Greedy Algorithms for Mapping onto a Coarse-grained Reconfigurable Fabric

This book chapter describes several greedy heuristics for mapping large data-flow graphs (DFGs) onto a stripe-based coarse-grained reconfigurable fabric. These DFGs represent the behavior of an application kernel in a high-level synthesis flow to convert computer software into custom computer hardware. The first heuristic is a limited lookahead greedy approach that provides excellent run times and a reasonable quality of result. The second heuristic expands on the first heuristic by introducing a random element into the flow, generating multiple solution instances and selecting the best of the set. Finally, the third heuristic formulates the mapping problem of a limited set of rows using a mixed-integer linear program (MILP) and creates a sliding heuristic to map the entire application. In this chapter we will discuss these heuristics, their run times, and solution quality tradeoffs. The greedy mapping heuristic follows a top-down approach to provide a feasible mapping for any given application kernel. Starting with the top row, it completely places each individual row using a limited look-ahead of two rows. After each row is mapped, the mapper will not modify the mapping of any portion of that row. This mapping approach is deterministic as it uses a priority scheme to determine which elements to place first based on factors such as the number of nodes to which it connects and second based on the desirability of a particular location in the row. While the limited information available to the mapper does not often allow it to produce optimal or minimum-size mappings, its runtime is typically a few seconds or less. We use a fabric interconnect model (FIM) file in the mapping flow to define a set of restrictions on what interconnect lines are available, the capabilities of particular functional units (e.g. dedicated vertical routes versus computational capabilities) in the system, etc. The greedy heuristic is deterministic in the priority system which it uses to place nodes. The second mapping heuristic we explore is based on this greedy algorithm and introduces randomness into the heuristic to make decisions along the priority list. In the first implementation the node selection order is selected randomly. In the second version, weights are assigned to nodes based on the deterministic placement order. Since the heuristic runs so quickly, we can run the heuristic 10’s or possibly 100’s of times and select the best result. This method is also parameterizable with the FIM.