Search Space Reductions for Nearest-Neighbor Queries

The vast number of applications featuring multimedia and geometric data has made the R-tree a ubiquitous data structure in databases. A popular and fundamental operation on R-trees is nearest neighbor search. While nearest neighbor on R-trees has received considerable experimental attention, it has received somewhat less theoretical consideration. We study pruning heuristics for nearest neighbor queries on R-trees. Our primary result is the construction of non-trivial families of R-trees where k-nearest neighbor queries based on pessimistic (i.e. min-max) distance estimates provide exponential speedup over queries based solely on optimistic (i.e. min) distance estimates. The exponential speedup holds even when k = 1. This result provides strong theoretical evidence that minmax distance heuristics are an essential component to depth-first nearest-neighbor queries. In light of this, we also consider the time-space tradeoffs of depth-first versus best-first nearest neighbor queries and construct a family of R-trees where best-first search performs exponentially better than depth-first search even when depth-first employs min-max distance heuristics.