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arXiv · 2608.30728

On the maximum weight convex problem for some geometric graph-convexities

Fariza Aklouche·Pierre Bergé·Michel Habib
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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.

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Fariza Aklouche, Pierre Bergé, Michel Habib. 2026-08-31. On the maximum weight convex problem for some geometric graph-convexities. https://arxiv.org/abs/2608.30728

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