Finding k-cuts within twice the optimal
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
On the approximability of trade-offs and optimal access of Web sources
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Multicriteria Optimization
Structural complexity of multiobjective NP search problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
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We study the approximability and the hardness of combinatorial multi-objective NP optimization problems (multi-objective problems, for short). Our contributions are: - We define and compare several solution notions that capture reasonable algorithmic tasks for computing optimal solutions. - These solution notions induce corresponding NP-hardness notions for which we prove implication and separation results. - We define approximative solution notions and investigate in which cases polynomial-time solvability translates from one to another notion. Moreover, for problems where all objectives have to be minimized, approximability results translate from single-objective to multi-objective optimization such that the relative error degrades only by a constant factor. Such translations are not possible for problems where all objectives have to be maximized (unless P = NP). As a consequence we see that in contrast to single-objective problems (where the solution notions coincide), the situation is more subtle for multiple objectives. So it is important to exactly specify the NP-hardness notion when discussing the complexity of multi-objective problems.