On the approximability of average completion time scheduling under precedence constraints
نویسندگان
چکیده
منابع مشابه
On the Approximability of Average Completion Time Scheduling under Precedence Constraints
We consider the scheduling problem of minimizing the average weighted job completion time on a single machine under precedence constraints. We show that this problem with arbitrary job weights, the special case of the problem where all job weights are one, and several other special cases of the problem all have the same approximability threshold with respect to polynomial time approximation alg...
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We show that minimizing the average job completion time on unrelated machines isAPX -hard if preemption of jobs is allowed. This provides one of the last missing pieces in the complexity classification of machine scheduling with (weighted) sum of completion times objective. The proof is based on a mixed integer linear program. This means that verification of the reduction is partly done by an I...
متن کاملOn the Approximability of Single-Machine Scheduling with Precedence Constraints
We consider the single-machine scheduling problem to minimize the weighted sum of completion times under precedence constraints. In a series of recent papers, it was established that this scheduling problem is a special case of minimum weighted vertex cover. In this paper, we show that the vertex cover graph associated with the scheduling problem is exactly the graph of incomparable pairs defin...
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In many scheduling situations, it is important to consider non-linear functions of job completions times in the objective. This was already recognized by Smith (1956). Recently, the theory community has begun a thorough study of the resulting problems, mostly on single-machine instances for which all permutations of jobs are feasible. However, a typical feature of many scheduling problems is th...
متن کاملTwo-machine Scheduling under Arbitrary Precedence Constraints
Suppose jobs, in the Johnson's two-machine n-job flow-shop scheduling problem, are grouped into disjoint subsets within which a job order that may not be preempted is specified. Furthermore, suppose that a precedence relation between these subsets is given such that the processing of a subset must be completed, on each machine, before the processing of another subset begins on the machine. This...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2003
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(02)00427-4