Topological methods are techniques for software component retrieval from repositories based on similarity between query specifications and component properties. They rely on defining a distance measure between queries and components. PageRank is used to calculate importance scores for components based on their relationships to other components defined by shared keywords. It is an iterative process where initial scores are calculated and used to recalculate new scores until they converge. PageRank allows for ranking of components in a repository based on their relevance to queries.

1. Topological methods
Presented by:
Sukhpal Singh
Thapar University

2. Topological methods
Topological methods are based on the simple
premise that, given a query that describes
some required features, we are interested in
identifying library assets that come closest to
providing these features. Such methods are
critically dependent on what it means to come
closest, which in turn depends on some
definition of distance between the query and
candidate assets [1].

3. Categories of Topological methods
• Exclusive approximate retrieval: Methods that
fall into this category make a distinction
between two retrieval goals: exact retrieval and
approximate retrieval, whereby we seek to
identify library assets that completely satisfy all
the requirements of the query.
• Inclusive approximate retrieval: Methods that
fall into this category make no distinction
between exact retrieval and approximate
retrieval. Rather, they focus on identifying
library assets that minimize some measure of
distance to the query.

4. Measures of distance can be divided into two
broad classes
• Measures of functional (semantic) distance,
which reflect the extent of similarity between
the functional properties of the query and those
of candidate components.
• Measures of structural (syntactic) distance,
which reflect the extent of similarity between
the structure of (solutions to) the query and
the structure of candidate components.

5. Characterizing topological methods

6. The Google PageRank Algorithm is
used in Topological methods to
retrieve a software assets from
software repository.

7. What is PageRank?
• In short PageRank is a “vote”, by all the other
pages on the Web, about how important a
page is [3].
• A link to a page counts as a vote of support
• PR(A) = (1-d) + d(PR(T1)/C(T1)
+…+PR(Tn)/C(Tn))

8. Breaking Down the Equation
• PR(Tn) - Each page has a notion of its own self-importance. That’s “PR(T1)”
for the first page in the web all the way up to “PR(Tn)” for the last page
• C(Tn) - Each page spreads its vote out evenly amongst all of it’s outgoing
links. The count, or number, of outgoing links for page 1 is “C(T1)”, “C(Tn)”
for page n, and so on for all pages.
• PR(Tn)/C(Tn) - so if our page (page A) has a backlink from page “n” the
share of the vote page A will get is “PR(Tn)/C(Tn)”
• d(… - All these fractions of votes are added together but, to stop the other
pages having too much influence, this total vote is “damped down” by
multiplying it by 0.85 (the factor “d”)
• (1 - d) - The (1 – d) bit at the beginning is a bit of probability math magic so
the “sum of all web pages’ PageRank's will be one”: it adds in the bit lost
by the d(…. It also means that if a page has no links to it (no backlinks) even
then it will still get a small PR of 0.15 (i.e. 1 – 0.85).

9. How is it Calculated?
• The PR of each page depends on the PR of the
pages pointing to it.
• But we won’t know what PR those pages have
until the pages pointing to them have their PR
calculated and so on.
• So what we do is make a guess.

10. Simple Example
• Each page has one outgoing link (backlink). So that
means [2] :
• C(T1) = 1 for A
and
• C(T2) = 1 for B

11. We don’t know what their PR should be to begin with, so we
will just guess 1 as a safe random number.
• d (damping factor) = 0.85
• PR(A)= (1 – d) + d(PR(T1)/C(T1))= (1 – d) + d(1/1)
i.e.
• PR(A)= 0.15 + 0.85 * 1
=1
• PR(B)= 0.15 + 0.85 * 1
=1

12. Let’s Do It Again with Another Number. Let’s try 0 and re-
calculate…
• PR(A)= 0.15 + 0.85 * 0
= 0.15
= 0.15 + 0.85 *
• PR(B) 0.15
= 0.2775
• Now we have calculated a “next best guess” so we just plug it in the
equation again…
• PR(A)= 0.15 + 0.85 * 0.2775
= 0.385875
• PR(B)= 0.15 + 0.85 * 0.385875
= 0.47799375
And again…
• PR(A)= 0.15 + 0.85 * 0.47799375
= 0.5562946875
• PR(B)= 0.15 + 0.85 * 0.5562946875
= 0.622850484375

13. Principle
• It doesn’t matter where you start your guess,
once the PageRank calculations have settled
down, the “normalized probability
distribution” (the average PageRank for all
pages) will be 1.0
• In software repository we are using software
assets instead of pages and also using
relationships among software assets based on
their keywords instead of links.

14. Summary

15. References:
[1] A survey of software reuse libraries A. Mili a,_, R. Mili
b and R.T. Mittermeir Annals of Software
Engineering 5 (1998) 349–414 349
[2] http://wwwdb.stanford.edu/~backrub/google.html
http://www-db.stanford.edu/~backrub/google.html
[3] Semantic Component Retrieval in Software
Engineering Inaugural dissertation zur Erlangung des
akademischen Grades eines Doktors der
Naturwissenschaften der, Universitat Mannheim,
Mannheim, 2008