Question 8576 – Data-Structures

Consider the scenario, you have k-way set associative cache, let us say a block b0 comes to set-0 and then there are k-1 unique blocks to the same set. Now the set-0 is full then one more block came to set-0 and the block b0 is replaced using LRU, if b0 comes again then it will cause a miss. But it is given that the set associativity A>=k, means the no. of blocks in a set is k or more so assume we have (k+1)-way set associativity, applying the above logic b0 comes first and then k-1 other unique accesses come to the same set-0 then there is still place for one more block in set-0 and if b0 comes again now then it will not cause a miss. As the associativity increases further there will not be any more misses other than the unique blocks we have a best case scenario. So out of N accesses only the unique blocks n can be missed and the miss ratio is n/N.
As the set associativity size keeps increasing then we don’t have to replace any block, so LRU is not of any significance here.