Mapping a class of algorithms from binary tree machines to linear arrays

Binary tree machines are convenient for designing parallel algorithms in many problems. However, when considering different engineering issues, linear arrays are easier to implement. A class of algorithms for binary tree machines that can be mapped onto linear arrays cost-effectively is identified, and the mapping for this class is presented. It is shown that if the input size is not too small, the algorithms that are optimal on a binary tree machine remain optimal on a linear array after its mapping.