Polyamorous Scheduling: Optimizing Complex Social Group Meetings

Core Concepts

Polyamorous Scheduling is a challenging optimization problem for complex social groups, aiming to minimize waiting times between meetings while considering different relationship needs.

Abstract

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.

Stats

Polyamorous Scheduling is NP-hard.
The problem has a density threshold similar to Pinwheel Scheduling.
An O(log n)-approximation algorithm exists.

Quotes

"Polyamorous Scheduling is a natural generalization of Pinwheel Scheduling."
"Our work contributes the first nontrivial hardness-of-approximation reduction for any periodic scheduling problem."

Key Insights Distilled From

Polyamorous Scheduling

by Lesz... at arxiv.org 03-04-2024

https://arxiv.org/pdf/2403.00465.pdf

Deeper Inquiries

질문 1

다각형 밀도 임계값은 다각형 스케줄링의 실행 가능성에 어떤 영향을 미치나요?
Answer 1 here

질문 2

다각형 스케줄링의 NP-완전성이 현실 세계 스케줄링 문제에 어떤 영향을 미치나요?
Answer 2 here

질문 3

밀도 개념을 다른 복잡한 사회적 시나리오에서 스케줄링을 최적화하는 데 어떻게 적용할 수 있나요?
Answer 3 here