Efficient Stack Simulation for Set-Associative Virtual Address Cache with Real Tags

719 the number of groups used is equal to 2°Rtn(tx. The time complexity of this algorithm is OCNlgN) because: Step 1 needs O(N1gN) time; Step 2 is a linear time labeling, and needs O(lg2N) time; Steps 3 and 4 need O(n) = O(lgN) to compute the group number for each row, and there are N rows. This time complexity is optimal when k = O(n) because there are kN = O(nN) = O(N1gN) binary variables to be assigned (assume each bit in a variable column needs a unit of time to assign a value). When k = o(n). this time complexity could be considered as optimal also if we consider setting SEs as a part of the whole process of routing, since there are O(N1gN) SEs to be set. In summary, we have the following main result.