I/O-Efficient Well-Separated Pair Decomposition and its Applications

We present an external memory algorithm to compute a well-separated pair decomposition (WSPD) of a given point set P in d in O sort N I/Os using O N B blocks of external memory, where N is the number of points in P, and sort N denotes the I/O complexity of sorting N items. (Throughout this paper we assume that the dimension d is fixed). We also show how to dynamically maintain the WSPD in O logB N I/O’s per insert or delete operation using O N B blocks of external memory. As applications of the WSPD, we show how to compute a linear size t-spanner for P within the same I/O and space bounds and how to solve the K-nearest neighbor and K-closest pair problems in O sort KN and O sort N K I/Os using O KN B and O N K B blocks of external memory, respectively. Using the dynamic WSPD, we show how to dynamically maintain the closest pair of P in O logB N I/O’s per insert or delete operation using O N B blocks of external memory.