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={a₁, a₂, ..., a_n } of items, a collection Q={q₁, q₂, ..., q _m} (1⩽m⩽n) of queries, a decision problem φ:Q×A→{“yes”, “no”}, and an associative and commutative function f operating on subsets of A. For every query q_i, let S_i be the set of items a_j in A for which φ(q_i, a_j)=“yes”. The solution of q_i is defined to be f(S_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 √n×√n then any algorithm that solves the MQ problem requires Ω(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