Simplicity is Beauty: Improved Upper Bounds for Vertex Cover

This paper presents an O(1.2738 + kn)-time polynomial-space algorithm for VERTEX COVER improving both the previous O(1.286 +kn)-time polynomial-space algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745k + kn)time exponential-space algorithm, by Chandran and Grandoni. Most of the previous algorithms rely on exhaustive case-bycase analysis, and an underlying conservative worst-case-scenario assumption. The contribution of the paper lies in the extreme simplicity, uniformity, and obliviousness of the algorithm presented. Several new techniques, as well as generalizations of previous techniques, are introduced including: general folding, struction, tuples, and local amortized analysis. The algorithm also induces improvement on the upper bound for the INDEPENDENT SET problem on graphs of degree bounded by 6.