Combinatorial filing schemes with fewer buckets and improved redundancy and construction characteristics

Abstract

This paper presents an interesting extension of the combinatorial filing scheme approach to information retrieval. It is appropriate both in the traditional large secondary memory architecture for information retrieval and in the distributed computing paradigm of powerful but cheaper, smaller machines. An important characteristic of the proposed scheme, unlike other combinatorial ones, is that redundancy can be decreased by varying a parameter. Moreover, the construction process is significantly simpler, the number of buckets smaller and the choice of parameters greater than for the typical combinatorial schemes, all of which make this scheme an attractive information retrieval approach for today's technology. In particular, families of balanced multiple-valued filing schemes of order k over the projective geometry PG( t, q) are constructed. Certain ( s + c)-flats formed from the union of distinct flats of a partial spread of order ( s + 1), such that c ¦(t − s) and which pass through the s-flat V s , are used to define the attributes and values. For order k queries, the buckets are the ( k + h)-flats through a fixed h-flat, V h , of PG( t, q), V h CV s . Storage and retrieval algorithms use difference set representation, and structural properties, of the bucket flats. The number of attributes and number of values per attribute are dependent on the values of s and c. The redundancy is made to vary with the value of h. A particular scheme of order k in the family is a balanced multiple-valued filing scheme, BMFS k , with parameters ( s, c, h).