Design of Dynamic Algorithms via 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(f)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, andm 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(log n) amortized update time, where n is the number of nodes in the graph.