We propose a distributed data structure for maintaining spatial data sets on message-passing, distributed memory machines. The data structure is based on orthogonal bisection trees and it captures relevant characteristics of parallel machines. The operations we consider include insertion, deletion, and range queries. We introduce parameters to control how much imbalance is tolerated at processors and how close to an optimal load to balance. When balancing, we first determine and broadcast point

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... counts of a datadependent partition of the data. Based on this partition, we propose load balancing methods with different communication and computation requirements. We present initial experimental results for the Cray T3D. © and¨© be the new total number of points and the new load in a completely balanced OBT, respectively. Load balancing proceeds if at least one processor is not balanced with respect to © and © ¦ © Q a nd ¦ © © Q be the upper and lower ¦