Michael R. Fellows

TL;DR: Under the (unlikely) assumption that NP=co-NP, it is shown that NP-complete problems can be self-reduced, and probabilism can be shown to help: any NP- complete problem has a randomized parallel self- reduction.

TL;DR: This work introduces an intuitive notion of diversity of a collection of solutions which suits a large variety of combinatorial problems of practical interest and presents an algorithmic framework which converts a tree-decomposition-based dynamic programming algorithm for a given combinatorsial problem X into a dynamic Programming algorithm for the diverse version of X.

TL;DR: In this article, a tree-decomposition-based dynamic programming algorithm for a given combinatorial problem X is converted into a dynamic programming for the diverse version of X. The algorithm has a polynomial dependence on the diversity parameter.

TL;DR: In this paper, a tree-decomposition-based dynamic programming algorithm for a given combinatorial problem X is converted into a dynamic programming for the diverse version of X. The algorithm has a polynomial dependence on the diversity parameter.

TL;DR: This work gives the first characterization of W[1] based on the weightedsatisfiability problem for monotone Boolean circuits rather than antimonotone, showing that it remains a key parameter governing the combinatorial nondeterministic computing strength of circuits no matter what type of gates these circuits have.