AmortizedAnalysis

By following the principle of designing algorithms

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Unformatted text preview: wing the principle of designing algorithms whose amortized complexity is low, we obtain "self-adjusting" data structures that are simple, flexible and efficient. This paper surveys recent work by several researchers on amortized complexity. ASM(MOS) subject classifications. 68C25, 68E05 1. Introduction. Webster’s [34] defines "amortize" as "to put money aside at intervals, as in a sinking fund, for gradual payment of (a debt, etc.)." We shall adapt this term to computational complexity, meaning by it "to average over time" or, more 10 A MORTIZED A NALYSIS ‣ binary counter ‣ multipop stack ‣ dynamic table CHAPTER 17 Binary counter Goal. Increment a k-bit binary counter (mod 2k). Counter value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Cost model. Number A[ 7 A[ ] 6] A[ 5 A[ ] 4 A[ ] 3 A[ ] 2] A[ 1 A[ ] 0] Representation. aj = jth l17.1 Aggregate analysis bit of counter. east significant 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 455 Total cost 0 1 3 4 7 8 10 11 15 16 18 19 22...
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