How Well Can Primal-Dual and Local-Ratio Algorithms Perform?

We define an algorithmic paradigm, the stack model, that captures most primal-dual and local-ratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations. Hence our approximation bounds are independent of the P vs NP question. We provide tools to bound the performance of primal dual and local ratio algorithms and supply a (log n+1)/2 inapproximability result for set-cover, a 4/3 inapproximability for min steiner tree, and a 0.913 inapproximability for interval scheduling on two machines.

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