Deferred data structuring: Query-driven preprocessing for geometric search problems

We consider the problem of answering a series of on-line queries on a static database. The conventional approach to such problems involves a preprocessing phase which constructs a data structure with good search behavior. The data structure is then used to process a series of queries without any further reordering. Our approach involves dynamic or query-driven structuring of the database, i.e. we process the database only when it is required for answering a query. We present optimal algorithms for the following problems in the plane: testing convex hull membership, half-plane intersection queries and fixed-constraint multi-objective linear programming. This technique is also applied to multidimensional dominance query problems.