Abstract
The problem of scheduling a partially ordered set of unit length tasks on m identical processors is known to be NP-complete. There are efficient algorithms for only a few special cases of this problem. The authors analyzed the effect of the structure of the precedence graph and the availability of the processors on the construction of optimal schedules. They proved that to find an optimal schedule it suffices to consider at each step only initial tasks which belong to the m - l highest components of the precedence graph. Their method leads to polynomial algorithms if the number of processors is fixed and the precedence graph has a certain form. In particular, if the precendence graph contains only intrees and outtrees, this result leads to linear algorithms for finding an optimal schedule on two or three processors.
Original language | English |
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Pages (from-to) | 638-657 |
Number of pages | 20 |
Journal | SIAM Journal on Computing |
Volume | 14 |
Issue number | 3 |
DOIs | |
State | Published - 1985 |