This work is generally aimed to synthesize POSS based BCPs via RAFT polymerization, to study their self-assembly behaviors, to research on the effect of POSS self-assembly structure on the bulk properties and to prepare nanostructured hybrid epoxy via self-assembly of POSS based copolymer. In Chapter1, We studied the RAFT polymerization of POSS macromers and capable to synthesize well defined POSS based BCPs with high POSS fraction and different topology such as AB，BAB and (BA)3. The vertex group and the morphology effect on thermo-mechanical properties of POSS based BCPs as well as the structure-property relationship was investigated. Dispersion RAFT polymerization in apolar solvent was applied and various aggregates with different morphology in Chapter2. Cooling induced reversible micelle formation and transition was found and the pathway selection in vesicle formation was investigated. Nano-construction of O/I hybrid epoxy materials based on POSS based copolymers was investigated in Chapter4. The effect of functional group content on miscibility of POSS based statistic copolymer and epoxy was investigated. A novel method to nanostructure epoxy hybrid involving self-assembly of POSS based BCPs in epoxy was presented. High homogeneity and well size/morphology control of core-corona structure containing rigid POSS core and soluble PMMA corona in networks were obtained.

We study various binomial and monomial ideals arising in the theory of divisors, orientations, and matroids on graphs. We use ideas from potential theory on graphs and from the theory of Delaunay decompositions for lattices to describe their minimal polyhedral cellular free resolutions. We show that the resolutions of all these ideals are closely related and that their Z-graded Betti tables coincide. As corollaries, we give conceptual proofs of conjectures and questions posed by Postnikov and Shapiro, by Manjunath and Sturmfels, and by Perkinson, Perlman, and Wilmes. Various other results related to the theory of chip-firing games on graphs also follow from our general techniques and results.

In the thesis robust routing design problems in resilient networks are considered. In the first part computational complexity of such problems are discussed. The following cases are considered: - path protection and path restoration - failure-dependent and failure-independent restoration - cases with and without stub-release - single-link failures and multiple-link failures (shared risk link group) - non-bifurcated (unsplittable) flows and bifurcated flows For each of the related optimization cases a mixed-integer (in the non-bifurcated cases) or linear programming formulation (in all bifurcated cases) is presented, and their computational complexity is investigated. For the NP-hard cases original NP-hardness proofs are provided, while for the polynomial cases compact linear programming formulations (which prove the polynomiality in the question) are discussed. Moreover, pricing problems related to each of the considered NP-hard problems are discussed. The second part of the thesis deals with various routing strategies in networks where the uncertainty issues are modeled using the polyhedral model. In such networks two extrema are possible. The simplest in terms of implementation, and simultaneously the least effective strategy, is the robust stable routing. On the other hand, the most effective strategy, i.e., the dynamic routing, is virtually impossible to implement in real world networks. Therefore, the major aim of this part of the thesis is to present novel routing strategies that merge the simplicity of the robust stable routing with the efficiency of the dynamic routing

This thesis presents cutter swept volume generation, in-process workpiece modeling and Cutter Workpiece Engagement (CWE) algorithms for finding the instantaneous intersections between cutter and workpiece in milling. One of the steps in simulating machining operations is the accurate extraction of the intersection geometry between cutter and workpiece. This geometry is a key input to force calculations and feed rate scheduling in milling. Given that industrial machined components can have highly complex geometries, extracting intersections accurately and efficiently is challenging. Three main steps are needed to obtain the intersection geometry between cutter and workpiece. These are the Swept volume generation, in-process workpiece modeling and CWE extraction respectively. In this thesis an analytical methodology for determining the shapes of the cutter swept envelopes is developed. In this methodology, cutter surfaces performing 5-axis tool motions are decomposed into a set of characteristic circles. For obtaining these circles a concept of two-parameter-family of spheres is introduced. Considering relationships among the circles the swept envelopes are defined analytically. The implementation of methodology is simple, especially when the cutter geometries are represented by pipe surfaces. During the machining simulation the workpiece update is required to keep track of the material removal process. Several choices for workpiece updates exist. These are the solid, facetted and vector model based methodologies. For updating the workpiece surfaces represented by the solid or faceted models third party software can be used. In this thesis multi-axis milling update methodologies are developed for workpieces defined by discrete vectors with different orientations. For simplifying the intersection calculations between discrete vectors and the tool envelope the properties of canal surfaces are utilized. A typical NC cutter has different surfaces with varying geometries and during the material removal process restricted regions of these surfaces are eligible to contact the in-process workpiece. In this thesis these regions are analyzed with respect to different tool motions. Later using the results from these analyses the solid, polyhedral and vector based CWE methodologies are developed for a range of different types of cutters and multi-axis tool motions. The workpiece surfaces cover a wide range of surface geometries including sculptured surfaces.

A simplicial cell complex K is the face poset of a regular CW complex W such that the boundary complex of each cell is isomorphic to the boundary complex of a simplex of same dimension. If a topological space X is homeomorphic to W then we say that K is a pseudotriangulation of X. For d 1, a (d + 1)-colored graph is a graph = (V; E) with a proper edge coloring : E ! f0; : : : ; dg. Such a graph is called contracted if (V; E n 1(i)) is connected for each color A contracted graph = (V; E) with an edge coloring : E ! f0; : : : ; dg determines a d-dimensional simplicial cell complex K( ) whose vertices have one to one correspondence with the colors 0; : : : ; d and the facets (d-cells) have one to one correspondence with the vertices in V . If K( ) is a pseudotriangulation of a manifold M then ( ; ) is called a crystallization of M. In [71], Pezzana proved that every connected closed PL manifold admits a crystallization. This thesis addresses many important results of crystallization theory in combinatorial topology. The main contributions in this thesis are the followings. We have introduced the weight of a group which has a presentation with number of relations is at most the number of generators. We have shown that the number of vertices of any crystallization of a connected closed 3-manifold M is at least the weight of the fundamental group of M. This lower bound is sharp for the 3-manifolds RP3, L(3; 1), L(5; 2), S1 S1 S1, S2 S1, S2 S1 and S3=Q8, where Q8 is the quaternion group. Moreover, there is a unique such vertex minimal crystallization in each of these seven cases. We have also constructed crystallizations of L(kq 1; q) with 4(q + k 1) vertices for q 3, k 2 and L(kq +1; q) with 4(q + k) vertices for q 4, k 1. In [22], Casali and Cristofori found similar crystallizations of lens spaces. By a recent result of Swartz [76], our crystallizations of L(kq + 1; q) are vertex minimal when kq + 1 are even. In [47], Gagliardi found presentations of the fundamental group of a manifold M in terms of a crystallization of M. Our construction is the converse of this, namely, given a presentation of the fundamental group of a 3-manifold M, we have constructed a crystallization of M. These results are in Chapter 3. We have de ned the weight of the pair (hS j Ri; R) for a given presentation hS j R of a group, where the number of generators is equal to the number of relations. We present an algorithm to construct crystallizations of 3-manifolds whose fundamental group has a presentation with two generators and two relations. If the weight of (hS j Ri; R) is n then our algorithm constructs all the n-vertex crystallizations which yield (hS j Ri; R). As an application, we have constructed some new crystallization of 3-manifolds. We have generalized our algorithm for presentations with three generators and a certain class of relations. For m 3 and m n k 2, our generalized algorithm gives a 2(2m + 2n + 2k 6 + n2 + k2)-vertex crystallization of the closed connected orientable 3-manifold Mhm; n; ki having fundamental group hx1; x2; x3 j xm1 = xn2 = xk3 = x1x2x3i. These crystallizations are minimal and unique with respect to the given presentations. If `n = 2' or `k 3 and m 4' then our crystallization of Mhm; n; ki is vertex-minimal for all the known cases. These results are in Chapter 4. We have constructed a minimal crystallization of the standard PL K3 surface. The corresponding simplicial cell complex has face vector (5; 10; 230; 335; 134). In combination with known results, this yields minimal crystallizations of all simply connected PL 4-manifolds of \standard" type, i.e., all connected sums of CP2, CP2, S2 S2, and the K3 surface. In particular, we obtain minimal crystallizations of a pair 4-manifolds which are homeomorphic but not PL-homeomorphic. We have also presented an elementary proof of the uniqueness of the 8-vertex crystallization of CP2. These results are in Chapter 5. For any crystallization ( ; ) the number f1(K( )) of 1-simplices in K( ) is at least d+1 . It is easy to see that f1(K( )) = d+1 if and only if (V; 1(A)) is connected for each d 2 2 1)-set A called simple. All the crystallization in Chapter 5 (. Such a crystallization is are simple. Let ( ; ) be a crystallization of M, where = (V; E) and : E ! f0; : : : ; dg. We say that ( ; ) is semi-simple if (V; 1(A)) has m + 1 connected components for each (d 1)-set A, where m is the rank of the fundamental group of M. Let ( ; ) be a connected (d +1)-regular (d +1)-colored graph, where = (V; E) and : E ! f0; : : : ; dg. An embedding i : ,! S of into a closed surface S is called regular if there exists a cyclic permutation ("0; "1; : : : ; "d) (of the color set) such that the boundary of each face of i( ) is a bi-color cycle with colors "j; "j+1 for some j (addition is modulo d+1). Then the regular genus of ( ; ) is the least genus (resp., half of genus) of the orientable (resp., non-orientable) surface into which embeds regularly. The regular genus of a closed connected PL 4-manifold M is the minimum regular genus of its crystallizations. For a closed connected PL 4-manifold M, we have provided the following: (i) a lower bound for the regular genus of M and (ii) a lower bound of the number of vertices of any crystallization of M. We have proved that all PL 4-manifolds admitting semi-simple crystallizations, attain our bounds. We have also characterized the class of PL 4-manifolds which admit semi-simple crystallizations. These results are in Chapter 6.

Geometric Multigrid (GMG) methods are widely used in numerical analysis to accelerate the convergence of partial differential equations solvers using a hierarchy of grid discretizations. These solvers find plenty of applications in various fields in engineering and scientific domains, where solving PDEs is of fundamental importance. Using multigrid methods, the pace at which the solvers arrive at the solution can be improved at an algorithmic level. With the advance in modern computer architecture, solving problems with higher complexity and sizes is feasible - this is also the case with multigrid methods. However, since hardware support alone cannot achieve high performance in execution time, there is a need for good software that help programmers in doing so. Multiple grid sizes and recursive expression of multigrid cycles make the task of manual program optimization tedious and error-prone. A high-level language that aids domain experts to quickly express complex algorithms in a compact way using dedicated constructs for multigrid methods and with good optimization support is thus valuable. Typical computation patterns in a GMG algorithm includes stencils, point-wise accesses, restriction and interpolation of a grid. These computations can be optimized for performance on modern architectures using standard parallelization and locality enhancement techniques. Several past works have addressed the problem of automatic optimizations of computations in various scientific domains using a domain-specific language (DSL) approach. A DSL is a language with features to express domain-specific computations and compiler support to enable optimizations specific to these computations. Halide and PolyMage are two of the recent works in this direction, that aim to optimize image processing pipelines. Many computations like upsampling and downsampling an image are similar to interpolation and restriction in geometric multigrid methods. In this thesis, we demonstrate how high performance can be achieved on GMG algorithms written in the PolyMage domain-specific language with new optimizations we added to the compiler. We also discuss the implementation of non-trivial optimizations, on PolyMage compiler, necessary to achieve high parallel performance for multigrid methods on modern architectures. We realize these goals by: • introducing multigrid domain-specific constructs to minimize the verbosity of the algorithm specification; • storage remapping to reduce the memory footprint of the program and improve cache locality exploitation; • mitigating execution time spent in data handling operations like memory allocation and freeing, using a pool of memory, across multiple multigrid cycles; and • incorporating other well-known techniques to leverage performance, like exploiting multi-dimensional parallelism and minimizing the lifetime of storage buffers. We evaluate our optimizations on a modern multicore system using five different benchmarks varying in multigrid cycle structure, complexity and size, for two-and three-dimensional data grids. Experimental results show that our optimizations: • improve performance of existing PolyMage optimizer by 1.31x; • are better than straight-forward parallel and vector implementations by 3.2x; • are better than hand-optimized versions in conjunction with optimizations by Pluto, a state-of-the-art polyhedral source-to-source optimizer, by 1.23x; and • achieve up to 1.5$\times$ speedup over NAS MG benchmark from the NAS Parallel Benchmarks. (The speedup numbers are Geometric means over all benchmarks)

XAVIER, Alinson Santos. Geração de Facetas para Politopos de Conjuntos Independentes. 2011. 141 f. : Dissertação (mestrado) - Universidade Federal do Ceará, Centro de Ciências, Departamento de Computação, Fortaleza-CE, 2011. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-05-23T19:04:42Z No. of bitstreams: 1 2011_dis_asxavier.pdf: 1098827 bytes, checksum: b69a55ab904901d692a7afbf26cfbb04 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-05-23T19:10:07Z (GMT) No. of bitstreams: 1 2011_dis_asxavier.pdf: 1098827 bytes, checksum: b69a55ab904901d692a7afbf26cfbb04 (MD5) / Made available in DSpace on 2016-05-23T19:10:07Z (GMT). No. of bitstreams: 1 2011_dis_asxavier.pdf: 1098827 bytes, checksum: b69a55ab904901d692a7afbf26cfbb04 (MD5) Previous issue date: 2011 / A stable set of a graph is a set of pairwise non-adjacent vertices. The maximum stable set problem is to find a stable set of maximum cardinality in a given graph. The maximum induced k-partite subgraph problem is to find k stable sets such that their union has maximum cardinality. Besides having applications in various fields, including computer vision, molecular biology and VLSI circuit design, these problems also model other important combinatorial problems, such as set packing and vertex coloring. In the present work, we study the facial structure of the polytopes associated with both problems. First, we describe a new facet generating procedure for the stable set polytope, which unifies and subsumes several previous procedures. Besides generating many well-known facet inducing inequalities, this procedure can also generate new facet-inducing inequalities which have not been previously described. Then, we study the maximum induced k-partite polytope formulated by asymmetric representatives. We describe its simplest facets, show that some of its facets arise from vertex induced subgraphs, and identify two classes of subgraphs which generate facets of the polytope. To reach these main results, we study the affine equivalence between polyhedra, and also develop a new facet generating procedure for general polyhedra which subsumes the many versions of the lifting of variables. / Um conjunto independente de um grafo é um subconjunto de vértices que não contém nenhum par de vértices vizinhos. O problema do maior conjunto independente consiste em encontrar um conjunto independente de cardinalidade máxima. O problema do maior subgrafo induzido k-partido consiste em encontrar k conjuntos independentes cuja união tenha cardinalidade máxima. Além de possuírem aplicação em diversas áreas, como visão computacional, biologia molecular e projeto de circuitos integrados, estes problemas também modelam outros problemas de otimização combinatória, como empacotamento de conjuntos e coloração de vértices. Neste trabalho, estudamos os politopos associados aos dois problemas. Primeiro, descrevemos um novo procedimento de geração de facetas para o politopo de conjuntos independentes, que unifica e generaliza diversos procedimentos anteriores. Além de gerar várias classes de desigualdades indutoras de facetas já conhecidas, este procedimento também gera novas desigualdades que ainda não foram descritas na literatura. Em seguida, estudamos o politopo do subgrafo induzido k-partido associado à formulação por representantes de cor. Identificamos suas facetas mais simples, mostramos que facetas podem ser geradas a partir de subgrafos induzidos, e descrevemos duas classes de subgrafos que geram facetas deste politopo. Para obter os principais resultados desta dissertação, fazemos um estudo da relação de afim-isomorfismo entre poliedros, e desenvolvemos um novo procedimento de conversão de faces em facetas que generaliza as diversas versões do procedimento de levantamento de variáveis.

Using concepts of the socio-technical systems theory, this dissertation defines mathematically the problems of cooperative teams formation considering social and technical constraints separately, and then presents their computational complexity. Mainly, it is defined and studied the central problem in this work, which jointly considers social and technical requirements for creating teams of cooperative work, to be called FEST (Socio-Technical Teams Formation Problem). Two mathematical formulations and a meta-heuristic are proposed for FEST. One formulation uses a cubic number of variables and constraints, whereas the second one has a quadratic number of variables but an exponential number of constraints. The proposed heuristic is based on the Non-monotonic Simulated Annealing meta-heuristic with local search using swap-like operators. The correctness of both formulations is proved. A polynomial algorithm to separate the constraints of the second formulation is presented. It is proved that the two formulations provide the same linear programming bound, and valid inequalities to strengthen it are proposed. For the compact formulation, some classes of valid inequalities are shown to be facet-inducing under suitable hypotheses. Finally, it is statistically analyzed the performance of the presented formulations and meta-heuristic. Real and random generated instances are used in the computational experiments. / Utilizando conceitos da Teoria dos Sistemas SociotÃcnicos, este trabalho define matematicamente os problemas de formaÃÃo de equipes cooperativas considerando separadamente restriÃÃes sociais e tÃcnicas e apresenta a complexidade computacional dos mesmos. Sobretudo, à definido e estudado o problema central deste trabalho, que considera conjuntamente requisitos sociais e tÃcnicos para criaÃÃo de equipes de trabalho cooperativo, denominado FEST (Problema de FormaÃÃo de Equipes SociotÃcnicas). Duas formulaÃÃes matemÃticas e uma meta-heurÃstica para o FEST sÃo propostas. Uma formulaÃÃo utiliza um nÃmero cÃbico de variÃveis e restriÃÃes, enquanto a segunda formulaÃÃo possui um nÃmero quadrÃtico de variÃveis, mas um nÃmero exponencial de restriÃÃes. A meta-heurÃstica proposta à baseada no Simulated Annealing NÃo-MonotÃnico com busca local que usa operadores tipo swap. A corretude de ambas as formulaÃÃes à provada. Um algoritmo polinomial para separar as restriÃÃes da segunda formulaÃÃo à apresentado. Mostra-se que as duas formulaÃÃes fornecem o mesmo limite de programaÃÃo linear, e desigualdades vÃlidas para fortalecÃ-lo sÃo propostas. Para a formulaÃÃo compacta, algumas classes de desigualdades vÃlidas sÃo demonstradas indutoras de facetas sob hipÃteses apropriadas. Por fim, foi analisado estatisticamente o desempenho das formulaÃÃes e da meta-heurÃstica apresentadas. InstÃncias reais e geradas aleatoriamente sÃo usadas nos experimentos computacionais.

O problema do Máximo Subgrafo Induzido Comum (MSIC) pertence a classe NP-difícil e possui aplicações em diversas áreas. Apesar de sua complexidade, ainda é importante conhecer soluções exatas para instâncias deste problema. Os algoritmos exatos encontrados na literatura buscam resolvê-lo através de técnicas de backtracking ou através de sua redução para o problema da Clique Máxima. Neste trabalho procuramos dar uma solução exata para o MSIC, tratando-o diretamente através da utilização de modelos de Programação Linear Inteira (PLI) e técnicas de combinatória poliédrica. Assim, realizamos um estudo teórico do poliedro do MSIC e fomos capazes de encontrar algumas desigualdades válidas fortes, inclusive com provas de que algumas delas representam facetas daquele poliedro. Adicionalmente, provamos que existe uma equivalâencia entre o modelo PLI aqui apresentado para o MSIC e uma formulação bem conhecida para o problema da Clique Máxima. Posteriormente, foram implementados algoritmos de Branch-and-Bound (B&B) e Branch-and-Cut (B&C) utilizando as desigualdades encontradas e algumas técnicas para tentar tornar os algoritmos mais eficientes. Experimentos foram executados com os algoritmos implementados neste trabalho e, também, com um algoritmo já existente para resolver o problema da Clique, chamado Cliquer. Os resultados foram comparados e, dentre os algoritmos de PLI, constatamos que o mais eficiente foi aquele que utilizou uma formulação para o MSIC que chamamos de Clique-IS, utilizando B&B e técnicas mais básicas que outros algoritmos. Este algoritmo mostrou-se mais eficiente, inclusive, que um algoritmo PLI com um modelo baseado no problema da Clique Máaxima. Este fato sugere que para uma abordagem baseada em PLI, vale a pena utilizar uma formulação do MSIC diretamente, ao invés de uma que se apóie na redução deste para o problema da Clique Máxima. Ja a comparaçao do melhor algoritmo desenvolvido neste trabalho com o Cliquer, mostrou que este último é mais eficiente. Para que um algoritmo baseado em PLI (utilizando uma formulação com as mesmas variáveis usadas por nós) tivesse alguma chance de vencer um algoritmo combinatório como o Cliquer, seria necessário conhecer mais desigualdades que estivessem ativas na solução ótima do problema._________________________________________________________________________________________ ABSTRACT: The Maximum Common Subgraph problem (MSIC) is in MV-hard and has applications in several fields. Despite its complexity, it is still important to know exact solutions for instances of this problem. The exact algorithms found in literature try to solve it through backtracking techniques or through its reduction to the Maximum Clique problem. In this work we try to give an exact solution to MSIC by addressing it directly, using Linear Integer Programming (PLI) and polyhedral combinatorics techniques. So, we performed a study of the MSIC polyhedron and we were able to find some strong valid inequalities, including some that were proven to define facets of that polyhedron. Additionally, we proved that an equivalence between the PLI model presented here for MSIC and a well known formulation for the Maximum Clique problem exists. Later, Branch-and-Bound (B&B) and Branch-and-Cut (B&C) algorithms were implemented using the inequalities found and some techniques to try to render the algorithms more efficient. Experiments were performed with the algorithms implemented in this work and, also, with an already existing algorithm to solve the Maximum Clique problem, called Cliquer. The results were compared and, among the PLI algorithms, we found that the most efficient was the one that used the formulation which we called Clique-IS, using B&B and more basic techniques than other algorithms. This algorithm was even more efficient than a PLI algorithm with a Clique-based model. This fact suggests that for a PLI approach it is worth to use a formulation based on the MSIC polyhedron instead of one based on its reduction to the Maximum Clique problem. The comparison of the best algorithm developed in this work with Cliquer, though, showed that the latest is more efficient. In order to some PLI-based algorithm (using a formulation with the same variables used by us) to have any chance of outperforming a combinatorial algorithm like Cliquer, it would be necessary to know more inequalities that are active in the problem's optimal solution.

Orientador: Cid Carvalho de Souza / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Computação / Made available in DSpace on 2018-08-15T07:24:38Z (GMT). No. of bitstreams: 1 Piva_Breno_M.pdf: 1251793 bytes, checksum: bf559620a7bdefeec032b5c87d196b5b (MD5) Previous issue date: 2009 / Resumo: O problema do Máximo Subgrafo Induzido Comum (MSIC) pertence a classe NP-difícil e possui aplicações em diversas áreas. Apesar de sua complexidade, ainda é importante conhecer soluções exatas para instâncias deste problema. Os algoritmos exatos encontrados na literatura buscam resolvê-lo através de técnicas de backtracking ou através de sua redução para o problema da Clique Máxima. Neste trabalho procuramos dar uma solução exata para o MSIC, tratando-o diretamente através da utilização de modelos de Programação Linear Inteira (PLI) e técnicas de combinatória poliédrica. Assim, realizamos um estudo teórico do poliedro do MSIC e fomos capazes de encontrar algumas desigualdades válidas fortes, inclusive com provas de que algumas delas representam facetas daquele poliedro. Adicionalmente, provamos que existe uma equivalâencia entre o modelo PLI aqui apresentado para o MSIC e uma formulação bem conhecida para o problema da Clique Máxima. Posteriormente, foram implementados algoritmos de Branch-and-Bound (B&B) e Branch-and-Cut (B&C) utilizando as desigualdades encontradas e algumas técnicas para tentar tornar os algoritmos mais eficientes. Experimentos foram executados com os algoritmos implementados neste trabalho e, também, com um algoritmo já existente para resolver o problema da Clique, chamado Cliquer. Os resultados foram comparados e, dentre os algoritmos de PLI, constatamos que o mais eficiente foi aquele que utilizou uma formulação para o MSIC que chamamos de Clique-IS, utilizando B&B e técnicas mais básicas que outros algoritmos. Este algoritmo mostrou-se mais eficiente, inclusive, que um algoritmo PLI com um modelo baseado no problema da Clique Máaxima. Este fato sugere que para uma abordagem baseada em PLI, vale a pena utilizar uma formulação do MSIC diretamente, ao invés de uma que se apóie na redução deste para o problema da Clique Máxima. Ja a comparaçao do melhor algoritmo desenvolvido neste trabalho com o Cliquer, mostrou que este último é mais eficiente. Para que um algoritmo baseado em PLI (utilizando uma formulação com as mesmas variáveis usadas por nós) tivesse alguma chance de vencer um algoritmo combinatório como o Cliquer, seria necessário conhecer mais desigualdades que estivessem ativas na solução ótima do problema / Abstract: The Maximum Common Subgraph problem (MSIC) is in MV-hard and has applications in several fields. Despite its complexity, it is still important to know exact solutions for instances of this problem. The exact algorithms found in literature try to solve it through backtracking techniques or through its reduction to the Maximum Clique problem. In this work we try to give an exact solution to MSIC by addressing it directly, using Linear Integer Programming (PLI) and polyhedral combinatorics techniques. So, we performed a study of the MSIC polyhedron and we were able to find some strong valid inequalities, including some that were proven to define facets of that polyhedron. Additionally, we proved that an equivalence between the PLI model presented here for MSIC and a well known formulation for the Maximum Clique problem exists. Later, Branch-and-Bound (B&B) and Branch-and-Cut (B&C) algorithms were implemented using the inequalities found and some techniques to try to render the algorithms more efficient. Experiments were performed with the algorithms implemented in this work and, also, with an already existing algorithm to solve the Maximum Clique problem, called Cliquer. The results were compared and, among the PLI algorithms, we found that the most efficient was the one that used the formulation which we called Clique-IS, using B&B and more basic techniques than other algorithms. This algorithm was even more efficient than a PLI algorithm with a Clique-based model. This fact suggests that for a PLI approach it is worth to use a formulation based on the MSIC polyhedron instead of one based on its reduction to the Maximum Clique problem. The comparison of the best algorithm developed in this work with Cliquer, though, showed that the latest is more efficient. In order to some PLI-based algorithm (using a formulation with the same variables used by us) to have any chance of outperforming a combinatorial algorithm like Cliquer, it would be necessary to know more inequalities that are active in the problem's optimal solution / Mestrado / Otimização Combinatoria / Mestre em Ciência da Computação