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
Fagin’s 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
RestId
Cusine
Location 1 2 3 4 5 6 7
RestId
Cusine 4 6 3 5 7 1 2
RestId
Location 2 5 4 1 7 3 6
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
Cusine 4 6 3 5 7 1 2
RestId
Location 2 5 4 1 7 3 6
1st Round
2nd Round
3rd Round 4 2 6 5 3
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.