Mixed Integer Optimization for Layout Arrangement

Arranging geometric entities in a two-dimensional layout is a common task for most information visualization applications, where existing algorithms typically rely on heuristics to position shapes such as boxes or discs in a visual space. Geometric entities are used as a visual resource to convey information contained in data such as textual documents or videos and the challenge is to place objects with similar content close to each other while still avoiding overlap. In this work we present a novel mechanism to arrange rectangular boxes in a two-dimensional layout which copes with the two properties above, that is, it keeps similar object close and prevents overlap. In contrast to heuristic techniques, our approach relies on mixed integer quadratic programming, resulting in well structured arrangements which can be easily be tuned to take different forms. We show the effectiveness of our methodology through a comprehensive set of comparisons against state-of-art methods. Moreover, we employ the proposed technique in video data visualization, attesting its usefulness in a practical application.