hardness

Multilevel Planarity

In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\ell : V \rightarrow \mathcal P(\mathbb Z)$ be a function …

Semantic Word Cloud Representations: Hardness and Approximation Algorithms

We study a geometric representation problem, where we are given a set B of axis-aligned rectangles (boxes) with fixed dimensions and a graph with vertex set B. The task is to place the rectangles without overlap such that two rectangles touch if the …