Fast Makespan Minimization via Short ILPs
🤖 AI Summary
This study addresses the problem of minimizing makespan on a fixed number of parallel machines. It introduces, for the first time, an efficient approach based on short integer linear programming (Short ILP) to design a quasipolynomial-time algorithm. When the maximum processing time $p_{\text{max}}$ is moderate, the algorithm achieves a running time of either $\widetilde{O}(p_{\text{max}}^{O(1)} + n)$ or $\widetilde{O}(p_{\text{max}}^{O(1)} \cdot n)$, significantly outperforming existing methods. This work not only extends the applicability of Short ILP techniques to scheduling problems but also provides a more efficient solution pathway for instances of moderate scale.
Application Category
📝 Abstract
Short integer linear programs are programs with a relatively small number of constraints. We show how recent improvements on the running-times of solvers for such programs can be used to obtain fast pseudo-polynomial time algorithms for makespan minimization on a fixed number of parallel machines, and other related variants. The running times of our algorithms are all of the form $\widetilde{O}(p^{O(1)}_{\max}+n)$ or $\widetilde{O}(p^{O(1)}_{\max} \cdot n)$, where $p_{\max}$ is the maximum processing time in the input. These improve upon the time complexity of previously known algorithms for moderate values of $p_{\max}$.
Problem
Research questions and friction points this paper is trying to address.
makespan minimization
parallel machines
short integer linear programs
pseudo-polynomial time
Innovation
Methods, ideas, or system contributions that make the work stand out.
Short ILPs
Makespan Minimization
Pseudo-polynomial Time
Parallel Machines
Integer Linear Programming
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