Design and analysis of heuristic functions for static task distribution

Two static task-scheduling algorithms are introduced. The first algorithm, called heavy-node first (HNF), is very simple and is based on a local analysis of program graph nodes at each level. The second method, called Weighted Length (WL), considers a more global view of the program graph, taking into account the relationship among the nodes at different levels. The two schemes are compared against the classical critical-path method (CPM). For a given directed acyclic graph of n nodes representing a program, it is shown that HNF requires O(n log n) steps, while WL and CPM require O(n²) steps to accomplish the allocation. The nontrivial worst-case performance of the three algorithms is analytically evaluated, and their average-case performance is evaluated through a simulation study. It is shown that the performance of the three algorithms is almost the same with respect to execution time and processor idle time. Therefore, taking into account the time complexity of the task distribution itself, it is concluded that a simple and fast heuristic algorithm such as HNF will achieve reasonable performance