TY - JOUR
T1 - Scheduling precedence graphs of bounded height
AU - Dolev, Danny
AU - Warmuth, Manfred K.
PY - 1984/3
Y1 - 1984/3
N2 - The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384-393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22-35; D. Dolev and M. K. Warmuth, "Scheduling Flat Graphs," IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.
AB - The existence of a schedule for a partially ordered set of unit length tasks on m identical processors is known to be NP-complete (J. D. Ullman, NP-complete scheduling problems, J. Comput. System Sci., 10 (1975), 384-393). The problem remains NP-complete even if we restrict the precedence graph to be of height bounded by a constant. (J. K. Lenkstra and A. H. G. Rinnooy Kan, Complexity of scheduling under precedence constraints, Operations Res., 26 (1978), 22-35; D. Dolev and M. K. Warmuth, "Scheduling Flat Graphs," IBM Research Report RJ 3398, 1982). In these NP-completeness proofs the upper bound on the number of available processors varies with the problem instance. We present a polynomial algorithm for the case where the upper bound on the number of available processors and the height of the precedence graph are both constants.
UR - http://www.scopus.com/inward/record.url?scp=0007441750&partnerID=8YFLogxK
U2 - 10.1016/0196-6774(84)90039-7
DO - 10.1016/0196-6774(84)90039-7
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AN - SCOPUS:0007441750
SN - 0196-6774
VL - 5
SP - 48
EP - 59
JO - Journal of Algorithms
JF - Journal of Algorithms
IS - 1
ER -