The complexity of optimization problems
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Journal of Computer and System Sciences
Completeness in approximation classes
Information and Computation
Approximating clique is almost NP-complete (preliminary version)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the theory of average case complexity
Journal of Computer and System Sciences
Complexity theory
On the NP-isomorphism problem with respect to random instances
Journal of Computer and System Sciences
Average-case computational complexity theory
Complexity theory retrospective II
The Complexity of Near-Optimal Graph Coloring
Journal of the ACM (JACM)
Structure in Approximation Classes
SIAM Journal on Computing
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Average-Case Intractability vs. Worst-Case Intractability
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Colouring Random Graphs in Expected Polynomial Time
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Some Results on Derandomization
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Greedily Approximating the r-independent Set and k-center Problems on Random Instances
RANDOM '97 Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science
Problems, complete in “average” instance
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Towards average-case complexity analysis of NP optimization problems
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Average-Case Computations " Comparing AvgP, HP, and Nearly-P
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Complete and incomplete randomized NP problems
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Proof verification and hardness of approximation problems
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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Both average-case complexity and the study of the approximability of NP optimisation problems are well established and active fields of research. Many results concerning the average behaviour of approximation algorithms for NP optimisation problems exist, both with respect to their running time and their performance ratio, but a theoretical framework to examine their structural properties with respect to their average-case approximability is not yet established. With this paper, we hope to fill the gap and provide not only the necessary definitions, but show that The class of NP optimisation problems with p-computable input distributions has complete problems with respect to an average-approximability preserving reduction. The average-time variants of worst-case approximation classes form a strict hierarchy if NP is not easy on average. By linking average-ratio approximation algorithms to p-time algorithms schemes, we can prove similar hierarchy results for the average-ratio versions of the approximation classes. This is done under the premise that not all NP-problems with p-computable input distributions have p-time algorithm schemes. The question whether NP is easy on average is equivalent to the question whether every NP optimisation problem with a p-computable input distribution has an average p-time approximation scheme. Classification: Computational and structural complexity.