The complexity of partial match retrieval in a dynamic setting

Abstract

The partial match retrieval problem analyzed in this paper is described as follows. Given a positive integer d, a record having d binary attributes consists of a d dimensional binary vector, referred to as the record's key, and a quantity which lies in a commutative semigroup, referred to as the value of the record. Given a set of such records having distinct keys, a partial match query is a request for the sum of the values of all records in the set whose keys lie in a hyperrectangle specified by the query. We consider the problem of designing data structures which permit insertions and deletions of records, and partial match queries. Among our results is the following. There exist data structures which accommodate arbitrary sequences of N manipulations (insertions, deletions, and queries) in (worst case) time approximately (1.226) d N. Moreover, relative to an appropriate model of computation, this complexity is best possible.