By Johannes Bisschop, Alexander Meeraus (auth.), Jean-Louis Goffin, Jean-Marc Rousseau (eds.)

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Maco and Y. Takahara, Theory of hierarchical multi-level systems (Academic Press, New York, 1970). Mathematical Programming Study 20 (1982) 39-53 North-Holland Publishing Company OPTIMAL LOCATION OF FILES AND PROGRAMS IN COMPUTER NETWORKS P. C A R R A R E S I Istituto di Scienze dell'Informazione, Universitit di Pisa, Italy G. , Pisa, Italy Received 16 May 1980 Revised manuscript received 14 April 1981 The problem of optimally locating copies of programs and files in a distributed data base is considered.

F) (4) If tOpy~< ffpi for each pair (p, f), Stop. Otherwise add s to /~(p, f) for each pair (p, [) such that topi > ffpi and go to step 2. For the theoretical background of this procedure and for the proof of its convergence we refer to [5]. This approach has two main drawbacks: (i) The computations involved are quite costly. In fact at step 2 a large scale linear program must be solved. The number of variables of this LP is of the order of nlPIIFI, while the number of constraints is of the order of IPIIFI.

Since M is very large, it follows that uj(p ) = 1 ~ Cry(p, D = O, from which, because of the nonnegativity of qi(P, f): ~;(p,/) = min{c~j(p, f) + ~'](p,/): uj(p) = l, j E N } , i E N , ~'~(p, f) = min{c~k(p, f): Vk(f) = l, k ~ N}, j E N. 1) determines fi;(p, f), for each i E N, and ~3'~(p,/) for each j E N, because of the existence in the network of one copy at least of both p and f. The optimal solution can be completed as follows: ~}(p, f) = max{0, max{~}(p, f ) - f,'~(p, f ) - ci;(p, f): i e N, j E N}}, ~ ( p , f) = max{0, max{fi'](p, f ) - Q~(p,/): j E N, k E N}}.

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