Scheduling with Communication Delays via LP Hierarchies and Clustering

Explore a groundbreaking approach to scheduling jobs with precedence constraints and communication delays in this 30-minute lecture by Thomas Rothvoß at the Hausdorff Center for Mathematics. Delve into the P | prec,c | Cmax problem, a challenging model in scheduling theory with significant real-world applications. Learn about the novel polynomial-time O(log c · log m)-approximation algorithm developed to address this long-standing issue. Discover how the algorithm combines Sherali-Adams lift of linear programming relaxation with randomized clustering of semimetric spaces. Follow the presentation from the introduction of the problem through the main result, key scheduling routines, and algorithm design. Gain insights into the reduction process, metric space clustering, and the intricacies of the scheduling algorithm. Conclude with an exploration of potential extensions and open problems in this cutting-edge area of scheduling theory.

Intro
What is known
Main result
Reduction to Pooprec, p = 1, c-interval Modification of original problem with
How to design a strong LP?
Clustering of metric spaces
The key scheduling routine
Two simple lemmas
The actual scheduling algorithm
The actual scheduling algo (2)
Extensions and open problems