From @baldur, this is the best article I have read explaining the differences between EU and US tech companies' view of competition and antitrust, and in particular why Apple has got its relationship with the EU horribly, horribly wrong.
baldurbjarnason.com/2024/facin…
Facing reality, whether it's about Apple or the EU, is a core requirement for good management
You can’t be a good manager or executive, in any industry, if you operate in constant denial of the facts on the ground.www.baldurbjarnason.com
![Preview of arXiv:2403.00465 (cs)
[Submitted on 1 Mar 2024]
Polyamorous Scheduling
Authors: Leszek Gasieniec, Benjamin Smith, Sebastian Wild
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the underlying optimisation problem: Polyamorous Scheduling. In Polyamorous Scheduling, we are given an edge-weighted graph and try to find a periodic schedule of matchings in this graph such that the maximal weighted waiting time between consecutive occurrences of the same edge is minimised. We show that the problem is NP-hard and that there is no efficient approximation algorithm with a better ratio than 13/12 unless P = NP. On the positive side, we obtain an O(log n) -approximation algorithm. We also define a generalisation of density from the Pinwheel Scheduling Problem, "poly density", and ask whether there exists a poly density threshold similar to the 5/6-density threshold for Pinwheel Scheduling [Kawamura, STOC 2024]. Polyamorous Scheduling is a natural generalisation of Pinwheel Scheduling with respect to its optimisation variant, Bamboo Garden Trimming. Our work contributes the first nontrivial hardness-of-approximation reduction for any periodic scheduling problem, and opens up numerous avenues for further study of Polyamorous Scheduling.](https://fedi.ml/photo/preview/640/525987 "Preview of arXiv:2403.00465 (cs)
[Submitted on 1 Mar 2024]
Polyamorous Scheduling
Authors: Leszek Gasieniec, Benjamin Smith, Sebastian Wild
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the underlying optimisation problem: Polyamorous Scheduling. In Polyamorous Scheduling, we are given an edge-weighted graph and try to find a periodic schedule of matchings in this graph such that the maximal weighted waiting time between consecutive occurrences of the same edge is minimised. We show that the problem is NP-hard and that there is no efficient approximation algorithm with a better ratio than 13/12 unless P = NP. On the positive side, we obtain an O(log n) -approximation algorithm. We also define a generalisation of density from the Pinwheel Scheduling Problem, \"poly density\", and ask whether there exists a poly density threshold similar to the 5/6-density threshold for Pinwheel Scheduling [Kawamura, STOC 2024]. Polyamorous Scheduling is a natural generalisation of Pinwheel Scheduling with respect to its optimisation variant, Bamboo Garden Trimming. Our work contributes the first nontrivial hardness-of-approximation reduction for any periodic scheduling problem, and opens up numerous avenues for further study of Polyamorous Scheduling.")
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