A unifying methodology for multiple querying on enhanced meshes

The main contribution of this work is to show that a number of seemingly unrelated problems in database design, pattern recognition, robotics, and image processing can be solved simply and elegantly by formulating them as instances of a general problem-the multiple query (MQ) problem. An arbitrary instance of the multiple query problem consists of a collection A={a/sub 1/, a/sub 2/, ..., a/sub n/} of items, a collection Q={q/sub 1/, q/sub 2/, ..., q/sub m/} (1/spl les/m/spl les/n) of queries, a decision problem /spl phi/:Q/spl times/A/spl rarr/{"yes", "no"}, and an associative and commutative function f operating on subsets of A. For every query q/sub i/, let S/sub i/ be the set of items a/sub j/ in A for which /spl phi/(q/sub i/, a/sub j/)="yes". The solution of q/sub i/ is defined to be f(S/sub i/). In this context, the multiple query problem involves solving all the queries in Q. We begin by showing that if the collections A and Q are stored one item and at most one query per processor on a mesh with multiple broadcasting of size /spl radic/n/spl times//spl radic/n then any algorithm that solves the MQ problem requires /spl Omega/(m1/3n1/6) time in the worst case. Second, we show that a number of fundamental problems can be solved simply and elegantly by formulating them as instances of the MQ problem.