Priority Algorithms for Graph Optimization Problems.
Allan Borodin, Joan Boyar, Kim S. Larsen, and Nazanin Mirmohammadi.
Theoretical Computer Science, 411(1): 239-258, 2010.
We continue the study of priority or "greedy-like" algorithms as initiated in [Borodin, Nielsen, Rackoff, "(Incremental) Priority Algorithms", Algorithmica 37 (2003), 295-326] and as extended to graph theoretic problems in [Davis, Impagliazzo, "Models of Greedy Algorithms for Graph Problems", Algorithmica 54 (2009), 269-317]. Graph theoretic problems pose some modeling problems that did not exist in the original applications of [Borodin et al. (2003)] and [Angelopoulos, Borodin, "On the Power of Priority Algorithms for Facility Location and Set Cover", APPROX, Lecture Notes in Computer Science 2462 (2002), 26-39]. Following [Davis et al. (2009)], 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".

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