Extending Rectangular Range Reporting with Query Sensitive Analysis

In this paper, we consider the problem of reporting the new points incorporated by on-line sequences of nested rectangular range queries where all queries in a sequence have the same orientation, but the orientation of each sequence may differ. Worst case lower bound results show that time and space efficient solutions to this problem are unlikely. Here we present a linear space solution that performs partially ordered searches of a box-decomposition subdivision. It uses information obtained from the results of processing previous queries to assist in processing each new query in a sequence. A query sensitive analysis shows the algorithm is most effective for “targeted” queries — queries that target space containing a high density of data relative to the space immediately surrounding the query. Such queries are typical of those made by region growing surface reconstruction techniques, the primary application considered here. To substantiate this intuition, we have implemented a version of the algorithm and run it on real range data and sequences of queries representative of those made by region growing surface reconstruction techniques. The empirical results provide strong support for this in-