Dynamic algorithms via the primal-dual method

We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an O(f2)-approximately optimal solution in O(f⋅log⁡(m+n)) amortized update time, where f is the maximum “frequency” of an element, n is the number of sets, and m is the maximum number of elements in the universe at any point in time. (2) For the dynamic b-matching problem, we maintain an O(1)-approximately optimal solution in O(log3⁡n) amortized update time, where n is the number of nodes in the graph.