Speaker:

Tian Bai (University of Bergen)

Time:

• 20:00-21:00 Beijing Time
• December 12, 2025 (Friday)

Venue:

518, Research Building 4

Abstract:

In the Subset Feedback Arc Set in Tournaments (Subset-FAST) problem, we are given as input a tournament T with a vertex set V(T) and an arc set A(T), along with a terminal set S \subseteq V(T), and an integer k. The objective is to determine whether there exists a set F \subseteq A(T) with |F| \leq k such that the resulting graph T – F contains no cycle that includes any vertex of S. When S = V(T), this is the classic Feedback Arc Set in Tournaments (FAST) problem. We obtain the first polynomial kernel for this problem parameterized by the solution size. More precisely, we obtain an algorithm that, given an input instance (T, S, k), produces an equivalent instance (T’,S’,k’) with k’ \leq k and |V(T’)|=O(k^2).

It was known that FAST admits a simple quadratic vertex kernel and a non-trivial linear vertex kernel. However, no such kernel was previously known for Subset-FAST. Our kernel employs variants of the most well-known reduction rules for FAST and introduces two new reduction rules to identify irrelevant vertices. As a result of our kernelization, we also obtain the first sub-exponential time FPT algorithm for Subset-FAST.

Speaker Bio:

Tian Bai is currently a postdoctoral researcher at the University of Bergen (UiB). Previously, he worked as a postdoctoral researcher at the University of Hong Kong (HKU) in the ALGO Lab. He received his Ph.D. from the University of Electronic Science and Technology of China (UESTC) as a member of the Algorithms and Logic Group, under the supervision of Prof. Mingyu Xiao.
His research is centered on the design and analysis of algorithms, particularly exact and parameterized algorithms for graph problems. He also has a strong interest in algorithmic game theory.