Priority and More

Many known efficient algorithms for computational problems can be classified into a few algorithm paradigms: greedy algorithms, divide-and-conquer, dynamic programming, linear programming and backtracking algorithms. An approach to evaluating different algorithm paradigms is to show approximability of a specific computational problem in each paradigm. A ncessary component of such evaluation is to formalize a precise model for each algorithm paradigm. Using the precise model, one can compare different algorithm paradigms. For a particular optimization problem, it may be the case that it can be proved that greedy algorithms captured by a specific model cannot be approximated beyond a certain ratio whereas algorithms within another model can. This provides not only the theoretical separation of these models but also practical guides to designing algorithms by ruling out possibilities. Furthermore, the formal model gives us a better understanding of the structure of the computational problem at hand. Using the model, one can joyfully wander between lower and upper bound. Because of its simplicity and efficiency on many computational problems, the greedy algorithm paradigm is one of most important tool in designing algorithms. Recently, Borodin, Nielsen and Rackoff, [3], introduced a model called priority algorithms which captures any reasonable greedy or greedy-like algorithms. Along with the idea of an optimal solution these algorithms also provide the idea of an approximation algorithm. The primal-dual and local ratio approaches for approximation algorithms are also two fundamental algorithm design paradigms. These two approaches usually encompass the greedy approach. That is, if one can prove arbitrary large competitive ratio in priority algorithm framework, one can hope to find a better approximation ratio using a more powerful algorithm paradigm such as primaldual and local ratio design paradigms. The paper of Allan Borodin, David Cashman, and Avner Magen [2] formalized a formal computational model that captures both the primal-dual and the local ratio approaches. This model is called a stack algorithm.