The Approximation Power of Priority Algorithms by Spyros Angelopoulos

The Approximation Power of Priority Algorithms Spyros Angelopoulos Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2006 Greedy-like algorithms have been a popular approach in combinatorial optimization, due to their conceptual simplicity and amenability to analysis. Surprisingly, it was only recently that a formal framework for their study emerged. In particular, Borodin, Nielsen and Rackoff introduced the class of priority algorithms as a model for abstracting the main properties of (deterministic) greedy-like algorithms; they also showed limitations on the approximation power of such algorithms for various scheduling problems. In this thesis we extend and modify the priority-algorithm framework so as to make it applicable to a wider class of optimization problems and settings. More precisely, we first derive strong lower bounds on the approximation ratio of priority algorithms for two wellstudied problems, namely facility location and set cover. These are problems for which several greedy-like algorithms with good performance guarantees exist. Subsequently, we address the issue of randomization in priority algorithms, and show how to prove bounds on the power of greedy-like algorithms with access to random bits. Finally, we propose a model for priority algorithms in the context of graph theoretic optimization problems; the later class of problems turns out to be of particular interest, since it poses certain conceptual challenges when studying priority algorithms. Our goal is to define a model in which it is possible to filter out certain overly powerful algorithms, while still capturing a very rich class of greedy-like algorithms.