Semantic Word Cloud Representations: Hardness and Approximation Algorithms

We study a geometric representation problem, where we are given a set \(\mathcal B\) of axis-aligned rectangles (boxes) with fixed dimensions and a graph with vertex set \(\mathcal B\). The task is to place the rectangles without overlap such that two rectangles touch if the graph contains an edge between them. We call this problem Contact Representation of Word Networks (Crown). It formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. Here, we represent words by rectangles and semantic relationships by edges.

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