Random Data Accesses on a Coarse-Grained Parallel Machine I. One-to-One Mappings

Random Data Accesses on a Coarse-Grained Parallel Machine II. One-to-Many and Many-to-One Mappings

“…It is not overly restrictive, because the underlying architecture is coarse-grained and p is usually not too large. Besides, even an algorithm that transfers data elements directly to the destination processors has to satisfy n p 2 τ/µ to ensure that startup overheads do not dominate time taken [26]. When message sizes are small and startup overheads begin to dominate, the above requirements can be brought down by transferring the data through more intermediate stages.…”

“…We use the term hot spots to refer to collisions that occur during a RAW or multiple reads from the same element during a RAR. Using the dynamic permutation algorithms from [26] without modification for the RAW/RAR could increase the time taken from O(n/ p)µ to O(n)µ, making the solution nonoptimal. The RAW/RAR algorithms presented in this paper solve this problem and retain the optimality by dynamically stretching and shrinking the hot spots as necessary.…”

“…This is a bounded transportation problem, similar to the communication that underlies a dynamic permutation. It can be performed in 2µn/ p time for n p 3 + p 2 τ/µ (see [26] for details).…”

“…• communication between the intermediate and destination processors (which resembles the communication underlying a monotonic dynamic permutation [26]), and…”

“…If t is total length of all the messages sent out and received at every processor, complete exchange can be performed in time pτ + µt. A linear permutation algorithm can be used to perform the complete exchange, as discussed in [26].…”