arXiv · 1704.02242
We show the hardness of the geodetic hull number for chordal graphs.
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Stéphane Bessy, Mitre C. Dourado, Lucia D. Penso, Dieter Rautenbach. 2017-03-28. The Geodetic Hull Number is Hard for Chordal Graphs. https://arxiv.org/abs/1704.02242
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We consider the two-machine open-shop scheduling problem in which one machine is unavailable during a fixed interval. We study the resumable setting: an operation interrupted by the unavailability interval may resume, without penalty, when the machine becomes available. The objective is to minimize the makespan. Although the problem is NP-hard and several approximation algorithms are known, whether it admits a fully polynomial-time approximation scheme (FPTAS) has remained open for two decades. We resolve this question affirmatively by giving the first FPTAS, thereby strengthening the previously known polynomial-time approximation scheme (PTAS). As an intermediate result, we develop a new pseudo-polynomial dynamic program with seven state dimensions, improving on the ten-dimensional formulation in the literature.
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