Reducing the number of sequential diagnosis iterations in hypercubes

We use a vertex-isoperimetric inequality to show that the number of test and repair iterations needed to perform sequential diagnosis of ddimensional hypercubes is upper bounded by d-r, where r(element of) (Theta)(d). This result improves the best bound of d test and repair iterations previously known. Numerical evaluation has shown that the actual value of r ranges from 0.16d to 0.31d.