# Proportional vs. Uniform policy for CQs

Assumption : Update distribution is uniform.
We compare weighted Uniform and weighted Proportional policies.

Number of  crawls allocated to
ith pagein the proportional policy is

where Wi and  are weight and change frequency of
ith page

respectively.

So Information gained for this page is equal to

where  is the update probability for

ith page at any update instant.

Information gained in case of the uniform allocation for the same page

is equal to

So ratio of performance of the proportion to the uniform policy over all

pages becomes


As we know ai.bi (ai.bi) for non-negative ai's and bi's, above ratio is always greater than 1.
This proves that Proportional always performs better than Uniform no matter how page weights and change frequencies are distributed.

Sandeep Pandey 2003-03-05