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Now, let us discuss two related algorithms for deciding which pages to evict. The clock algorithm is one of the most popular choices. It works by keeping frames in a circular structure. (Note that this circle may be very large: a 32-bit machine with 4k pages can have up to 220 1 million frames.) When a page fault occurs, it checks the reference bit of the next frame. If that bit is zero, it evicts that page and sets its bit to 1; if the reference bit is 1, the algorithm sets the bit to 0 and advances the pointer to next frame.
An implementation which is often used in real operating systems is a segmented queue. This type of algorithm divides all existing pages into two sets of pages. The most-active one-third of all pages use a clock algorithm. After that, pages that are evicted out of the clock are moved to a "uncommon" linked list, in which we use exact LRU. This way, we approximate LRU for the frequently-referenced pages (1/3 of the page frames - fast clock algorithm), and at the same time use exact LRU on the infrequently accessed pages (2/3 of all page frames). Since the pages in the uncommon list are not accessed very frequently, it is okay if their accesses are a little slower due to some pointer manipulation.
Find the optimal solution and optimal value of the following linear program. Use both (a) the enumerating the corner points method and (b) the iso-profit line method. Also identify
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