时态有向无环图路径覆盖的算法与复杂度：Dilworth定理何时是动态的？

DAG 覆盖：Steiner 点效应

DAG Covers for Structured Graphs: The Steiner Point Effect

研究了Steiner DAG覆盖，针对平面有向图和低树宽图，提出具有特定伸缩因子和额外边数的DAG覆盖方法，揭示了Steiner与非Steiner覆盖之间的显著差异。

Sparsifying, Shrinking and Splicing for Minimum Path Cover in Parameterized Linear Time

A minimum path cover (MPC) of a directed acyclic graph (DAG) $G = (V,E)$ is a minimum-size set of paths that together cover all the vertices of the DAG. Computing an MPC is a basic polynomial problem, dating back to Dilworth's and Fulkerson's results in the 1950s. Since the size $k$ of an MPC (also known as the width) can be small in practical applications, research has also studied algorithms whose complexity is parameterized on $k$. We obtain two new MPC parameterized algorithms for DAGs running in time $O(k^2|V|\log{|V|} + |E|)$ and $O(k^3|V| + |E|)$. We also obtain a parallel algorithm run…

Verification and search algorithms for causal DAGs

We study two problems related to recovering causal graphs from interventional data: (i) $\textit{verification}$, where the task is to check if a purported causal graph is correct, and (ii) $\textit{search}$, where the task is to recover the correct causal graph. For both, we wish to minimize the number of interventions performed. For the first problem, we give a characterization of a minimal sized set of atomic interventions that is necessary and sufficient to check the correctness of a claimed causal graph. Our characterization uses the notion of $\textit{covered edges}$, which enables us to …

因果DAG的子集验证与搜索算法

Subset verification and search algorithms for causal DAGs

本文研究识别学习目标边因果关系所需最小干预集的问题，提出子集验证的高效算法并扩展至复杂干预设定，同时证明子集搜索问题在最坏情况下的近似比下界及干预因果图的结构性质。

参数化路径划分

Parameterizing Path Partitions

研究将图顶点集划分为路径的PP、IPP和SPP问题的算法复杂度，证明了多种图类上的困难性，并基于邻域多样性、顶点覆盖和对偶参数给出了FPT算法。

基于彩色边 pebbling 的有向无环图（DAG）中紧凑路径表示

Compact Path Representation in DAGs via Colored Edge Pebbling

本文提出以拓扑为中心的彩色边 pebbling 框架，解决变异图紧凑表示问题，最小规模 pebbling 可多项式求解，饱和 pebbling 为 NP 难但可归约为集合覆盖，能实现更快查询。

最小路径覆盖：参数化的力量

Minimum Path Cover: The Power of Parameterization

本文实现了包括参数化方法在内的最先进MPC算法，并提出传递边稀疏化预处理启发式，实验表明其在稠密随机DAG上可带来数个数量级的性能提升。

路径覆盖、哈密顿性与独立数：从FPT视角看

Path Cover, Hamiltonicity, and Independence Number: An FPT Perspective

本文从FPT视角扩展了Gallai-Milgram定理，提出一个算法可高效判断图的路径覆盖并证明其最优性或独立集性质。

Covering Pairs in Directed Acyclic Graphs

The Minimum Path Cover problem on directed acyclic graphs (DAGs) is a classical problem that provides a clear and simple mathematical formulation for several applications in different areas and that has an efficient algorithmic solution. In this paper, we study the computational complexity of two constrained variants of Minimum Path Cover motivated by the recent introduction of next-generation sequencing technologies in bioinformatics. The first problem (MinPCRP), given a DAG and a set of pairs of vertices, asks for a minimum cardinality set of paths "covering" all the vertices such that both …

顶点覆盖数为二时时间路径覆盖的紧致困难性

Tight Hardness for Temporal Path Covers at Vertex-Cover Number Two

本文通过从相异数值匹配归约，证明顶点覆盖数为二时时间路径覆盖与时间不相交路径覆盖均为NP完全，并给出时间有向星上基于跨度参数的XP算法。

Safety and Completeness in Flow Decompositions for RNA Assembly

Decomposing a network flow into weighted paths has numerous applications. Some applications require any decomposition that is optimal w.r.t. some property such as number of paths, robustness, or length. Many bioinformatic applications require a specific decomposition where the paths correspond to some underlying data that generated the flow. For real inputs, no optimization criteria guarantees to uniquely identify the correct decomposition. Therefore, we propose to report safe paths, i.e., subpaths of at least one path in every flow decomposition. Ma, Zheng, and Kingsford [WABI 2020] addressed…

有向（无环）图上测地集的结构参数化

Structural parameterizations of Geodetic Set on directed (acyclic) graphs

研究有向测地集问题的结构参数化，通过顶点覆盖数和可达直径等参数设计核化算法，并证明条件最优性。