Hitting Diamonds and Growing Cacti

Hitting forbidden minors: Approximation and Kernelization

We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any graph from the family F of forbidden minors. We obtain a number of algorithmic results on the F-deletion problem when F contains a planar graph. We give (1) a linear vertex kernel on graphs excluding $t$-claw $K_{1,t}$, the star with $t$ leves, as an induced subgraph, where $t$ is a fixed integer. (2) an approximation algorithm achieving an approximation rati…

An Improved Deterministic Parameterized Algorithm for Cactus Vertex Deletion

A cactus is a connected graph that does not contain $K_4 - e$ as a minor. Given a graph $G = (V, E)$ and integer $k \ge 0$, Cactus Vertex Deletion (also known as Diamond Hitting Set) is the problem of deciding whether $G$ has a vertex set of size at most $k$ whose removal leaves a forest of cacti. The current best deterministic parameterized algorithm for this problem was due to Bonnet et al. [WG 2016], which runs in time $26^kn^{O(1)}$, where $n$ is the number of vertices of $G$. In this paper, we design a deterministic algorithm for Cactus Vertex Deletion, which runs in time $17.64^kn^{O(1)}…

几何命中集问题的线约束圆盘情形及相关问题

Geometric Hitting Set for Line-Constrained Disks and Related Problems

本文针对圆心共线的圆盘集合，提出高效算法求解加权命中集问题，单位圆盘及 $L_\infty$/$L_1$ 度量下时间更优，并将技术推广至半平面情形，将复杂度从 $O(n^6)$ 降至 $O(n^4\log n)$。

加权 Bond Cover 的常数因子近似算法

A Constant-factor Approximation for Weighted Bond Cover

本文研究无 $\theta_c$ 子式图上的加权顶点删除问题，等价于 Weighted $c$-Bond Cover，并借助结构定理与原始-对偶方法给出首个常数因子近似算法。