User blog comment:Wythagoras/New bound for SSCG(2)/@comment-5529393-20130714151318/@comment-1605058-20130714192429

Consider any optimization algorithm with some notion of value, like travelling salesman. Greedy algorithm is going to seek best overall solution by looking at best choice at single step, e.g. it will always choose edge with smallest weight. It is easy to see that greedyness may often lead to suboptimal solution. In Goucher's "algorithm" we seek longest sequence of path forests. Goucher gives every tree an ordinal value, and greedy algorithm proceeds by choosing as next value a forest with highest possible ordinal value.