Algorithmic Studies in Mass Storage Systems by C.K. Wong

By C.K. Wong

A significant technological development for giant database platforms has been the creation of ever-larger mass garage structures. this permits computing facilities and company facts processing installations to take care of on-line their software libraries, much less usually used info records, transaction logs and backup copies less than unified method regulate. Tapes, disks and drums are classical examples of mass garage media. The newer IBM 3851 Mass garage Facility, a part of the IBM 3850 Mass garage approach, represents a brand new course in mass garage improvement, specifically, it truly is two-dimensional. With the adulthood of magnetic bubble expertise, extra subtle, immense, multi-trillion-bit garage platforms should not a long way sooner or later. whereas huge in means, mass garage platforms have often particularly lengthy entry instances. due to the fact list entry chances are not uniform, a variety of algorithms were devised to place the files to diminish the common entry time. the 1st chapters of this e-book are committed in general to such algorithmic stories in linear and two-dimensional mass garage structures. within the 3rd bankruptcy, we view the bubble reminiscence as greater than a garage medium. actually, we talk about diverse buildings the place regimen operations, resembling info rearrangement, sorting, looking out, etc., should be performed within the reminiscence itself, releasing the CPU for extra complex initiatives. the issues mentioned during this ebook are combinatorial in nature.

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I 1= '.. J=I+ I . I m=J+ 1 m 46 LINEAR STORAGE and v i-I . :L ac. :L ac. = :L ac. :L ac. :L ac ' 1= 1.. )=1+ I 1 . 1= I ')=1+ . I 1m=)+ . I then by gathering terms, T 2 becomes v v + xg'('lT)g"('lT)/2 + g'('lT):L ac. :L ac. I 1= '.. I 1 )=1+ m 47 UNEQUAL RECORD SIZE Therefore, D( 'TT) becomes Observe that Kl and K2 are independent of the arrangement 'TT. Thus, to minimize D('TT), we need to minimize K 4 . Since x<2a n + l' K4 will be minimized if g' ('TT )g" ('TT) is maximized. g'('IT) + g"('IT) = if g'('IT) n Since L ai' g'('TT)g"('TT) achieves the maximum if and only i=l n = g"('IT) = (l/2)L a·.

We are interested in devising fast algorithms which will determine an optimal arrangement for any given set of records. Finding an optimal arrangement for a set of equal-sized records is a relatively easy task. " That is, the record with highest access probability is placed in the middle and records with successively lower probabilities are placed adjacently on alternate sides. Finding an optimal arrangement for a set of equal-access-probability records is equally simple. , the shortest record is placed in the middle and successively longer ones are placed adjacently on alternate sides).

P/Pj 1=1 where gj = bj[E(j) + 2gj) ). 6). We shall omit the derivation of this formula, trusting that readers can derive it without any difficulties. Using this formula, we can now bound the performance of an arbitrary bell-shaped arrangement with respect to an optimal arrangement. 3 Let f3' and f3" be any two bell-shaped arrangements of a set of n records. Then we have D(f3')/D(f3") ~ 1 Proof Let f3' = + n/2. (b'l ,... ,b' n) and f3" = (b" I , ... ,b" n) be any two bell-shaped arrangements of a set of n records.

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