Reference points and approximation algorithms in multicriteria discrete optimization

We study the connection between reference point methods and approximation algorithms for multicriteria optimization problems over discrete sets. In particular, we establish that, in terms of computational complexity, computing approximate reference point solutions is polynomially equivalent to approximating the Pareto set. Complementing these results, we show for a number of general algorithmic techniques in single criteria optimization how they can be lifted to reference point optimization. In particular, we lift the link between dynamic programming and FPTAS, as well as certain LP-rounding techniques. The latter applies, e.g., to Set Cover and several machine scheduling problems.