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The theoretically optimal page replacement algorithm (also known as OPT, clairvoyant replacement algorithm, or Bélády's optimal page replacement policy) [3] [4] [2] is an algorithm that works as follows: when a page needs to be swapped in, the operating system swaps out the page whose next use will occur farthest in the future. For example, a ...
Bélády's algorithm is the optimal cache replacement policy, but it requires knowledge of the future to evict lines that will be reused farthest in the future. A number of replacement policies have been proposed which attempt to predict future reuse distances from past access patterns, [23] allowing them to approximate the optimal replacement ...
For example, Graph (c) is produced after page E is accessed on Graph (a). When there is a miss and a resident page has to be replaced, the resident HIR page at the bottom of Stack Q is selected as the victim for replacement. For example, Graphs (d) and (e) are produced after pages D and C are accessed on Graph (a), respectively.
This can be emulated in practice with the Least Recently Used policy, which is shown to be within a small constant factor of the offline optimal replacement strategy [4] [5] To measure the complexity of an algorithm that executes within the cache-oblivious model, we measure the number of cache misses that the algorithm experiences.
This phenomenon is commonly experienced when using the first-in first-out page replacement algorithm. In FIFO, the page fault may or may not increase as the page frames increase, but in optimal and stack-based algorithms like LRU, as the page frames increase, the page fault decreases. László Bélády demonstrated this in 1969. [1]
Adaptive Replacement Cache (ARC) is a page replacement algorithm with better performance [1] than LRU (least recently used). This is accomplished by keeping track of both frequently used and recently used pages plus a recent eviction history for both. The algorithm was developed [2] at the IBM Almaden Research Center.
A page is in the working set if it is referenced in the working set window. To avoid the overhead of keeping a list of the last k referenced pages, the working set is often implemented by keeping track of the time t of the last reference, and considering the working set to be all pages referenced within a certain period of time.
For example, if we are multiplying chain A 1 ×A 2 ×A 3 ×A 4, and it turns out that m[1, 3] = 100 and s[1, 3] = 2, that means that the optimal placement of parenthesis for matrices 1 to 3 is and to multiply those matrices will require 100 scalar calculations.