Problem
Research questions and friction points this paper is trying to address.
geometric graph-convexity
maximum weight convex set
interval graphs
On the maximum weight convex problem for some geometric graph-convexities
🤖 AI Summary
该研究解决了最大权重凸集问题，通过将最大子序列问题推广到层状树，提出了针对适当区间图的线性算法和区间图的二次算法。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
maximum subsequence problem
laminar trees
proper interval graphs
interval graphs
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2024-03-01arXiv.orgCitations: 14
