## The Complexity of Computation on the Parallel Random Access Machine (1993)

Citations: | 31 - 3 self |

### BibTeX

@MISC{Fich93thecomplexity,

author = {Faith E. Fich},

title = {The Complexity of Computation on the Parallel Random Access Machine},

year = {1993}

}

### Years of Citing Articles

### OpenURL

### Abstract

PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much more powerful than restricted instruction set PRAMs. THEOREM 21.16 Any function of n variables can be computed by an abstract EROW PRAM in O(log n) steps using n= log 2 n processors and n=2 log 2 n shared memory cells. PROOF Each processor begins by reading log 2 n input values and combining them into one large value. The information known by processors are combined in a binary-tree-like fashion. In each round, the remaining processors are grouped into pairs. In each pair, one processor communicates the information it knows about the input to the other processor and then leaves the computation. After dlog 2 ne rounds, one processor knows all n input values. Then this processor computes th...