A branch-and-bound-with-underestimates algorithm for the task assignment problem with precedence constraint

The problem of finding an optimal assignment of task modules with a precedence relationship in a distributed computing system is considered. The objective of task assignment is to minimize the task turnaround time. The problem is known to be NP-complete for more than three processors. To solve the problem, a well-known state-space reduction technique, branch-and-bound-with-underestimates, is applied, and two underestimate functions are defined. Through experiments, their effectiveness is shown by comparing the proposed algorithm with both Wang and Tsai´s (1988) algorithm and the A* algorithm with h( x)=0