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Popular Ranking Algorithms. Prepared by -Ranjan Dash. Contents. Efficient ways of Ranking Algorithms for ranking Sort Algorithm Scan Algorithm FA Algorithm TA Algorithm. Efficient ways of Ranking.

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popular ranking algorithms

Popular Ranking Algorithms

Prepared by

-Ranjan Dash

contents
Contents
  • Efficient ways of Ranking
  • Algorithms for ranking
  • Sort Algorithm
  • Scan Algorithm
  • FA Algorithm
  • TA Algorithm
efficient ways of ranking
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.
algorithms for ranking
Algorithms for ranking
  • Prominent Algorithms to get top K results are
  • Sort Algorithm
  • Scan Algorithm
  • FA Algorithm
  • TA Algorithm
sort algorithm
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.
scan algorithm
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.
fa algorithm
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.
fa algorithm1
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

fa algorithm2
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

fa algorithm3
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.
ta algorithm
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.
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