Constrained graph problems are about finding graphs respecting a given set of constraints. These problems occur in many areas. For example, security properties, biological reaction mechanisms, ecological predator/prey relationships, compiler code optimizations, and logic circuit fault diagnosis are just a few of the areas in which graph constraints play an important role. This thesis proposes a constraint programming approach for solving these problems. We present new constraints defined on top of the notions of domination and transitive closure, and their search algorithms. We have implemented these constraints in the state-of-the-art Gecode system and shown that they are competitive with or better than other approaches in realistic scenarios. / Les problèmes de graphes contraints concernent la recherche de graphes qui respectent un ensemble donné de contraintes. Ils apparaissent dans de nombreux domaines. Par exemple, la sécurité dans les logiciels, les méchanismes des réactions biologiques, les relations prédateur/proie en écologie, l'optimisation de code par les compilateurs, et le diagnostic de pannes dans des circuits logiques sont quelques-uns des domaines dans lesquels les contraintes de graphes jouent un rôle important. Cette thèse propose une approche basée sur la programmation par contraintes pour résoudre ces problèmes. Nous présentons de nouvelles contraintes définies sur les notions de domination et de clôture transitive, ainsi que leurs algorithmes de recherche. Nous avons implémenté ces contraintes dans le système de pointe Gecode, et avons montré notre approche compétitive et parfois meilleure que d'autres approches dans des cas réalistes.

Constrained graph problems are about finding graphs respecting a given set of constraints. These problems occur in many areas. For example, security properties, biological reaction mechanisms, ecological predator/prey relationships, compiler code optimizations, and logic circuit fault diagnosis are just a few of the areas in which graph constraints play an important role. This thesis proposes a constraint programming approach for solving these problems. We present new constraints defined on top of the notions of domination and transitive closure, and their search algorithms. We have implemented these constraints in the state-of-the-art Gecode system and shown that they are competitive with or better than other approaches in realistic scenarios. / Les problèmes de graphes contraints concernent la recherche de graphes qui respectent un ensemble donné de contraintes. Ils apparaissent dans de nombreux domaines. Par exemple, la sécurité dans les logiciels, les méchanismes des réactions biologiques, les relations prédateur/proie en écologie, l'optimisation de code par les compilateurs, et le diagnostic de pannes dans des circuits logiques sont quelques-uns des domaines dans lesquels les contraintes de graphes jouent un rôle important. Cette thèse propose une approche basée sur la programmation par contraintes pour résoudre ces problèmes. Nous présentons de nouvelles contraintes définies sur les notions de domination et de clôture transitive, ainsi que leurs algorithmes de recherche. Nous avons implémenté ces contraintes dans le système de pointe Gecode, et avons montré notre approche compétitive et parfois meilleure que d'autres approches dans des cas réalistes.

Optical signal-to-noise ratio (OSNR) is considered as the dominant performance parameter at the physical layer in optical networks. This thesis is interested in control and optimization of channel OSNR by using optimization and game-theoretic approaches, incorporating two physical constraints: the link capacity constraint and the channel OSNR target. To start, we study OSNR optimization problems with link capacity constraints in single point-to-point fiber links via two approaches. We first present a framework of a Nash game between channels towards optimizing individual channel OSNR. The link capacity constraint is imposed as a penalty term to each cost function. The selfish behavior in a Nash game degrades the system performance and leads to the inefficiency of Nash equilibria. From the system point of view, we formulate a system optimization problem with the objectives of achieving an OSNR target for each channel while satisfying the link capacity constraint. As an alternative to study the efficiency of Nash equilibria, we use the system framework to investigate the effects of parameters in cost functions in the game-theoretic framework. Then extensions to multi-link and mesh topologies are carried out. We propose a partition approach by using the flexibility of channel power adjustment at optical switches. The multi-link structure is partitioned into stages with each stage being a single sink. By fully using the flexibility, a more natural partition approach is applied to mesh topologies where each stage is a single link. The closed loop in mesh topologies can be unfolded by selecting a starting link. Thus instead of maximization of channel OSNR from end to end, we consider minimization of channel OSNR degradation between stages. We formulate a partitioned Nash game which is composed of ladder-nested stage Nash games. Distributed algorithms towards the computation of a Nash equilibrium solution are developed for all different game frameworks. Simulations and experimental implementations provide results to validate the applicability of theoretical results.

Optical signal-to-noise ratio (OSNR) is considered as the dominant performance parameter at the physical layer in optical networks. This thesis is interested in control and optimization of channel OSNR by using optimization and game-theoretic approaches, incorporating two physical constraints: the link capacity constraint and the channel OSNR target. To start, we study OSNR optimization problems with link capacity constraints in single point-to-point fiber links via two approaches. We first present a framework of a Nash game between channels towards optimizing individual channel OSNR. The link capacity constraint is imposed as a penalty term to each cost function. The selfish behavior in a Nash game degrades the system performance and leads to the inefficiency of Nash equilibria. From the system point of view, we formulate a system optimization problem with the objectives of achieving an OSNR target for each channel while satisfying the link capacity constraint. As an alternative to study the efficiency of Nash equilibria, we use the system framework to investigate the effects of parameters in cost functions in the game-theoretic framework. Then extensions to multi-link and mesh topologies are carried out. We propose a partition approach by using the flexibility of channel power adjustment at optical switches. The multi-link structure is partitioned into stages with each stage being a single sink. By fully using the flexibility, a more natural partition approach is applied to mesh topologies where each stage is a single link. The closed loop in mesh topologies can be unfolded by selecting a starting link. Thus instead of maximization of channel OSNR from end to end, we consider minimization of channel OSNR degradation between stages. We formulate a partitioned Nash game which is composed of ladder-nested stage Nash games. Distributed algorithms towards the computation of a Nash equilibrium solution are developed for all different game frameworks. Simulations and experimental implementations provide results to validate the applicability of theoretical results.

We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments. Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists. Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths.

To satisfy the requirements of small satellites with attitude control requirements, a guidance, navigation, and control module was designed at the Texas Spacecraft Laboratory. However, these small satellites tend to have attitude constraints in the form of keep-in and keep-out cones. Two methods for autonomous constrained attitude guidance are presented. The first satisfies the problem of guiding a single axis through keep-out constraints while satisfying a second keep-in constraint through an adjoined optimization routine. The method leverages methods for discretizing the attitude shell combined with the graph pathfinding algorithm A*. The second approach generalizes the problem to any number of attitude constraints in the body and inertial frame by discretizing the quaternion space using a series of concentric discretized shells. An approach for discretized attitude optimization is created to allow the vehicle to identify which attitude mode to operate under while simultaneously optimizing the solar power input. The discretized constrained attitude guidance and attitude optimization techniques are tied together in the flight software architecture and tested in a hardware-in-the-loop simulation environment. / text

Imposing additional constraints on multiple sequence alignment (MSA) algorithms can often produce more biologically meaningful alignments. Hence, various constrained multiple sequence alignment (CMSA) algorithms have been developed in the literature, where researchers used anchor points, regular expressions, or context-free-grammars to specify the constraints, wherein alignments produced are forced to align around segments that match the constraints. In this thesis, we propose CSA-X, a modularized program of constrained multiple sequence alignment that accepts constraints in the form of regular expressions. It uses an arbitrary underlying multiple sequence alignment program to generate alignments, and is therefore modular. The name CSA-X refers to our proposed program generally, where the letter X is substituted with the name of a (non-constrained) multiple sequence alignment algorithm which is used as underlying MSA engine in the proposed program. We compare the accuracy of our program with another constrained multiple sequence alignment program called RE-MuSiC that similarly uses regular expressions for constraints. In addition, comparisons are also made to the underlying MSA programs (without constraints). The BAliBASE 3.0 benchmark database is used to assess the performance of the proposed program CSA-X, other MSA programs, and CMSA programs considered in this study. Based on the results presented herein, CSA-X outperforms RE-MuSiC, and scores well against the underlying alignment programs. It also shows that the use of regular expression constraints, if chosen well, created from the least conserved region of the correct alignments, improves the alignment accuracy. In this study, ProbCons and T-Coffee are used as the underlying MSA programs in CSA-X, and the accuracy of the alignments are measured in terms of Q score and TC score. On average, CSA-X used with constraints identified from the least conserved regions of the correct alignments achieves results that are 17.65% more for Q score, and 23.7% more for TC score compared to RE-MuSiC. In fact, CSA-X with ProbCons (CSA-PC) achieves a higher score in over 97.9% of the cases for Q score, and over 96.4% of the cases for TC score. In addition, CSA-X with T-Coffee (CSA-TCOF) achieves a higher score in over 97.7% of the cases for Q score, and over 94.8% of the cases for TC score. Furthermore, CSA-X with regular expressions created from the least conserved regions of the correct alignments achieves higher accuracy scores compared to standalone ProbCons and T-Coffee. To measure the statistical significance of CSA-X results, the Wilcoxon rank-sum test and Wilcoxon signed-rank test are performed, and these tests show that CSA-X results for the least conserved regular expression constraint sets from the correct BAliBASE 3.0 alignments are significantly different than those from RE-MuSiC, ProbCons, and T-Coffee.

A guidance, navigation, and control (GN&C) module is being designed and fabricated as part of a series of CubeSats being built by the Satellite Design Laboratory at the University of Texas. A spacecraft attitude control simulation environment called StarBox was created in order to perform trade studies and conduct performance analysis for the GN&C module. Navigation and control algorithms were tested using StarBox and then implemented onto an embedded flight computer. These algorithms were then tested in a hardware-in-the-loop simulation. In addition, the feasibility of utilizing advanced constrained attitude control algorithms was investigated by focusing on implementation in flight software. A mechanical and electrical design for the GN&C module was completed. A prototype system was set up on a bench-top for integrated testing. The analysis indicates that the system will satisfy the requirements of several CubeSat missions, including the current missions at the University of Texas known as Bevo2 and ARMADILLO. / text

We consider the problem of finding a bounded-curvature path in the plane from one configuration αs to another configuration αt that avoids the interior of a set of polygonal obstacles Ε. We call any such path from αs to αt a feasible path. In this thesis, we develop algorithms to find feasible paths that have explicit guarantees on when they will return a feasible path. We phrase our guarantees and run time analysis in terms of the complexity of the desired solution (see k and λ below). In a sense, our algorithms are output sensitive, which is particularly desirable because there are no known bounds on the solution complexity amid arbitrary polygonal environments. Our first major result is an algorithm that given Ε, αs, αt, and a positive integer k either (i) verifies that every feasible path has a descriptive complexity greater than k or (ii) outputs a feasible path. The run time of this algorithm is bounded by a polynomial in n (the total number of obstacle vertices in Ε), m (the bit precision of the input), and k. This result complements earlier work by Fortune and Wilfong: their algorithm considers paths of arbitrary descriptive complexity (it has no dependence on k), but it never outputs a path, just whether or not a feasible path exists. Our second major result is an algorithm that given E, αs, αt, a length λ, and an approximation factor Ε, either (i) verifies that every feasible path has length greater than λ or (ii) constructs a feasible path that is at most (1+ Ε) times longer than the shortest feasible path. The run time of this algorithm is bounded by a polynomial in n, m, Ε-1, and λ. This algorithm is the result of applying the techniques developed earlier in our thesis to the previous approximation approaches. A shortcoming of these prior approximation algorithms is that they only search a special class of feasible paths. This restriction implies that the path that they return may be arbitrarily longer than the shortest path. Our algorithm returns a true approximation because we search for arbitrary shortest paths.

Triangle meshes can provide an effective geometric representation of images. Although many mesh generation methods have been proposed to date, many of them do not explicitly take image discontinuities into consideration. In this thesis, a new mesh model for images, which explicitly represents discontinuities (i.e., image edges), is proposed along with two corresponding mesh-generation methods that determine the mesh-model parameters for a given input image. The mesh model is based on constrained Delaunay triangulations (DTs), where the constrained edges correspond to image edges. One of the proposed methods is named explicitly-represented discontinuities-with error diffusion (ERDED), and is fast and easy to implement. In the ERDED method, the error diffusion (ED) scheme is employed to select a subset of sample points that are not on the constrained edges. The other proposed method is called ERDGPI. In the ERDGPI method, a constrained DT is first constructed with a set of prespecified constrained edges. Then, the greedy point insertion (GPI) scheme is employed to insert one point into the constrained DT in each iteration until a certain number of points is reached. The ERDED and ERDGPI methods involve several parameters which must be provided as input. These parameters can affect the quality of the resulting image approximations, and are discussed in detail. We also evaluate the performance of our proposed ERDED and ERDGPI methods by comparing them with the highly effective ED and GPI schemes. Our proposed methods are demonstrated to be capable of producing image approximations of higher quality both in terms of PSNR and subjective quality than those generated by other schemes. For example, the reconstructed images produced by the proposed ERDED method are often about 3.77 dB higher in PSNR than those produced by the ED scheme, and our proposed ERDGPI scheme produces image approximations of about 1.08 dB higher PSNR than those generated by the GPI approach. / Graduate