Cs 598csc: Approximation Algorithms 1 Multiprocessor Scheduling with Precedence Constraints 1.1 Problem Description
نویسنده
چکیده
In the Multiprocessor Scheduling with Precedence Constraints, we are given n-jobs denoted by {J1, J2, · · · , Jn}, the associated processing time pi, i = 1, · · · , n and m identical machines to which jobs are needed to be assigned. In addition, jobs have precedence constraints between them, and we use notation Jj ≺ Ji to imply that Ji cannot be done before completing Jj (the smaller runs earlier). A directed acyclic graph (DAG) can encode these constraints. The goal of this problem is to minimize the makespan. Denote the start time and completion time of Jj by sj and cj , respectively. Then job Jj occupies time slots from sj+1 to cj . The goal is thus minmaxj cj . This problem is also strongly NP-hard as the scheduling problem without constraints.
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