Consecutive Retrieval with Redundancy: An Optimal Linear and an Optimal Cyclic Arrangement and Their Storage Space Requirements

Ghosh [2,3 j has introduced a very economic method of organizing records in an information retrieval system : the records relevant to a query are stored in consecutive locations and cne location may be significant for several queries (see also Ghosh [5], Lipski [7] and Lipski and Marek [S]). Thus, the record sets corresponding to queries form overlapping segments in storage. In general, repetitions are necessary, so redundancy has to be taken into account (see Ghosh [4,5] and Lipski and Marek [9]). A problem is to minimize this redundancy. In more abstract terms the problem is as follows: given a family % = {Mr , Mz, . . . . M,} of subsets of a finite set X, find an arrangement of all elements of x such that (i) each Mi forms a segment and (ii) the total number of repetitions is minimal. Such an arrangement is called an optimal arrangement, Kou [6] has shown that this problem (for linear arrangements) is NP-complete. Ehrich and Lipski [ 1 ] discovered a method for producing linear arrangements which satisfy (i) and (ii). They call these arrangements suboptimal. They have calculated B, tU), the storage space required, and found