Asawaree Kalavade and Edward A. Lee,
"The Extended Partitioning Problem: Hardware/Software Mapping, Scheduling, and Implementation-bin Selection," Journal of Design Automation of Embedded Systems, special issue on System Partitioning Issues, submitted. Postscript version
We first present an efficient (O(N2)) heuristic, called GCLP, to solve the binary partitioning problem. The heuristic reduces the greediness associated with traditional list-scheduling algorithms by formulating a global measure, called global criticality (GC). The GC measure also permits an adaptive selection of the optimization objective at each step of the algorithm; since the optimization problem is constrained by a deadline, either area or time is optimized at a given step based on the value of GC. The selected objective is used to determine the mapping of nodes that are "normal", i.e. nodes that do not exhibit affinity for a particular mapping. To account for nodes that are not "normal", we define "extremities" and "repellers". Extremities consume disproportionate amounts of resources in hardware and software. Repellers are inherently unsuitable to either hardware or software based on certain structural properties. The mapping of extremities and repellers is determined jointly by GC and their local preference.
We then present an efficient (O(N3 + N2B), for N nodes and B bins per node) heuristic for extended partitioning, called MIBS, that alternately uses GCLP and an implementation-bin selection procedure. The implementation-bin selection procedure chooses, for a node with already determined mapping, an implementation bin that maximizes the area-reduction gradient of as-yet unmapped nodes. Solutions generated by both heuristics are shown to be reasonably close to optimal. Extended partitioning generates considerably smaller overall hardware as compared to binary partitioning.