LRU Page replacement

Least Recently Used (LRU) page replacement algorithm

The idea behind LRU page replacement is to use recent past as an approximation of the near future. Replace the page that has not been used for the longest period of time.

LRU is considered a good replacement policy, and is often used. The problem is how exactly to implement it. There are two simple approaches commonly used:

1. Counters. Every memory access increments a counter, and the current value of this counter is stored in the page table entry for that page. Then finding the LRU page involves simple searching the table for the page with the smallest counter value. Note that overflowing of the counter must be considered.
2. Stack. Another approach is to use a stack, and whenever a page is accessed, pull that page from the middle of the stack and place it on the top. The LRU page will always be at the bottom of the stack. Because this requires removing objects from the middle of the stack, a doubly linked list is the recommended data structure.

Note that both implementations of LRU require hardware support, either for incrementing the counter or for managing the stack, as these operations must be performed for every memory access.

Neither LRU or OPT exhibit Belady's anomaly. Both belong to a class of page-replacement algorithms called stack algorithms, which can never exhibit Belady's anomaly. 

A stack algorithm is one in which the pages kept in memory for a frame set of size N will always be a subset of the pages kept for a frame size of N + 1.