Knuth-Plass Revisited: Flexible Line-Breaking for Automatic Document Layout

There is an inherent flexibility in typesetting a block of text. Traditionally, line breaks would be manually chosen at strategic points in such a way as to minimize the amount of whitespace in each line. Hyphenation would only be used as a last resort. Knuth and Plass automated this optimization procedure, which has been used in various typesetting systems and DTP applications ever since. However, an optimal solution for the line-breaking problem does not necessarily lead us to an optimal document layout on the whole. The flexibility of choosing line breaks enables us, in many cases, to adjust the height of a paragraph by changing the number of lines, without having to make adjustments to font size, leading, etc. In many cases, the word spacing remains within the usual tolerances and visual quality does not noticeably suffer. This paper presents a modification to the Knuth-Plass algorithm to return several results for a given column of text, each corresponding to a different height, and describes steps to quantify the amount of expected flexibility in a given paragraph. We conclude with a discussion on how such "sub-optimal" results can lead to a better overall document layout, particularly in the context of mobile layouts, where flexibility is of key importance.