1. On every access, mark the page with a timestamp. Whenever we need to evict a page, we search through memory for the oldest page, the least-recently used page. But we need memory accesses to be fast. With this approach, on every memory access we would also need to read(load) a clock (or counter) and perform a store.
2. Maintain a queue of pages. Every time we touch a page, wemove that page to the beginning of the queue. When we need to evict a page, we evict the last element of the queue. Again, the pointer manipulation to do this would slow down the memory accesses, which we need to be fast on average.
3. Use a hash table rather than a queue. In this case, we have to compute a hash address on every memory access. Bad idea.
4. Approximate LRU.We can do this by maintaining reference bits for every page. On each memory access, the MMU hardware sets the page's reference bit to 1. Periodically, the OS tells the MMU to reset all the reference bits. Whenever we need to evict a page, we select one that has a reference bit not set. (So eviction may require an O(n) search through page tables to ?nd a page with reference bit not set, but the common case, cache hits, are very fast, done in hardware.) This algorithm considers any page which is zeroed to be "old enough". Then, although we can't know exactly what is the least-recently used, we do know that whatever is marked is a least more recent than something not marked. In practice, this approach works pretty well.
LRU is already only an approximation to OPT. In practice, we also approximate LRU itself. Our LRU approximation optimizes for the common case, which is cache hits, rather than cache misses. (If the common case is not cache hits, then your cache is not helping you.)