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 \u2265 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 \u2212 )-approximate for the last one. 1<\/p>\n","protected":false},"excerpt":{"rendered":"
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. 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