Optimization Using Tuple Subsumption

. A tuple t1 of relation R subsumes tuple t2 of R, with respect to a query Q if for every database, tuple t1 derives all, and possibly more, answers to query Q than derived by tuple t2 . Therefore, the subsumed tuple t2 can be ignored with respect to Q in the presence of tuple t1 in relation R. This property finds use in a large number of problems. For instance: during query optimization subsumed tuples can be ignored thereby avoiding the computation of redundant answers; the size of cached information in distributed and object oriented systems can be reduced by omitting subsumed tuples; constraints need not be checked and rules need not be recomputed when provably subsumed updates are made. We give algorithms for deciding efficiently when a tuple subsumes another tuple for queries that use arbitrary mathematical functions. We characterize queries for which, whenever a set of tuples T subsumes a tuple t then one of the tuples in T also subsumed t, yielding efficiently verifiable cases..