A survey of parameterized algorithms and the complexity of edge modification

The survey is a comprehensive overview of the developing area of parameterized algorithms for graph modification problems. It describes state of the art in kernelization, subexponential algorithms, and parameterized complexity of graph modification. The main focus is on edge modification problems, where the task is to change some adjacencies in a graph to satisfy some required properties. To facilitate further research, we list many open problems in the area.publishedVersio

Computational methods in protein structure comparison and analysis of protein interaction networks

Proteins are versatile biological macromolecules that perform numerous functions in a living organism. For example, proteins catalyze chemical reactions, store and transport various small molecules, and are involved in transmitting nerve signals. As the number of completely sequenced genomes grows, we are faced with the important but daunting task of assigning function to proteins encoded by newly sequenced genomes. In this thesis we contribute to this effort by developing computational methods for which one use is to facilitate protein function assignment. Functional annotation of a newly discovered protein can often be transferred from that of evolutionarily related proteins of known function. However, distantly related proteins can still only be detected by the most accurate protein structure alignment methods. As these methods are computationally expensive, they are combined with less accurate but fast methods to allow large-scale comparative studies. In this thesis we propose a general framework to define a family of protein structure comparison methods that reduce protein structure comparison to distance computation between high-dimensional vectors and therefore are extremely fast. Interactions among proteins can be detected through the use of several mature experimental techniques. These interactions are routinely represented by a graph, called a protein interaction network, with nodes representing the proteins and edges representing the interactions between the proteins. In this thesis we present two computational studies that explore the connection between the topology of protein interaction networks and protein biological function. Unfortunately, protein interaction networks do not explicitly capture an important aspect of protein interactions, their dynamic nature. In this thesis, we present an automatic method that relies on graph theoretic tools for chordal and cograph graph families to extract dynamic properties of protein interactions from the network topology. An intriguing question in the analysis of biological networks is whether biological characteristics of a protein, such as essentiality, can be explained by its placement in the network. In this thesis we analyze protein interaction networks for Saccharomyces cerevisiae to identify the main topological determinant of essentiality and to provide a biological explanation for the connection between the network topology and essentiality