Scheduling Unrelated Machines of Few Different Types
Vincenzo Bonifaci, Andreas Wiese

TL;DR
This paper develops polynomial time approximation schemes for scheduling jobs on unrelated machines with a limited number of machine types, improving upon previous results for specific machine configurations.
Contribution
It introduces PTASs for minimizing makespan and L_p-norm in a setting with a fixed number of machine types, generalizing prior work.
Findings
PTASs for multidimensional jobs with fixed dimensions
PTASs for minimizing L_p-norm
Generalizes existing PTASs for related machine models
Abstract
A very well-known machine model in scheduling allows the machines to be unrelated, modelling jobs that might have different characteristics on each machine. Due to its generality, many optimization problems of this form are very difficult to tackle and typically APX-hard. However, in many applications the number of different types of machines, such as processor cores, GPUs, etc. is very limited. In this paper, we address this point and study the assignment of jobs to unrelated machines in the case that each machine belongs to one of a fixed number of types and the machines of each type are identical. We present polynomial time approximation schemes (PTASs) for minimizing the makespan for multidimensional jobs with a fixed number of dimensions and for minimizing the L_p-norm. In particular, our results subsume and generalize the existing PTASs for a constant number of unrelated machines…
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Taxonomy
TopicsOptimization and Search Problems · Scheduling and Optimization Algorithms · Complexity and Algorithms in Graphs
