Generic case completeness

Generic case completeness

In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.

Average Case Completeness

We explain and advance Levin’s theory of average case completeness. In particular, we exhibit examples of problems complete in the average case and prove a limitation on the power of deterministic reductions. ∗J. Computer and System Sciences 42:3, June 1991, 346–398. †Partially supported by NSF grant DCR 85-03275.

A Generic Greedy Algorithm, Partially-Ordered Graphs and NP-Completeness

Report on Generic Case Complexity

This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity applies to both recursively solvable and recursively unsolvable problems.

Musings on generic-case complexity

We propose a more general definition of generic-case complexity, based on using a random process for generating inputs of an algorithm and using the time needed to generate an input as a way of measuring the size of that input.