Design of a balanced multiple-valued file-organization scheme with the least redundancy

A new balanced file-organization scheme of order two for multiple-valued records is presented. This scheme is called HUBMFS<subscrpt>2</subscrpt> (Hiroshima University Balanced Multiple-valued File-organization Scheme of order two). It is assumed that records are characterized by <italic>m</italic> attributes having <italic>n</italic> possible values each, and the query set consists of queries which specify values of two attributes. It is shown that the redundancy of the bucket (the probability of storing a record in the bucket) is minimized if and only if the structure of the bucket is a partite-claw. A necessary and sufficient condition for the existence of an HUBMFS<subscrpt>2</subscrpt>, which is composed exclusively of partite-claw buckets, is given. A construction algorithm is also given. The proposed HUBMFS<subscrpt>2</subscrpt> is superior to existing BMFS<subscrpt>2</subscrpt> (Balanced Multiple-valued File-organization Schemes of order two) in that it has the least redundancy among all possible BMFS<subscrpt>2</subscrpt>'s having the same parameters and that it can be constructed for a less restrictive set of parameters.

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