A primal-dual parallel approximation technique applied to weighted set and vertex cover

We give an efficient deterministic parallel approximation algorithm for the minimumweight vertexand set-cover problems and their duals (edge/element packing). The algorithm is simple and suitable for distributed implementation. It fits no existing paradigm for fast, efficient parallel algorithms — it uses only “local” information at each step, yet is deterministic. (Generally, such algorithms have required randomization.) The result demonstrates that linear-programming primal-dual approximation techniques can lead to fast, efficient parallel algorithms. The presentation does not assume knowledge of such techniques.