Given a large network of computers, each keeping log files of visited
urls, find the top ten of the most visited urls. 
(i.e. have many large <string (url) -> int (visits)> maps, calculate
implicitly <string (url) -> int (sum of visits among all distributed
maps), and get the top ten in the combined map) 
The result list must be exact, and the maps are too large to transmit
over the network (especially sending all of them to a central server or
using MapReduce directly, is not allowed)

Presuming a protocol exists that can ask three questions to each server:

  • the score of a single url
  • the top 10
  • the top n that satisfy score >= N

We program a two pass solution like so:

We denote the number of servers as S.

[First pass]

(1) Ask every server for its own top ten

(2) merge the results. For all URLs in the merged set calculate correct values by asking all servers for their scores for each URL. Calculate a set of top ten from our sample.

(3) pick score of the now tenth URL as the threshold that we try to beat in the second round. We denote the threshold as T.

[Second pass]

(4) Ask every server for all its top N that satisfy score >= T/S

(5) Merge these bigger samples again as in step (2)

(6) We now have the correct top ten with correct scores.

X:Y Means Urls X has a count of Y
We want top 2 uRLs

M/C A=> 1:100 2:96 7:94 
M/C B=> 3:99 5:97 7:4 
M/C C=> 4:98 6:95 7:4

1st Step
A=>1,2
B=>3,5
C=>4,6

2nd Step
Top two after merging
1,3 Urls are selected

3rd Step
Threshold=99(Selected from url 3)

4th Step
Score = 99/3=33
A=>1,2,7
B=>3,5
C=>4,6

5th Step
Merging will again give us 1,3 when infact Url 7 has the highest count

Find the top ten of visited urls