List Ranking

For each object in the list, compute distance to the end of the list.

$$d(i) \;=\; \left\{ \begin{array}{ll} 0 & {\rm if} \;next(i) \... ...+ 1 & {\rm if} \;next(i) \;\neq \;{\rm NIL} \end{array} \right.$$

Serial:

Parallel:

O(lg n)

Idea:

   repeat
      pointer jump
      add number of objects jumped to current distance
   until all next(i) = NIL

Speedup:

S = T (best serial algorithm) / T (parallel algorithm)