Using the Traveling Salesman Problem

Theoretical computer science has given birth to a very intriguing and fascinating class of problems known as Nondeterministic Polynomial-time (NP) complete problems. Among their captivating properties are their computational complexity despite often deceptively simple formulations. An example of this is the ubiquitous Traveling Salesman Problem (TSP). This problem has had an uncontested popularity in computational mathematics leading to a plethora of techniques and programs for solving it, both exactly and heuristically. Another remarkable property of NP complete problems is their frequent occurrence in real life problems, making them more than just theoretical constructions. A practical example of this is the field of bioinformatics where many of the challenges faced by its researchers have turned out to be NP complete problems. Yet another tantalising characteristic of the NP complete problems is their reduction property, making every problem equally difficult (or easy) to solve. In other words: to solve them all, we only have to solve one of them. This thesis aims at utilising the above properties with the purpose of examining the effect of trying to solve bioinformatic problems using the reduction property and a state of the art implementation for solving the TSP. The practical bioinformatic problem is the Shortest Superstring Problem (SSP). To asses the quality of the obtained solutions, they are compared to solutions from four approximation algorithms. To convey a full understanding of the algorithms and their approximation factors, the thesis additionally includes a self-contained survey of approximation algorithms for the SSP. The thesis further examines the bioinformatic problems concerning Multiple Sequence Alignment (MSA) and hereby presents the definition of a TSP based scoring function. A near-optimal MSA construction algorithm that uses this scoring and additionally a divide-and-conquer algorithm for refining MSAs are implemented and experimentally tested. Based on truely convincing results the main conclusion of the thesis is that it is definitely a promising idea to apply efficient TSP solver implementations to solve NP complete problems within bioinformatic applications. The results obtained for the implemented MSA algorithms are far more modest, although the MSA construction algorithm and the scoring function should not be dismissed without further study. i