Let be a set of vectors on which we are going to perform point-based DP update. As mentioned earlier, we can assume that we know a witness point for each vector in . Denote the witness point for a vector by . Point-based DP update first backs up on these points and thereby obtains a new set of vectors. To be more specific, it begins with the following subroutine:

:1. .

2.

foreach3. .

4.

if5. .

6. .

7. return .

In this subroutine, line 4 makes sure that the resulting set contains no duplicates and line 5 takes note of the fact that is also a witness point for (w.r.t ).

Thu Feb 15 14:47:09 HKT 2001