I want to take measurements of algorithm performance. I have two algorithms A and B that run one after the other (composition)
I want to measure how well the composition of algorithms is better than the algorithms individually.
I propose to get run times of A and B individually as rA and rB and their run times when composed together as prA and prB (pr for partial run time) and take the min(prA/rA, prB/rB) as a performance metric.
What properties does min(x,y) have? I know max(x,y) gives the $L^{\infty}$ norm on $\mathbb{R}^2$ but what about min? What other performance metrics are good for comparing a composition of algorithms?