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

By C.K. Wong

A significant technological development for giant database structures has been the advent of ever-larger mass garage platforms. this enables computing facilities and company information processing installations to take care of online their application libraries, much less often used information documents, transaction logs and backup copies less 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, particularly, it truly is two-dimensional. With the adulthood of magnetic bubble know-how, extra subtle, enormous, multi-trillion-bit garage structures are usually not a long way sooner or later. whereas huge in ability, mass garage platforms have ordinarily particularly lengthy entry instances. given that list entry possibilities should not uniform, a number of algorithms were devised to put the files to diminish the common entry time. the 1st chapters of this ebook are committed normally to such algorithmic reviews 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 speak about various constructions the place regimen operations, reminiscent of info rearrangement, sorting, looking out, etc., will be performed within the reminiscence itself, releasing the CPU for extra complex projects. the issues mentioned during this ebook are combinatorial in nature.

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It is 1=1 J=I+lm=J+l 1=1 )l clear that this transformation can be done in polynomial time. We need to show that the PARTITION problem has a solution if and only if the ALLOCATION problem has a solution. The ALLOCATION problem generated is a very special one in terms of the ratios p/ ej • It can easily be seen that p/ ej = 1/z for 1 $i$n and Pn+l/f n+l = 2a n+/(xz» 1/z. Therefore, Pn+l/f n+l is LINEAR STORAGE 44 the highest such ratio, and any arrangement 1T 1T can be represented as = (bl, ... ,b u ' n + 1, cl, ...

Note that by assumption of uniform distribution, for o~ x I ~ X2 ~ ... 26) since Pr(xk = xk+ l ) = O. 27) where integration is taken over the region 0 ~ xl ~ X2 ~ ... ~ Xn ~ 1. Let YI = xl' Yj = Xj-Xj_ 1 , for 2~i~n. 28) where integration is taken over the region n YI~O, .. ·,yn~O, LYk~1. k=l This is the well-known Dirichlet integral [25, p. 258] for which f .. ·f YmYpdYI .. ·dYn = Yl~o'''''Yn~o { l/(n + 2)! for m~p, 2/(n + 2)! [2i/(n + 2)! 30) = i(j + l)/«n + l)(n + 2)). J i j> 1 12(ij + i)d(i,j) .

2g(e,n), where By choosing x large enough, the ratio D('IT')/D('IT") can be made to approach l/(2e) e/2 arbitrarily closely. + Since e = min {Pj}, we have the desired 1 ~j~n result. 2 shows that an arbitrary arrangement can perform quite poorly in comparison with an optimal arrangement. 2 that an optimal arrangement is a bell-shaped arrangement, it is interesting to see how an arbitrary bell-shaped arrangement might compare with an optimal arrangement. Before we derive this result, we need to introduce a different notation for representing bell-shaped arrangements and their expected head travel.