Optimization Problems in Computational Molecular Biology Contents 1 a Primer in Molecular Biology 1 6 a Tree{based Algorithm for Multiple Alignment 77 a Primer in Molecular Biology 1.1 Introduction 1.2 the Dna

To my father. Acknowledgments. I wish to thank everybody who advised me and with whom I had the pleasure to work. In particular, I would like to thank Egon Balas and R. Ravi. I am grateful to Egon Balas who encouraged me to continue with my work, even in hard times, and suggested computational biology as a research topic for my thesis. And I must say that not only I enjoyed working with him but, maybe even more, competing in some pleasant evenings on a tennis court. Finally, I thank R. Ravi for the many things he taught me, and exposing me to his enthusiasm and energy. It's been real fun working with him. In the last few years, molecular biology has been experiencing an exponential growth, in terms of results, discoveries, availability of data. This growth has few parallels in modern science, a very prominent one being that with computer science hardware and software development. This is not an accident, since molecular biology has beneeted greatly from the automation of many procedures, ranging from data interpretation to their storage in large distributed data bases. Hence, with no doubts molecular biology has become an informational science, posing challenging questions on data management and retrieval. Recently however, it has become a computational science as well. In fact, many problems arising in molecular biology concern building maps, aligning DNA fragments, guessing evolutionary trees, reconstructing large sequences from smaller ones. All of these and similar problems can be cast in mathematical models and considered optimization problems to be attacked by means of standard techniques. While years ago their solution could conceivably be sought by \pen{and{paper", the enormous quantity and/or the size of data available today makes this approach no longer feasible. Therefore, modern molecular biologists must resort to the use of computer science approaches in order to solve these problems. Conversely, computer scientists can nd a fertile eld, full of challenging questions, both practical and theoretical, in molecular biology. The new research area, known as computational molecular biology (or, shortly, computational biology), is concerned exactly with the solution of computational problems arising in molecular biology. It is a discipline whose questions can be often posed in terms of graph theory, network ows, integer and linear programming problems. Henceforth, computational biology can today be considered as one of the many branches of Theoretical Computer Science and Operations Research. For a review of some of …