The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.

We address a generalization of graphs, the directed hypergraphs, and show that they are a powerful tool in modelling and solving several relevant problems in many application areas. Such application areas include Linear Production Problems, Flexible Manufacturing Systems, Propositional Logic, Relational Databases, and Public Transportation Systems.

To Mom, for making this dream possible, Ian, for supporting and sharing it and Lillian for making it all worthwhile. ii In this era where healthcare is one of the world’s largest and fastest growing industries, there is great interest in understanding what is happening within our cells and organs at the molecular level. Fortunately, innovations and improvements in technology continue to spur the quantity and types of high-throughput (a process where large amounts of samples can be measured by a system at once) biological data that can be measured. Additionally, abundant information from many years of detailed research can be found in annotated or computationally extracted databases. These data sets, especially combined, have great potential for novel discoveries that can lead to advances in biology and medicine. The main focus of this thesis is the investigation of machine learning techniques for inferring gene regulatory networks from the combination of high-throughput time series gene expression array data and other data sources. A gene regulatory network is a collection