Greed, for lack of a better word, is good. One of the first algorithmic paradigms taught in introductory algorithms course is the greedy approach. Greedy approach results in simple and intuitive algorithms for many problems in P. More interestingly, for some NP-hard problems the obvious and natural greedy/local algorithm results in (provably) optimal approximation factor (under suitable complexity theoretic assumptions). A classic example is the Set Cover Problem. A natural greedy algorithm gives an O(ln n) approximation factor, which is optimal unless P = NP.Name some natural greedy/local algorithms for NP-hard problems that are provably optimal under suitable complexity theoretic assumptions.
Optimal greedy algorithms for NP-hard problems
cc.complexity theory;lower bounds;approximation algorithms;greedy algorithms;approximation hardness