Abstractions for Polyhedral Topology-Aware Tasking [Position Paper]

Abstract

Traditional polyhedral compilation techniques rely on Integer Linear Programming (ILP) and lexicographic optimization to compute optimal transformations. Although, these techniques excel at exposing and leveraging data and pipeline parallelism as well as exploiting (hidden) available locality, they are not the best suited when tackling problems such as the Manhattan distance in a grid.

In this short paper we propose techniques to sort and rank the various orderings of tasks mapped onto a network, while considering 3 different network topologies. We introduce new abstractions and develop a new compiler analysis to determine an optimal order of tasks w.r.t to the user-provided execution location. We propose a closed form for encoding in a single set all the possible orderings of tasks. In a nutshell, the encoding represents the topological orderings of nodes in a task graph. Once the closed form is built, we proceed to iteratively evaluate the total cost of each point in the set (an execution order). This involves computing the cost between every pair of adjacent tasks, and aggregating them to obtain the total cost. Finally, an optimal ordering is obtained by applying lexicographic minimization over all the points in the set.