Popular Ranking Algorithms

1
Popular Ranking Algorithms

• Prepared by
• -Ranjan Dash

2
Contents

• Efficient ways of Ranking
• Algorithms for ranking
• Sort Algorithm
• Scan Algorithm
• FA Algorithm
• TA Algorithm

3
Efficient ways of Ranking

• Besides choosing a proper ranking function,
  efficient way to execute also decides the
  performance.
• So given a ranking function the execution of this
  following a particular ranking algorithm plays a
  key role in the efficiency.

4
Algorithms for ranking

• Prominent Algorithms to get top K results are
• Sort Algorithm
• Scan Algorithm
• FA Algorithm
• TA Algorithm

5
Sort Algorithm

• Most simple way to decide the top K results of a
  ranking function like
• Score (ObjectId) Linear combinations of
  attributes
• is to sort the result and take the top K.
• This will take nlogn time.
• Very slow for very large relations where n is
  quite large.

6
Scan Algorithm

• Keep K tuples in a buffer.
• Scan this buffer for every tuple in the relation.
• Replace the lowest one in the buffer if the input
  tuple is more than that.
• Takes O(n.K) time.
• Still low for a large n.

7
FA Algorithm

• Fagins Algorithm known as FA Algorithm.
  Developed by Ron Fagin.
• Takes the help of data structures prepared
  offline.
• Though there is a cost associated with these data
  structures, yet the amortized cost is very low.
• Sorted access to the attributes. Supports
  GetNext() operation and is sequential. One sorted
  table per attribute.
• Random access through the ObjectId. Supports
  Get(ObjId) operation.
• The pre processing requires the preparation of
  above two types of data structures which will be
  used again and again during the processing.

8
FA Algorithm

• Step1
• Example of determining top 1 restaurant based on
  the given ranking function
• Score(RestId) 2.Cusine Location

Sorted for Cusine
Sorted for Location
Original relation
9
FA Algorithm

• Step1
• Do the GetNext from both sorted tables in round
  robin.
• Stop when K objects have been seen in common from
  all lists 1 in our example

RestId 4 is winner in our case
Sorted for Location
Sorted for Cusine
10
FA Algorithm

• Step2
• Random access to calculate the score for all
  visited tuples in step 1.
• Take the top K after evaluation
• This algorithm is applicable if the problem shows
  monotonic property.
• The worst case will be same as scan algorithm.
• The worst case memory requirement is unbounded.

11
TA Algorithm

• Known as Threshold Algorithm
• Similar to FA but sorted access and random access
  are interleaved.
• Step 1
• Do sorted access (and corresponding random
  accesses) until you have seen the top K answers.
• Step 2
• Determine threshold value (Hypothetical tuple)
  based on objects currently seen under sorted
  access.
• K objects with overall score threshold value ?
  Stop.
• Else go to next entry position in sorted list and
  repeat step 1
• Faster than FA.
• Requires less memory.