Quantitative relativizations of complexity classes
SIAM Journal on Computing
The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Languages that are easier than their proofs
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
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
SIAM Journal on Computing
The relative complexity of NP search problems
Journal of Computer and System Sciences
The complexity of restricted spanning tree problems
Journal of the ACM (JACM)
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Some Comments on Functional Self-Reducibility and the NP Hierarchy
Some Comments on Functional Self-Reducibility and the NP Hierarchy
Approximability and hardness in multi-objective optimization
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
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An NP search problem is a multivalued function that maps instances to polynomially length-bounded solutions such that the validity of solutions is testable in polynomial time. NPMVg denotes the class of these functions. There are at least two computational tasks associated with an NP search problem: (i) Find out whether a solution exists. (ii) Compute an arbitrary solution. Further computational tasks arise in settings with multiple objectives, for example: (iii) Compute a solution that is minimal w.r.t. the first objective, while the second objective does not exceed some budget. Each such computational task defines a class of multivalued functions. We systematically investigate these classes and their relation to traditional complexity classes and classes of multivalued functions, like NP or max·P. For multiobjective problems, some classes of computational tasks turn out to be equivalent to the function class NPMVg, some to the class of decision problems NP, and some to a seemingly new class that includes both NPMVg and NP. Under the assumption that certain exponential time classes are different, we show that there are computational tasks of multiobjective problems (more precisely functions in NPMVg) that are Turing-inequivalent to any set.