Beijing Institute of Mathematical Sciences and Applications

Song Cheng , Dawei Ding , Jinpeng Liu , Zhengwei Liu , Ziwen Liu

Jinguo Liu

Tuesday, May 20, 2025 2:00 PM - 3:00 PM

A3-2a-302

Zoom 230 432 7880 (BIMSA)

The branching algorithm is a fundamental technique for designing fast exponential-time algorithms to solve combinatorial optimization problems exactly. It divides the entire solution space into independent search branches using predetermined branching rules, and ignores the search on suboptimal branches to reduce the time complexity. The complexity of a branching algorithm is primarily determined by the branching rules it employs, which are often designed by human experts. In this paper, we show how to automate this process with a focus on the maximum independent set problem. The main contribution is an algorithm that efficiently generate optimal branching rules for a given sub-graph with tens of vertices. Its efficiency enables us to generate the branching rules on-the-fly, which is provably optimal and significantly reduces the number of branches compared to existing methods that rely on expert-designed branching rules. Numerical experiment on 3-regular graphs shows an average complexity of $O(1.0441^n)$ can be achieved, better than any previous methods.

Dr. Jinguo Liu is an assistant professor at Hong Kong University of Science and Technology (Guangzhou). He acquired his Ph.D. training in Prof. Qiang-Hua Wang's group at Nanjing University on condensed matter physics. After that, he has been a postdoc in Prof. Lei Wang's group at the Institute of Physics (CAS) for two years, a full-time consultant in QuEra computing for half a year, and a postdoc in Prof. Mikhail Lukin's group at Harvard University for two years. His research direction is diverse, while all his studies are about developing new and better algorithms for solving existing or new problems. He is a passionate open source scientific software developer and he has the superpower of speeding up code in his lab by two orders.