Priority algorithms for graph optimization problems

We continue the study of priority or “greedy-like” algorithms as initiated in Borodin et al. (2003) [10], and as extended to graph theoretic problems in Davis and Impagliazzo (2009) [12], . Graph theoretic problems pose some modeling problems that did not exist in the original applications of Borodin et al. and Angelopoulos and Borodin (2002) [3]. Following the work of Davis and Impagliazzo, we further clarify these concepts. In the graph theoretic setting, there are several natural input formulations for a given problem and we show that priority algorithm bounds in general depend on the input formulation. We study a variety of graph problems in the context of arbitrary and restricted priority models corresponding to known “greedy algorithms”.