Pipelining computations in a tree of processors

The computational power of a tree of processors is investigated. It is demonstrated that a tree of processors can solve certain problems impressively fast by exploiting the internal pipelining capabilities. Efficient tree algorithms are designed for two different problems: selection and maintaining dictionaries. It is shown that an O(log n)-height tree of processors can find the k th smallest element of n numbers in deterministic O ((log n)^2+o(1)) steps, an impressive improvement over previous results. The main tools are the development of a new sampling technique and an elegant internal pipelining strategy. A lower bound is established for this selection problem. Another variant of the sampling technique reduces the storage requirement of R.M. Karp et al.´s (1986) tree searching algorithm while maintaining its speed. It is established that dictionary operations can be performed with a pipelined interval of O(1) and a response time of O(height of the tree), which again improves a known result and settles an open problem. This is based on being able to make the tree operate like a complete tree view from the root