An Almost Linear-Time Algorithm for Computing a Dependency Basis in a Relational Database

Abstract

All algonthm that constructs, for a given set of (functional and multwalued) dependencJes X and a set of attributes X, the dependency basis of X as described. The algorithm runs in time O((1 + min(E, logp))llZl[), where p is the number of sets m the dependency basas of X,/i Js the number of multivalued dependencies in X, and IlXll as the length of i. a A variant of the algorithm tests whether a dependency a is unplied by X m time O((1 + mm(/i, log p-))lli.ll), where ff is the number of sets m the dependency basas of the left-hand side of o that intersect the right-hand sade of o Whenever all the dependencies in X are functaonal dependenoes, these algorithms are linear time. © 1982, ACM. All rights reserved.