 Line-breaking fitness class

A line-breaking fitness class is a coarse description of how tightly or loosely a line is spaced. The Knuth-Plass line-breaking algorithm distinguishes tight, normal, loose and very loose lines. A transition between sufficiently different classes adds typesetting demerits, even when each line's own spacing is individually acceptable.^[ref]

For example, imagine one feasible line has line adjustment ratio $-0.7$ and the next has $0.8$. One compresses its spaces substantially, while the other expands them. That contrast can be more conspicuous than two lines with similar spacing. A paragraph objective can express this using an added termwhere $f_j\in \{0,1,2,3\}$ indexes the classes. The indicator function adds the charge only for a sufficiently large class change.

Consequently, the dynamic programming state needs the previous fitness information. Suppose two routes to the same break cost 10 and 12, but the cheaper route's class would add a transition charge of 5 to the next line while the other adds none. Their relevant totals become 15 and 12: discarding the second route solely because $12>10$ would be premature. The principle of optimality applies to states that retain the information the future cost needs.

TeX computes its categories using integer typesetting badness thresholds and handles special glue cases explicitly. Its implementation should therefore be consulted for exact boundary behaviour rather than inferring it from rounded decimal adjustment ratios.^[ref]