1.10 Let A be an algorithm for minimization NP-optimization problem such that the expected cost of the solution produced by A is at most $\alpha OPT$, for a constant $\alpha>1$. What is the best approximation guarantee you can establish for this problem using algorithm A?
Hint: A guarantee of $2\alpha-1$ follows easily. to be honest, I don't really understand the question good. So usually when we want an approximation factor we take the ratio between solution of algorithm A and OPT of problem. could you explain the problem in other way! and how we get factor of $2\alpha-1$. Suppose I want to use Markov's bound, since the information we know is expected value. Thus, I would get $\alpha OPT/a$ for $a>0$. I don't see any logic here! I would like any help in terms of explanation!