I am attempting to understand exactly how the terminology for k-approximation algorithms work, from when k is known and determining what k is.
If we assume that a vertex cover in a graph G is of size 7 and that there is a 3-approximation algorithm for finding the minimum vertex cover. Does that mean the algorithm could return values between 7 and 21 inclusive?
If the maximum independent set in a graph is of size 12 and an algorithm returns for a complement graph a clique of size 6 in the worst case. Would that algorithm be a 2-approximation or a .5-approximation?
