GRAMM: Fast CGRA Application Mapping Based on A Heuristic for Finding Graph Minors

A graph $H$ is a minor of a second graph $G$ if $G$ can be transformed into $H$ by two operations: 1) deleting nodes and/or edges, or 2) contracting edges. Coarse-grained reconfigurable array (CGRA) application mapping is closely related to the graph minor problem, where $H$ is the application's dataflow graph and $G$ is the CGRA's device-model graph. A heuristic algorithm to find graph minors has proven to be practical for sparse graphs with hundreds of vertices in a quantum computing application. In this work, we adapt the heuristic to CGRA application mapping, where the graphs have directed edges, and the vertices have unique types (e.g., representing ALUs or interconnect). Additionally, we alter the original cost function, taking inspiration from PathFinder, an iterative negotiated-congestion routing algorithm. In an experimental study comparing with a CGRA mapper based on integer linear programming, we demonstrate a higher rate of successful mappings and from 80× to up to orders of magnitude lower runtime.