This thesis presents the first sub-quadratic circle graph recognition algorithm, and develops improved algorithms for two important hierarchical decomposition schemes: modular decomposition and split decomposition. The modular decomposition algorithm results from unifying two different approaches previously employed to solve the problem: divide-and-conquer and factorizing permutations. It runs in linear-time, and is straightforward in its understanding, correctness, and implementation. It merely requires a collection of trees and simple traversals of these trees. The split-decomposition algorithm is similar in being straightforward in its understanding and correctness. An efficient implementation of the algorithm is described that uses the union-find data-structure. A novel charging argument is used to prove the running-time. The algorithm is the first to use the recent reformulation of split decomposition in terms of graph-labelled trees. This facilitates its extension to circle graph recognition. In particular, it allows us to efficiently apply a new lexicographic breadth-first search characterization of circle graphs developed in the thesis. Lexicographic breadth-first search is additionally responsible for the efficiency of the split decomposition algorithm, and contributes to the simplicity of the modular decomposition algorithm.

This thesis presents the first sub-quadratic circle graph recognition algorithm, and develops improved algorithms for two important hierarchical decomposition schemes: modular decomposition and split decomposition. The modular decomposition algorithm results from unifying two different approaches previously employed to solve the problem: divide-and-conquer and factorizing permutations. It runs in linear-time, and is straightforward in its understanding, correctness, and implementation. It merely requires a collection of trees and simple traversals of these trees. The split-decomposition algorithm is similar in being straightforward in its understanding and correctness. An efficient implementation of the algorithm is described that uses the union-find data-structure. A novel charging argument is used to prove the running-time. The algorithm is the first to use the recent reformulation of split decomposition in terms of graph-labelled trees. This facilitates its extension to circle graph recognition. In particular, it allows us to efficiently apply a new lexicographic breadth-first search characterization of circle graphs developed in the thesis. Lexicographic breadth-first search is additionally responsible for the efficiency of the split decomposition algorithm, and contributes to the simplicity of the modular decomposition algorithm.

Poorly water-soluble drugs (PWSDs), to date, require advanced formulation techniques to improve solubility and achieve the required plasma concentration to show a therapeutic effect when orally administered. Lipid-based formulations (LBFs) are an enabling strategy that is being used to improve the oral delivery of PWSDs. The aim of this study was to investigate the effect of lipid-based formulation, Type IIIA-LC, on the solubilization patterns of PWSDs, namely, carvedilol and felodipine. Solubility studies, for both drugs, were performed with LBF dispersed in -1) dog intestinal fluid (DIF), and 2) water, to identify and compare the extent of solubility in different matrices, and in silico to identify interesting patterns with any correlations in experimental and computational data. Solubility studies showed that carvedilol had better solubility in LBF when compared to felodipine. Computational studies showed that both drugs solubilized in the colloid in both digested and undigested states. Effect of drug loading had no significant difference on the solubilization patterns of both drugs. The maximum drug loading done was for 100 molecules though there is the possibility of the colloid having a higher capacity. Digestion did not seem to have a significant effect on the distribution of both drugs. In vitro and in silico data were in qualitative agreement and therefore, this computational model can be further used to study the specific processes causing solubilization, improvement, and development of new LBFs.