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Backing Up on Witness Points of Input Vectors

Let tex2html_wrap_inline1142 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 tex2html_wrap_inline1142 . Denote the witness point for a vector tex2html_wrap_inline1138 by tex2html_wrap_inline1438 . 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:

 		   tex2html_wrap_inline1440 :

1. tex2html_wrap_inline1442 .

2. for each tex2html_wrap_inline1444

3. tex2html_wrap_inline1446 .

4. if tex2html_wrap_inline1448

5. tex2html_wrap_inline1450 .

6. tex2html_wrap_inline1452 .

7. return tex2html_wrap_inline1144 .

In this subroutine, line 4 makes sure that the resulting set tex2html_wrap_inline1144 contains no duplicates and line 5 takes note of the fact that tex2html_wrap_inline1458 is also a witness point for tex2html_wrap_inline1138 (w.r.t tex2html_wrap_inline1230 ).

Dr. Lian Wen Zhang
Thu Feb 15 14:47:09 HKT 2001