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Sinno Jialin Pan是南洋理工大学计算机科学与工程学院院长兼副教授，研究方向是迁移学习、数据挖掘、人工智能、机器学习。

### 热门内容

The quest of can machines think' and can machines do what human do' are quests that drive the development of artificial intelligence. Although recent artificial intelligence succeeds in many data intensive applications, it still lacks the ability of learning from limited exemplars and fast generalizing to new tasks. To tackle this problem, one has to turn to machine learning, which supports the scientific study of artificial intelligence. Particularly, a machine learning problem called Few-Shot Learning (FSL) targets at this case. It can rapidly generalize to new tasks of limited supervised experience by turning to prior knowledge, which mimics human's ability to acquire knowledge from few examples through generalization and analogy. It has been seen as a test-bed for real artificial intelligence, a way to reduce laborious data gathering and computationally costly training, and antidote for rare cases learning. With extensive works on FSL emerging, we give a comprehensive survey for it. We first give the formal definition for FSL. Then we point out the core issues of FSL, which turns the problem from "how to solve FSL" to "how to deal with the core issues". Accordingly, existing works from the birth of FSL to the most recent published ones are categorized in a unified taxonomy, with thorough discussion of the pros and cons for different categories. Finally, we envision possible future directions for FSL in terms of problem setup, techniques, applications and theory, hoping to provide insights to both beginners and experienced researchers.

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Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characterization results in well-known subclasses of chordal graphs such as interval graphs or split graphs. A typical example that behaves computationally different in subclasses of chordal graph is the \textsc{Subset Feedback Vertex Set} (SFVS) problem: given a graph $G=(V,E)$ and a set $S\subseteq V$, SFVS asks for a minimum set of vertices that intersects all cycles containing a vertex of $S$. SFVS is known to be polynomial-time solvable on interval graphs, whereas SFVS remains \NP-complete on split graphs and, consequently, on chordal graphs. Towards a better understanding of the complexity of SFVS on subclasses of chordal graphs, we exploit structural properties of a tree model in order to cope with the hardness of SFVS. Here we consider variants of the \emph{leafage} that measures the minimum number of leaves in a tree model. We show that SFVS can be solved in polynomial time for every chordal graph with bounded leafage. In particular, given a chordal graph on $n$ vertices with leafage $\ell$, we provide an algorithm for SFVS with running time $n^{O(\ell)}$. Pushing further our positive result, it is natural to consider a slight generalization of leafage, the \emph{vertex leafage}, which measures the smallest number among the maximum number of leaves of all subtrees in a tree model. However, we show that it is unlikely to obtain a similar result, as we prove that SFVS remains \NP-complete on undirected path graphs, i.e., graphs having vertex leafage at most two. Moreover, we strengthen previously-known polynomial-time algorithm for SFVS on directed path graphs that form a proper subclass of undirected path graphs and graphs of mim-width one.

### 最新论文

Chordal graphs are characterized as the intersection graphs of subtrees in a tree and such a representation is known as the tree model. Restricting the characterization results in well-known subclasses of chordal graphs such as interval graphs or split graphs. A typical example that behaves computationally different in subclasses of chordal graph is the \textsc{Subset Feedback Vertex Set} (SFVS) problem: given a graph $G=(V,E)$ and a set $S\subseteq V$, SFVS asks for a minimum set of vertices that intersects all cycles containing a vertex of $S$. SFVS is known to be polynomial-time solvable on interval graphs, whereas SFVS remains \NP-complete on split graphs and, consequently, on chordal graphs. Towards a better understanding of the complexity of SFVS on subclasses of chordal graphs, we exploit structural properties of a tree model in order to cope with the hardness of SFVS. Here we consider variants of the \emph{leafage} that measures the minimum number of leaves in a tree model. We show that SFVS can be solved in polynomial time for every chordal graph with bounded leafage. In particular, given a chordal graph on $n$ vertices with leafage $\ell$, we provide an algorithm for SFVS with running time $n^{O(\ell)}$. Pushing further our positive result, it is natural to consider a slight generalization of leafage, the \emph{vertex leafage}, which measures the smallest number among the maximum number of leaves of all subtrees in a tree model. However, we show that it is unlikely to obtain a similar result, as we prove that SFVS remains \NP-complete on undirected path graphs, i.e., graphs having vertex leafage at most two. Moreover, we strengthen previously-known polynomial-time algorithm for SFVS on directed path graphs that form a proper subclass of undirected path graphs and graphs of mim-width one.

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