AI 中文总结
本文研究几何图凸性下的最大权凸问题，将最大子序列问题推广到层状树，提出适用于真区间图的线性算法和区间图的二次算法，改进了现有成果。
AI 中文摘要
对于给定的、配备顶点权函数（取值为整数）的图G上的几何图凸性，最大权凸集问题旨在确定具有最大权值（S中顶点权值之和）的凸集S。尽管该问题在一般情况下是NP完全的，但在特定情形下仍为多项式时间可解。在综述已有成果后，本文的主要贡献是将最大子序列问题推广到层状树，进而推导得到适用于真区间图的线性算法和适用于区间图的二次算法，二者均改进了现有技术水平。
英文摘要
For a given geometric graph-convexity on a graph $G$ equipped with a weight function on the vertices with value in $\mathbb{Z}$, the Max Weight Convex Set problem consists in determining the convex set $S$ with maximum weight (sum of the weight of the vertices in $S$). Although the problem is NP-complete in general, it remains polynomial for particular cases. After a survey of known results, our main contribution uses a generalisation of the maximum subsequence problem to laminar trees. Then we derive a linear algorithm for proper interval graphs and a quadratic one for interval graphs. Both improve the state of the art.
CommentsFull version of the extended abstract presented at conference COSI 2025, Bejaia, Algeria
