핵심 개념
Polyamorous Scheduling is a challenging optimization problem for complex social groups, aiming to minimize waiting times between meetings while considering different relationship needs.
초록
The content introduces the Polyamorous Scheduling problem, discussing its complexity, NP-hardness, and approximation algorithms. It defines decision and optimization versions, highlighting the importance of density thresholds. The construction of the polycule involves gadgets for variables, duplication, clauses, sorting, and tensioning. The True Clock and Colour Slots are used to ensure slot-respecting schedules. The duplication of variables and constants is achieved through 3-Duplicators, ensuring accurate reproduction of input edges.
통계
Polyamorous Scheduling is NP-hard.
The problem has a density threshold similar to Pinwheel Scheduling.
An O(log n)-approximation algorithm exists.
인용구
"Polyamorous Scheduling is a natural generalization of Pinwheel Scheduling."
"Our work contributes the first nontrivial hardness-of-approximation reduction for any periodic scheduling problem."