Three problems in discrete optimization are considered and solved to varying degrees using novel algorithms. Worst case behavior experiments were run in all chapters. First, a seating arrangement problem is shown to be NP-hard. A simplified case is solved using a greedy algorithm and we use a two phase approach to find a 2-factor approximation for a slightly more complex version of the problem. Next, we bound the performance of a recently published approach to DNA copy number analysis. We then devise a dynamic programming PTAS and an integer programming formulation which outperformed the published approach. Finally, we introduce a dynamic load balancing problem. For this NP-hard problem we devise a lower bound, a 2.7-factor heuristic and an experimentally promising heuristic. We experimentally compared the solution quality of our algorithms to some suggested heuristics. | 74 page
