Abstract
In the integrated network design and scheduling problem (INDS-P), we are asked to repair edges in a graph by using parallel machines so that the performance of the network is recovered by a certain level, and the objective is to minimize the makespan required to finish repairing edges. The main aim of this paper is to show that polynomial-time approximation schemes exist for some class of the problem (INDS-P), including the problems associated with minimum spanning tree, shortest path, maximum flow with unit capacity, and maximum-weight matching.
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Notes
- 1.
This problem is denoted as “\(Pm | \beta | C_\textrm{max}\)-Threshold” in [15].
- 2.
By guessing we mean trying all possible assignments by enumeration.
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Saito, Y., Shioura, A. (2022). Polynomial-Time Approximation Schemes for a Class of Integrated Network Design and Scheduling Problems with Parallel Identical Machines. In: Ljubić, I., Barahona, F., Dey, S.S., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2022. Lecture Notes in Computer Science, vol 13526. Springer, Cham. https://doi.org/10.1007/978-3-031-18530-4_24
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