We review the literature on automatic document formatting with an emphasis on recent work in the field. One common way to frame document formatting is as a constrained optimization problem where decision variables encode element placement, constraints enforce required geometric relationships, and the objective function measures layout quality. We present existing research using this framework, describing the kind of optimization problem being solved and the basic optimization techniques used to solve it. Our review focuses on the formatting of primarily textual documents, including both micro-and macro-typographic concerns. We also cover techniques for automatic table layout. Related problems such as widget and diagram layout, as well as temporal layout issues that arise in multimedia documents are outside the scope of this review.

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In many text-processing applications, we would like shapes that expand (or shrink) in size to fit their textual content. We address how to efficiently compute the minimum size for such text shapes. A variant of this problem is to take a fixed shape and determine the maximal size font that will still allow the content to fit into it. Our approach is to model the problem as a constrained optimisation problem with a single variable that controls the geometry of the text shape. We use a variant of secant search to determine the minimum area for the shape, guided by the area of the text. We represent the shape by regions that are composed of trapezoids whose coordinates are a linear function of the unknown variable. This allows us to use a novel linear time algorithm (based on computing Minkowski difference) that takes a trapezoid list and text height and determines the region in which a line of text of that height and some minimum width can start and still remain inside the shape.