Iterative Rounding for Multi-Objective Optimization Problems

In this paper we show that iterative rounding is a powerful and flexible tool in the design of approximation algorithms for multiobjective optimization problems. We illustrate that by considering the multi-objective versions of three basic optimization problems: spanning tree, matroid basis and matching in bipartite graphs. Here, besides the standard weight function, we are given k length functions with corresponding budgets. The goal is finding a feasible solution of maximum weight and such that, for all i, the ith length of the solution does not exceed the ith budget. For these problems we present polynomial-time approximation schemes that, for any constant > 0 and k ≥ 1, compute a solution violating each budget constraint at most by a factor (1 + ). The weight of the solution is optimal for the first two problems, and (1 − )-approximate for the last one. 1