Design of file organization schemes for selected query set on binary-valued attributes and their redundancies

Abstract

In this paper we consider file organization schemes for binary-valued records and a selected set Q ( k )} of queries, each specifying k attributes. We let a partition of Q ( k )} into non-empty subsets correspond to the directory of a file organization scheme in such a manner that each area (bucket) in the directory is associated with one of those subsets. Then we consider the redundancy of the scheme which is defined as the average number of times the accession number of a record is stored. The record distribution used to estimate redundancies has the invariant property relative to the permutation of the attributes. A bucket corresponding to a set of queries in Q ( k )} which specify k − 1 attributes in common is called k -hyperclaw ( k − HC ) type. It is shown that the redundancy of a file organization scheme (called a k-HC -type scheme) whose buckets all are k − HC type is not greater than that of every possible file organization scheme with the same parameters. Furthermore, given the number of buckets a procedure for obtaining a k − HC type scheme with less redundancy than that of the other is also shown. Finally, in the case k = 2 a balanced file organization scheme having the least redundancy among all possible balanced file organization schemes with the same parameters is given from the graph-theoretic approach.