Order-Preserving Transformations and Greedy-Like Algorithms

Borodin, Nielsen and Rackoff [5] proposed a framework for abstracting the main properties of greedy-like algorithms with emphasis on scheduling problems, and Davis and Impagliazzo [6] extended it so as to make it applicable to graph optimization problems. In this paper we propose a related model which places certain reasonable restrictions on the power of the greedy-like algorithm. 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. We argue that this approach better motivates the lower-bound proofs and possibly yields better bounds. To illustrate the techniques involved we apply the model to the well-known problems of (complete) facility location and dominating set.

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