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Download PDF by C.K. Wong: Algorithmic Studies in Mass Storage Systems

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By C.K. Wong

A significant technological pattern for big database structures has been the creation of ever-larger mass garage structures. this permits computing facilities and enterprise facts processing installations to take care of on-line their software libraries, much less often used facts records, transaction logs and backup copies lower than unified procedure keep an eye on. Tapes, disks and drums are classical examples of mass garage media. The more moderen IBM 3851 Mass garage Facility, a part of the IBM 3850 Mass garage method, represents a brand new path in mass garage improvement, specifically, it really is two-dimensional. With the adulthood of magnetic bubble know-how, extra refined, monstrous, multi-trillion-bit garage platforms should not a ways sooner or later. whereas huge in capability, mass garage platforms have quite often really lengthy entry instances. due to the fact that list entry chances are not uniform, numerous algorithms were devised to place the files to diminish the common entry time. the 1st chapters of this publication are committed quite often to such algorithmic experiences in linear and two-dimensional mass garage platforms. within the 3rd bankruptcy, we view the bubble reminiscence as greater than a garage medium. in reality, we talk about various constructions the place regimen operations, comparable to information rearrangement, sorting, looking out, etc., should be performed within the reminiscence itself, releasing the CPU for extra advanced initiatives. the issues mentioned during this e-book are combinatorial in nature.

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L. id(i,j) = _1 (n 2 48 1)(5n2 + 4n + 3). 18) I>J For n even, the sums are not sufficiently different to affect our results. 4. Random placement For a sequence {ft } of independent, identically distributed arrivals, random placement can be achieved in a variety of ways. We will assume that the arrival at time t, 1:S t:S n, is placed in location i=t. Under the stated assumptions, it is equivalent to assume that the arrival at time t is placed in any of the remaining vacant locations, at random. 1 Let Dr denote the average distance under random placement; then 2 E(Dr):::::(n - 1)/(3n + 1).

The distance function dT(i,j) is easily seen to be j-I .. ) _ d T (l,j - L [17 { k=i+I . 2) 1 k for i~j. 1) and simplifying, we derive the expected head travel function D T( 'IT) to be More specifically, from the distance function dT(i,j), we obtain dT(i,i) = [17. j-I 2 L k=i+ I I for 1 ~ i ~ nand dT(i,j) + dT(j,i) = [17. + [17. + I [17 for l~i

Thus, it follows that if p/ Ei = p/ Ej for all 1 ~ i, j ~ n, then all arrangements give the same value. The record(s) with the highest p/ Ei ratio play an important role in the optimal arrangement. Our next result shows that these UNEQUAL RECORD SIZE 41 records must be placed contiguously in an optimal arrangement. That is, if there are r+ 1 records with the highest p/ f i ratio, then they must be placed in positions h, h+l, ... , h+r for some I~h~n - r. Moreover, the optimal arrangement is in a class of arrangements which we call the "bell-shaped" arrangements.

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