Mapping tree-structured computations onto mesh-connected arrays of processors

The author shows how to parallelize tree-structured computations for d-dimensional (d⩾1) mesh-connected arrays of processors. A tree-structured computation T consists of n computational tasks whose dependencies form a task tree T of n constant degree nodes. Each task can be executed in unit time and sends one value to its parent task after it has been executed. The author presents linear time algorithms for partitioning and mapping the task tree T onto a p¹d/×. . .×p¹d/ mesh-connected array of processors so that one can schedule the processors to perform computation T in O(n/p) time, for p⩽ min{n /h, n^d(d+1)/}. It is shown that one can schedule a p¹d/ × . .× p ¹d/ mesh to evaluate an n-node expression tree of associative operators in O(n/p) optimal time, for p⩽ n^d(d+1)/