坏三角形横截的简单算法及其在相关聚类中的应用

磁盘图上环击中问题的更快算法

Faster Algorithms for Cycle Hitting Problems on Disk Graphs

针对磁盘交图的三角形击中集、反馈顶点集、奇环横贯三类环击中问题，提出无需几何表示的亚指数参数化算法，给出几何表示时效率更高，改进了已有算法的时间复杂度。

Known Algorithms on Graphs of Bounded Treewidth are Probably Optimal

We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot be solved in (2-ε)^{n}m^{O(1)} time, we show that for any e > 0; {\sc Independent Set} cannot be solved in (2-e)^{tw(G)}|V(G)|^{O(1)} time, {\sc Dominating Set} cannot be solved in (3-e)^{tw(G)}|V(G)|^{O(1)} time, {\sc Max Cut} cannot be solved in (2-e)^{tw(G)}|V(G)|^{O(1)} time, {\sc Odd Cycle Transversal} cannot be solved in (3-e)^{tw(G)}|V(G)|^…

Beyond the Lovasz Local Lemma: Point to Set Correlations and Their Algorithmic Applications

Following the groundbreaking algorithm of Moser and Tardos for the Lovasz Local Lemma (LLL), there has been a plethora of results analyzing local search algorithms for various constraint satisfaction problems. The algorithms considered fall into two broad categories: resampling algorithms, analyzed via different algorithmic LLL conditions; and backtracking algorithms, analyzed via entropy compression arguments. This paper introduces a new convergence condition that seamlessly handles resampling, backtracking, and hybrid algorithms, i.e., algorithms that perform both resampling and backtracking…

基于次二次网格子式性质的几何图次指数算法：局部半径的作用

Subexponential algorithms in geometric graphs via the subquadratic grid minor property: the role of local radius

本文研究几何图中三类环击中问题的次指数算法，在ETH假设下证明部分瘦对象图类的下界，并给出带限制的线段接触图、d-DIR图的对应次指数参数化算法。

Structural Parameterization for Graph Deletion Problems over Data Streams

The study of parameterized streaming complexity on graph problems was initiated by Fafianie et al. (MFCS'14) and Chitnis et al. (SODA'15 and SODA'16). Simply put, the main goal is to design streaming algorithms for parameterized problems such that $O\left(f(k)\log^{O(1)}n\right)$ space is enough, where $f$ is an arbitrary computable function depending only on the parameter $k$. However, in the past few years, very few positive results have been established. Most of the graph problems that do have streaming algorithms of the above nature are ones where localized checking is required, like Verte…

几何最大覆盖的近似算法

Approximation Algorithms for Geometric Maximum Coverage

本文研究几何最大覆盖问题，提出多种近似算法，针对不同几何对象族改进了近似因子与运行时间，并给出了对应的难度下界结果。

有界树宽图上的基本问题：难度的真正来源

Fundamental Problems on Bounded-Treewidth Graphs: The Real Source of Hardness

本文证明了在更受限的图结构（即连接到常数大小组件的顶点块）上，多个基本算法问题（如独立集、顶点覆盖等）在SETH或SCC假设下仍具有与一般树分解相同的指数下界难度。