A Proof for P vs. NP Problem

http://arxiv.org/abs/1005.3010

``This paper proposes a theoretic proof for P vs. NP problem. The central idea of this proof is a recursive definition for Turing machine (shortly TM). By the definition, an infinite sequence of TM is constructed and it is proved that the sequence includes all TM. Based on these TM, the class D that includes all decidable languages is defined. By proving P=D, the result P=NP is proved.''

>>16
Efficient implementations of a large class of algos which are currently way too slow if you want to get a perfect solution? (less than perfect, but okay ones at reasonable performance can be usually done with the right heuristics).