Improved Results on Models of Greedy and Primal-dual Algorithms

A class of priority algorithms that capture reasonable greedy-like algorithms was introduced by Borodin, Nielson, and Rackoff [7]. Later, Borodin, Cashman, and Magen [4] introduced the stack algorithms, advocating that they capture reasonable primal-dual and local-ratio algorithms. In this thesis, some NP -hard graph optimization problems Maximum Acyclic Subgraph (MAS) problem and Minimum Steiner Tree (MST) problem are studied in priority and stack models. First, a 2− 1 k priority lower bound in the edge model is shown for the MAS problem. Secondly, a 4 3 priority lower bound in the edge model is presented for the MST problem, improving the result of Davis and Impagliazzo [10]. Making variations on input instances and the stack model, we show a 2− 2 k stack lower bound improving the 4 3 stack lower bound in Borodin, Cashman, and Magen [4].