is to make the Falcon platform agnostic, and additionally process large scale graphs on multi-devices of a single node and multi-node clusters seamlessly. Our framework performs similar to the existing frameworks, but at the same time, it targets several types of architectures which are not possible in the existing works. Advanced optimizations are beyond the scope of this thesis. 2. Comment: The translation of Falcon to OpenCL is simple. While the translation of Falcon to OpenCL was not hard, figuring out the details of the translation for multi-device and multi-node architectures was not simple. For example, design of implementations for collection, set, global variables, concurrency, etc., were non-trivial. These designs have already been explained in the appropriate places in the thesis. Further, such large software introduced its own intricacies during development. 3. Comment: Lines between Falcon work and this work are not clear. Response: Appendix-A shows the falcon implementation of all the algorithms which we used to run the experiments. We compiled these falcon implementations through our framework and subsequently ran the generated code on different types of target architectures and compared the results with other framework's generated code. These falcon programs were written by us. We have also used the front-end of the Falcon compiler and this has already been stated in the thesis (page 16). 4. Comment: There should be a summary of observations in chapter 3. Response: Summary of observations have been added to chapter 3 (pages 35-36), chapter 4 (page 46), and chapter 5 (page 51) of the thesis. 5. Comment: Speedup and scalability achieved with multiple nodes are not great. Response: For the multi-node architecture, we were not able to achieve linear scalability because, with the increase in number of nodes, communication cost increases significantly. Unless the computation cost in the nodes is significant and is much more than the communication cost, this is bound to happen. 6. Comment: It will be good to separate the related work coverage into a separate chapter. Response: The related work is coherent with the flow in chapter 1. It consists of just 4.5 pages and separating it into a separate chapter would make both (rest of) chapter 1 and the new chapter very small. Therefore, we do not recommend it. 7. Comment: The code should be made available for use by the community. Response: The code includes some part of Falcon code (front-end parsing/grammar) also. After discussion with the author of Falcon, the code can be made available to the community. 8. Comment: Page 28: Shouldn’t the else part be inside the kernel? Response: There was some missing text and a few minor changes in Figure 3.14 (page 28) which have been incorporated in the corrected thesis. 9. Comment: Figure 4.1 needs to be explained better. Response: Explanation for Figure 4.1 (pages 38-39) has been added to the thesis. 10. Comment: The problem size justification in the multi-node results is not clear. Response: Single node machine used in the experiments of “multi-device architecture” contains multiple devices while each node used in experiments of “multi-node architecture” contains only a single device. So, the graph which does not fit into single-node-single-device memory can fit into single-node-multi-device after partitioning. Name of the Candidate: Parita Patel (S.R. No. 04-04-00-10-21-14-1-11610) Degree Registered: M.Sc(Engg.) Department: Computer Science & Automation Title of the Thesis: Compilation of Graph Algorithms for Hybrid, Cross-Platform and Graph algorithms are abundantly used in various disciplines. These algorithms perform poorly due to random memory access and negligible spatial locality. In order to improve performance, parallelism exhibited by these algorithms can be exploited by leveraging modern high performance parallel computing resources. Implementing graph algorithms for these parallel architectures requires manual thread management and memory management which becomes tedious for a programmer. Large scale graphs cannot fit into the memory of a single machine. One solution is to partition the graph either on multiple devices of a single node or on multiple nodes of a distributed network. All the available frameworks for such architectures demand unconventional programming which is difficult and error prone. To address these challenges, we propose a framework for compilation of graph algorithms written in an intuitive graph domain-specific language, Falcon. The framework targets shared memory parallel architectures, computational accelerators and distributed architectures (CPU and GPU cluster). First, it analyses the abstract syntax tree (generated by Falcon) and gathers essential information. Subsequently, it generates optimized code in OpenCL for shared-memory parallel architectures and computational accelerators, and OpenCL coupled with MPI code for distributed architectures. Motivation behind generating OpenCL code is its platform-agnostic and vendor-agnostic behavior, i.e., it is portable to all kinds of devices. Our framework makes memory management, thread management, message passing, etc., transparent to the user. None of the available domain-specific languages, frameworks or parallel libraries handle portable implementations of graph algorithms. Experimental evaluations demonstrate that the generated code performs comparably to the state-of-the-art non-portable implementations and hand-tuned implementations. The results also show portability and scalability of our framework.

This thesis mainly focuses on algorithmic and combinatorial questions related to some geometric problems on graphs. In the last part of this thesis, a graph coloring problem is also discussed. Boxicity and Cubicity: These are graph parameters dealing with geomet-ric representations of graphs in higher dimensions. Both these parameters are known to be NP-Hard to compute in general and are even hard to approximate within an O(n1− ) factor for any > 0, under standard complexity theoretic assumptions. We studied algorithmic questions for these problems, for certain graph classes, to yield efficient algorithms or approximations. Our results include a polynomial time constant factor approximation algorithm for computing the cubicity of trees and a polynomial time constant (≤ 2.5) factor approximation algorithm for computing the boxicity of circular arc graphs. As far as we know, there were no constant factor approximation algorithms known previously, for computing boxicity or cubicity of any well known graph class for which the respective parameter value is unbounded. We also obtained parameterized approximation algorithms for boxicity with various edit distance parameters. An o(n) factor approximation algorithm for computing the boxicity and cubicity of general graphs also evolved as an interesting corollary of one of these parameterized algorithms. This seems to be the first sub-linear factor approximation algorithm known for computing the boxicity and cubicity of general graphs. Planar grid-drawings of outerplanar graphs: A graph is outerplanar, if it has a planar embedding with all its vertices lying on the outer face. We give an efficient algorithm to 2-vertex-connect any connected outerplanar graph G by adding more edges to it, in order to obtain a supergraph of G such that the resultant graph is still outerplanar and its pathwidth is within a constant times the pathwidth of G. This algorithm leads to a constant factor approximation algorithm for computing minimum height planar straight line grid-drawings of outerplanar graphs, extending the existing algorithm known for 2-vertex connected outerplanar graphs. n−1 3 Maximum matchings in triangle distance Delaunay graphs: Delau-nay graphs of point sets are well studied in Computational Geometry. Instead of the Euclidean metric, if the Delaunay graph is defined with respect to the convex distance function defined by an equilateral triangle, it is called a Trian-gle Distance Delaunay graph. TD-Delaunay graphs are known to be equivalent to geometric spanners called half-Θ6 graphs. It is known that classical Delaunay graphs of point sets always contain a near perfect matching, for non-degenerate point sets. We show that Triangle Distance Delaunay graphs of a set of n points in general position will always l m contain a matching of size and this bound is tight. We also show that Θ6 graphs, a class of supergraphs of half-Θ6 graphs, can have at most 5n − 11 edges, for point sets in general position. Heterochromatic Paths in Edge Colored Graphs: Conditions on the coloring to guarantee the existence of long heterochromatic paths in edge col-ored graphs is a well explored problem in literature. The objective here is to obtain a good lower bound for λ(G) - the length of a maximum heterochro-matic path in an edge-colored graph G, in terms of ϑ(G) - the minimum color degree of G under the given coloring. There are graph families for which λ(G) = ϑ(G) − 1 under certain colorings, and it is conjectured that ϑ(G) − 1 is a tight lower bound for λ(G). We show that if G has girth is at least 4 log2(ϑ(G))+2, then λ(G) ≥ ϑ(G)− 2. It is also proved that a weaker requirement that G just does not contain four-cycles is enough to guarantee that λ(G) is at least ϑ(G) −o(ϑ(G)). Other special cases considered include lower bounds for λ(G) in edge colored bipartite graphs, triangle-free graphs and graphs without heterochromatic triangles.

This thesis deals with shortest paths problem in graphs. Shortest paths problem is the basic issue of graph theory with many pracitcal applications. We can divide this problem into two following generalizations: single-source shortest path problem and all-pairs shortest paths problem. This text introduces principles and algorithms for generalizations. We describe both classical and new more efficient methods. It contains information about how some of these algorithms were implemented and offers an experimental comparison of these algorithms.

[pt] Consideramos, nesta dissertação, a questão de determinar se um grafo tem uma propriedade P, tal como G é livre de triângulos ou G é 4- colorível. Em particular, consideramos para quais propriedades P existe um algoritmo aleatório com probabilidades de erro constantes que aceita grafos que satisfazem P e rejeita grafos que são epsilon-longe de qualquer grafo que o satisfaça. Se, além disso, o algoritmo tiver complexidade independente do tamanho do grafo, a propriedade é dita testável. Discutiremos os resultados de Alon, Fischer, Newman e Shapira que obtiveram uma caracterização combinatória de propriedades testáveis de grafos, resolvendo um problema em aberto levantado em 1996. Essa caracterização diz informalmente que uma propriedade P de um grafo é testável se e somente se testar P pode ser reduzido a testar a propriedade de satisfazer uma das finitas partições Szemerédi. / [en] We consider, in this thesis, the question of determining if a graph has a property P such as G is triangle-free or G is 4-colorable. In particular, we consider for which properties P there exists a random algorithm with constant error probabilities that accept graphs that satisfy P and reject graphs that are epsilon-far from any graph that satisfies it. If, in addition, the algorithm has complexity independent of the size of the graph, the property is called testable. We will discuss the results of Alon, Fischer, Newman, and Shapira that obtained a combinatorial characterization of testable graph properties, solving an open problem raised in 1996. This characterization informally says that a graph property P is testable if and only if testing P can be reduced to testing the property of satisfying one of finitely many Szemerédi-partitions.

Dans cette thèse, nous nous intéressons à la recherche d’images similaires avec des descripteurs structurés par découpages d’images sur les graphes.Nous proposons une nouvelle approche appelée “bag-of-bags of words” (BBoW) pour la recherche d’images par le contenu (CBIR). Il s’agit d’une extension du modèle classique dit sac-de-mots (bag of words - BoW). Dans notre approche, une image est représentée par un graphe placé sur une grille régulière de pixels d’image. Les poids sur les arêtes dépendent de caractéristiques locales de couleur et texture. Le graphe est découpé en un nombre fixe de régions qui constituent une partition irrégulière de l’image. Enfin, chaque partition est représentée par sa propre signature suivant le même schéma que le BoW. Une image est donc décrite par un ensemble de signatures qui sont ensuite combinées pour la recherche d’images similaires dans une base de données. Contrairement aux méthodes existantes telles que Spatial Pyramid Matching (SPM), le modèle BBoW proposé ne repose pas sur l’hypothèse que des parties similaires d’une scène apparaissent toujours au même endroit dans des images d’une même catégorie. L’extension de cette méthode ` a une approche multi-échelle, appelée Irregular Pyramid Matching (IPM), est ´ également décrite. Les résultats montrent la qualité de notre approche lorsque les partitions obtenues sont stables au sein d’une même catégorie d’images. Une analyse statistique est menée pour définir concrètement la notion de partition stable.Nous donnons nos résultats sur des bases de données pour la reconnaissance d’objets, d’indexation et de recherche d’images par le contenu afin de montrer le caractère général de nos contributions / Image representation is a fundamental question for several computer vision tasks. The contributions discussed in this thesis extend the basic bag-of-words representations for the tasks of object recognition and image retrieval.In the present thesis, we are interested in image description by structural graph descriptors. We propose a model, named bag-of-bags of words (BBoW), to address the problems of object recognition (for object search by similarity), and especially Content-Based Image Retrieval (CBIR) from image databases. The proposed BBoW model, is an approach based on irregular pyramid partitions over the image. An image is first represented as a connected graph of local features on a regular grid of pixels. Irregular partitions (subgraphs) of the image are further built by using graph partitioning methods. Each subgraph in the partition is then represented by its own signature. The BBoW model with the aid of graphs, extends the classical bag-of-words (BoW) model by embedding color homogeneity and limited spatial information through irregular partitions of an image. Compared to existing methods for image retrieval, such as Spatial Pyramid Matching (SPM), the BBoW model does not assume that similar parts of a scene always appear at the same location in images of the same category. The extension of the proposed model to pyramid gives rise to a method we named irregular pyramid matching (IPM).The experiments demonstrate the strength of our approach for image retrieval when the partitions are stable across an image category. The statistical analysisof subgraphs is fulfilled in the thesis. To validate our contributions, we report results on three related computer vision datasets for object recognition, (localized)content-based image retrieval and image indexing. The experimental results in a database of 13,044 general-purposed images demonstrate the efficiency and effectiveness of the proposed BBoW framework.

Les réseaux dynamiques sont constitués d’entités établissant des contacts les unes avec les autres dans le temps. Un défi majeur dans les réseaux dynamiques est de prédire les modèles de mobilité et de décider si l’évolution de la topologie satisfait aux exigences du succès d’un algorithme donné. Les types de dynamique résultant de ces réseaux sont variés en échelle et en nature. Par exemple,certains de ces réseaux restent connexes tout le temps; d’autres sont toujours déconnectés mais offrent toujours une sorte de connexité dans le temps et dans l’espace(connexité temporelle); d’autres sont connexes de manière récurrente, périodique,etc. Tous ces contextes peuvent être représentés sous forme de classes de graphes dynamiques correspondant à des conditions nécessaires et/ou suffisantes pour des problèmes ou algorithmes distribués donnés. Étant donné un graphe dynamique,une question naturelle est de savoir à quelles classes appartient ce graphe. Dans ce travail, nous apportons une contribution à l’automatisation de la classification de graphes dynamiques. Nous proposons des stratégies pour tester l’appartenance d’un graphe dynamique à une classe donnée et nous définissons un cadre générique pour le test de propriétés dans les graphes dynamiques. Nous explorons également le cas où aucune propriété sur le graphe n’est garantie, à travers l’étude du problème de maintien d’une forêt d’arbres couvrants dans un graphe dynamique. / Dynamic networks consist of entities making contact over time with one another. A major challenge in dynamic networks is to predict mobility patterns and decide whether the evolution of the topology satisfies requirements for the successof a given algorithm. The types of dynamics resulting from these networks are varied in scale and nature. For instance, some of these networks remain connected at all times; others are always disconnected but still offer some kind of connectivity over time and space (temporal connectivity); others are recurrently connected,periodic, etc. All of these contexts can be represented as dynamic graph classes corresponding to necessary or sufficient conditions for given distributed problems or algorithms. Given a dynamic graph, a natural question to ask is to which of the classes this graph belongs. In this work we provide a contribution to the automation of dynamic graphs classification. We provide strategies for testing membership of a dynamic graph to a given class and a generic framework to test properties in dynamic graphs. We also attempt to understand what can still be done in a context where no property on the graph is guaranteed through the distributed problem of maintaining a spanning forest in highly dynamic graphs.

<p>Minimum cycle mean (MCM) is an important concept in directed graphs. From clock period optimization, timing analysis to layout optimization, minimum cycle mean algorithms have found widespread use in VLSI system design optimization. With transistor size scaling to 10nm and below, complexities and size of the systems have grown rapidly over the last decade. Scalability of the algorithms both in terms of their runtime and memory usage is therefore important. </p> <p><br></p> <p>Among the few classical MCM algorithms, the algorithm by Young, Tarjan, and Orlin (YTO), has been particularly popular. When implemented with a binary heap, the YTO algorithm has the best runtime performance although it has higher asymptotic time complexity than Karp's algorithm. However, as an efficient implementation of YTO relies on data redundancy, its memory usage is higher and could be a prohibitive factor in large size problems. On the other hand, a typical implementation of Karp's algorithm can also be memory hungry. An early termination technique from Hartmann and Orlin (HO) can be directly applied to Karp's algorithm to improve its runtime performance and memory usage. Although not as efficient as YTO in runtime, HO algorithm has much less memory usage than YTO. We propose several improvements to HO algorithm. The proposed algorithm has comparable runtime performance to YTO for circuit graphs and dense random graphs while being better than HO algorithm in memory usage. </p> <p><br></p> <p>Minimum balancing of a directed graph is an application of the minimum cycle mean algorithm. Minimum balance algorithms have been used to optimally distribute slack for mitigating process variation induced timing violation issues in clock network. In a conventional minimum balance algorithm, the principal subroutine is that of finding MCM in a graph. In particular, the minimum balance algorithm iteratively finds the minimum cycle mean and the corresponding minimum-mean cycle, and uses the mean and cycle to update the graph by changing edge weights and reducing the graph size. The iterations terminate when the updated graph is a single node. Studies have shown that the bottleneck of the iterative process is the graph update operation as previous approaches involved updating the entire graph. We propose an improvement to the minimum balance algorithm by performing fewer changes to the edge weights in each iteration, resulting in better efficiency.</p> <p><br></p> <p>We also apply the minimum cycle mean algorithm in latency insensitive system design. Timing violations can occur in high performance communication links in system-on-chips (SoCs) in the late stages of the physical design process. To address the issues, latency insensitive systems (LISs) employ pipelining in the communication channels through insertion of the relay stations. Although the functionality of a LIS is robust with respect to the communication latencies, such insertion can degrade system throughput performance. Earlier studies have shown that the proper sizing of buffer queues after relay station insertion could eliminate such performance loss. However, solving the problem of maximum performance buffer queue sizing requires use of mixed integer linear programming (MILP) of which runtime is not scalable. We formulate the problem as a parameterized graph optimization problem where for every communication channel there is a parameterized edge with buffer counts as the edge weight. We then use minimum cycle mean algorithm to determine from which edges buffers can be removed safely without creating negative cycles. This is done iteratively in the similar style as the minimum balance algorithm. Experimental results suggest that the proposed approach is scalable. Moreover, quality of the solution is observed to be as good as that of the MILP based approach.</p><p><br></p>

In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of $m$-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape simplification (sparsification) and early prediction of AD. / Ministerio de Economía, Industria y Competitividad (Referencia TIN2012-32839 BES-2013-064482)