581257 Information Retrieval Methods Autumn 2010 Exercise 2 ...

4. (Course book's exercise 2.7) Consider a postings intersection between this postings list, with skip
pointers:
and the following intermediate result postings list (which hence has no skip pointers):
Trace through the postings intersection algorithm in Figure 2.10 (page 37).
a) How often is a skip pointer followed (i.e., p1 is advanced to skip(p2))?
Solution: The skip pointer is followed once (from 24 to 75).
b) How many postings comparisons will be made by this algorithm while intersecting the two
lists?
Solution: 19 comparisons are made. Let (x,y) denote a posting comparison. The
comparisons are: (3,3), (5,5), (9,89), (15,89), (24,89), (75,89), (75,89), (92,89), (81,89),
(84,89), (89,89), (92,95), (115,95), (96,95), (96,97), (97,97), (100,99), (100,100), (115,101).
c) How many postings comparisons would be made if the postings lists are intersected without
the use of skip pointers?
Solution: 19 comparisons are made. The comparisons are: (3,3), (5,5), (9,89), (15,89),
(24,89), (39,89), (60,89), (68,89), (75,89), (81,89), (84,89), (89,89), (92,95), (96,95), (96,97),
(97,97), (100,99), (100,100), (115,101).
5. (Course book's exercise 2.6) We have a two-word query. For one term the postings list consists of
the following 16 entries:
[4,6,10,12,14,16,18,20,22,32,47,81,120,122,157,180]
and for the other it is the one entry postings list:
[47]
Work out how many comparisons would be done to intersect the two postings lists with the following
two strategies. Briefly justify your answers:
a) Using standard postings lists
Solution: Applying MERGE on the standard postings list, comparisons will be made
unless either of the postings list end, i.e., till we reach 47 in the upper postings list, after
which the lower list ends and no more processing needs to be done. Therefore, the
number of comparisons made is 11.
b) Using postings lists stored with skip pointers, with a skip length of √P, as suggested in
Section 2.3
Solution: Using skip pointers of length 4 for the longer list and of length 1 for the shorter
list, the following comparisons will be made: (4,47), (14,47), (22,47), (120,47), (22,47),
(120,47), (32,47), (47,47). Therefore, the number of comparisons made in this case is 8.
This is not, however, an optimal approach, because comparisons (22,47) and (120,47)
are made two times. The solution would be more optimal, if we would add command “p 1
← next(p1)” directly after the while loop. Then the number of comparisons would be
decreased to 6.
2