Abstract:
Online load balancing for heterogeneous machines aims to minimize the makespan (maximum machine workload) by scheduling arriving jobs with varying sizes on different machines. In the adversarial setting, where an adversary chooses not only the collection of job sizes but also their arrival order, the problem is well-understood and the optimal competitive ratio is known to be $\Theta(\log m)$ where $m$ is the number of machines. In the more realistic random arrival order model, the understanding is limited. Previously, the best lower bound on the competitive ratio was only $\Omega(\log \log m)$.
We significantly improve this bound by showing an $\Omega( \sqrt {\log m})$ lower bound, even for the restricted case where each job has a unit size on two machines and infinite size on the others. On the positive side, we propose an $O(\log m/\log \log m)$-competitive algorithm, demonstrating that better performance is possible in the random arrival model.
This is based on a joint work with Sungjin Im, Ravi Kumar, Aditya Petty and Manish Purohit.
About the speaker:
Shi Li is a professor in the department of computer science and technology at Nanjing University. He completed his undergraduate studies at Tsinghua University in the Department of Computer Science and Technology, where he was a member of Andrew Yao's esteemed theoretical computer science pilot class. He earned his Ph.D. from Princeton University and later served as an assistant research professor at the Toyota Technological Institute in Chicago. In September 2015, he joined the faculty at the State University of New York at Buffalo as an assistant professor and was promoted to associate professor in September 2020. He joined Nanjing University in early 2023. His research is on theoretical computer science, and more specifically, the design of efficient algorithms with provable guarantees under different computation models.