Complexity of Online Algorithms - CSIS

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Paging Algorithm – Competitive Analysis Claim: • C LRU = k • Proof: • Partition the input sequence into rounds R 0 , R 1 ... R t • such that each round R j results in exactly k misses by LRU. • In each round R j , all the k+1 pages must have been accessed. • Why? • So, the ratio of misses by LRU to optimal misses is at most k i.e. for any input sequence • f LRU () / f OPT ()
Paging Algorithm – Competitive Analysis Claim: C FIFO = k • Proof: (similar to the proof for LRU: left as exercise) Claim: C LFU > k • Proof: • Consider a sequence where • 0 , 1 , ... j are k-1 distinct pages with 2 accesses each and • j+2*i-1 , j+2*i are a pair of different pages repeated for each i = 1, 2, ... • and are different from 0 , 1 , ... j • f LFU () = n – 2*k + 1 and f OPT () = 2 • Therefore the ratio f LFU () / f OPT () is O(n) • i.e. not bounded
Page 1 and 2: CS/IS C442 Advanced Algorithms & Co
Page 3 and 4: Paging Problem Consider a 2 level
Page 5 and 6: Paging Algorithms Typical performa
Page 7 and 8: Paging Algorithm - Miss Rates Assu
Page 9: Paging Algorithm - Competitive Anal
Page 13 and 14: Paging Algorithm - Competitive Anal
Page 15 and 16: Adversary Models There are differe
Page 17 and 18: Competitiveness of Randomized Algor
Page 19 and 20: Competitiveness of Randomized Algor
Page 21 and 22: Paging against an oblivious adversa
Page 27 and 28: Online Paging - Marker Algorithm T
Page 29 and 30: Online Paging - Marker Algorithm T
Page 31 and 32: Relating the Adversaries How do ra

Complexity of Online Algorithms - CSIS

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