Martingale Inequalities, Interpolation and NP-Complete Problems

In a previous work Rhee, W., Talagrand, M. 1987. Martingale inequalities and NP-complete problems. Math. Oper. Res.121 177--181., we showed how to use martingale inequalities in the probabilistic analysis of stochastic models of NP-complete problems to obtain sharp bounds on P|Un-EUn| ≥ t, where Un is the objective function value of the problem with n random data. Here, we show how to interpolate between martingale inequalities to obtain even sharper bounds.