In this paper we formally introduce the distinction between strong and weak
precedence relation in scheduling for the case of trees. We demonstrate th
at this distinction in precedence relation for trees (as demonstrated in ea
rlier work for chains) is a proper one in the sense that some problems are
solvable in polynomial time if weak tree relation is assumed and are NP-har
d in the case of strong tree relations. For some other problems, both weak
tree and strong tree relations are NP-hard, and for yet other problems both
weak and strong tree relations are polynomially solvable. Since the distin
ction between strong and weak tree precedence was not clearly recognized in
the past, this work establishes the existence of new problem categories in
scheduling. (C) 1999 Elsevier Science B.V. All rights reserved.