{Using the Knuth-Plass algorithm to help control widow and orphan lines}
{Robert Rundell}
{The Knuth-Plass line-breaking algorithm is one of the many exceptional
features of \TeX, taking a paragraph of text and converting it to a vertical
list of well-proportioned lines. Through glue and penalty markers \TeX\ gives
the user almost complete control over the spacing and look of the paragraph.

However, in some instances \TeX\ does not provide the user quite as rich a
set of options to control the vertical list as in other areas.  In
particular, eliminating widow and orphan lines can require inserting forced
break points into the text, break points that can only be found from
previous passes of \TeX.  Subsequent changes to the document can require
changes to some or all of these manually inserted line or page breaks.

In \AML, an experimental typesetting program under development, the
Knuth-Plass algorithm is enhanced to find not only the optimal line-break
points for a paragraph, but also to give alternate mappings of the paragraph
into different numbers of lines (where possible).  \AML\ stores
these different sets of break points and uses this information, along with
natural page break points, to automatically eliminate widow and orphan
lines in many cases.  Once a bad page break point is detected, \AML\ will
backtrack and adjust previous paragraphs to create better page breaks.  With
far greater memory and processing capabilities than were available at \TeX's
creation, multiple pages can be examined and processed before a final page
break needs to be finalized, allowing the overall document layout to be
improved.  The combination of keeping multiple pages and also keeping
alternative paragraph line-breaking sets in memory allows \AML\ to automate
and improve this aspect of document typesetting.
}