Tree-based scheduling algorithm for control-dominated circuits

Abstract

Scheduling algorithms for control dominated applications have not been widely published. Path-based scheduling was the first attempt to tackle this problem. This approach works well on the benchmark examples. However, it imposes a restriction on the execution order of the operations before scheduling. We alleviate this restriction by representing all execution paths by a tree. Tree representation not only inherits all the advantages of the path representation, but also releases the execution order constraint. A two phase algorithm is proposed to solve the scheduling problem on the tree representation. In the first phase, a partitioning algorithm is performed on the tree in a topdown manner in order to optimally execute every path. In the second phase, the corresponding state transition graph is constructed in a bottom-up manner in order to minimize the total number of states as well as the control logic. By utilizing node unification, the complexity of the algorithm can be restricted to O(pbn2), where p is the number of paths, b is the number of blocks and n is the number of operations. We tested the algorithm on a set of benchmarks and achieved on the number of states as compared with previous algorithms.