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The Knuth-Plass line-breaking algorithm chooses paragraph breaks using dynamic programming over a representation of the material as typesetting boxes, typesetting glue and typesetting penalties. Boxes supply unbreakable widths; glue supplies normal spacing together with stretch and shrink allowances; penalties express preferences about permitted breaks and can account for a hyphen added when a break is taken.^[ref]

Text justification makes the glue geometry useful. In an illustrative line, suppose box widths total 24 and two glues each have normal width 3 and stretch allowance 2. To fill width 32, the line adjustment ratio isEach glue then becomes $3+r\cdot 2=4$, giving $24+4+4=32$. This example demonstrates proportional stretching; it is one ingredient of paragraph optimization.

The dynamic programming state retains information needed to score later choices. In particular, a line-breaking fitness class records a spacing category, allowing an abrupt change between neighbouring lines to affect the cost. Break position alone would discard that relevant history. The original active nodes include line number and fitness class, with the best accumulated demerits stored as their value.^[ref]

The line breaking with squared slack cost example isolates break selection with fixed word spacing. Here, adjustable typesetting glue and typesetting penalties participate in the paragraph optimization. Donald E. Knuth and Michael F. Plass's 1981 paper documents the method and its development in the TeX project.^[ref]

Text justification adjusts the contents of a line to occupy its available typesetting line width, often aligning both ends of the text. Changing word spacing is one method; permissible adjustments depend on the writing system. Typographic alignment more generally includes leaving the opposite edge ragged or centring a line.^[ref]

In an illustrative line with natural line width $N=30$ and target width $W=32$, two equally flexible spaces can each gain 1. If their stretch coefficients are instead 1 and 3, proportional adjustment allocates the required extra 2 asBoth choices reach the same width; their internal spacing differs. Typesetting glue expresses that flexibility, and the line adjustment ratio computes the common proportional change.

Line breaking and text justification interact: a different break changes the number of spaces available to absorb the width difference. A good paragraph layout therefore considers spacing quality when choosing breaks, rather than merely stretching an already chosen set of lines. The Knuth-Plass line-breaking algorithm makes that interaction explicit.

Typesetting glue represents adjustable space between pieces of typeset material. In a finite, single-order model, describe a glue item by a nominal width $g_i$, stretch coefficient $s_i\ge 0$ and shrink coefficient $t_i\ge 0$. A shared line adjustment ratio $r$ givesThus a negative $r$ reduces the gap. The coefficients describe relative flexibility; they need not be identical for all spaces. This model is a useful part of text justification.^[ref]

For example, two nominal gaps of width 3 with stretch coefficients 1 and 3 become $3.5$ and $4.5$ when $r=1/2$. Their total extra width is 2. With shrink coefficients 1 and 1, $r=-1$ makes both gaps width 2. The same natural line can therefore reach different targets by using the appropriate coefficients.

TeX also distinguishes typesetting glue orders, so the finite model above does not describe every glue setting. In a horizontal line, typesetting glue changes gaps rather than stretching the outlines of the glyphs.

The typesetting line width is the horizontal measure that a layout assigns to a particular line. It supplies a target for text justification and a fitting constraint for line breaking. Write it as $W_j$ when it can depend on line number $j$. The Knuth-Plass line-breaking algorithm permits a sequence of target widths, rather than requiring the entire text paragraph to be rectangular.^[ref]

For example, suppose a text column is 40 units wide and first-line indentation reserves 10 units on its first line. ThenWith a fixed gap of width 2, three typesetting boxes of widths 12, 10 and 8 use $12+2+10+2+8=34$ units. They exceed the first line's available width, although they fit a later line in the fixed-space model. When typesetting glue can shrink, feasibility must also account for that permitted shrinkage.

Width and line height measure different directions. Changing the font size can alter both the widths of the typesetting boxes and their vertical metrics, so preserving the same column width does not preserve the same breaks.

Typographic alignment places a line's content relative to its available horizontal space. Common choices align its left edge, align its right edge, centre it or apply text justification. In CSS, text-align specifies alignment within the line's container, rather than positioning the entire container in the page.^[ref]

For a rigid line with natural line width $N\le W$, no indentation, and a left boundary at $x=0$, the starting positions areThus $N=24$ and $W=40$ give starts 0, 8 and 16. These three choices preserve the internal word spacing. Text justification can instead change that spacing through typesetting glue so the content reaches the intended edges. The alignments therefore solve different geometric tasks even when the same words and computer font are used.

Word spacing is the separation between adjacent words in a line of text. Its nominal value comes from the computer font and layout settings; text justification can adjust it through typesetting glue. Letter spacing instead changes spacing within the text's sequence of letters. A script without visible word separators needs a different spacing strategy from an English sentence.^[ref]

Suppose three typesetting boxes have widths 8, 6 and 10, and the two intervening spaces each have width 3. The natural line width isAdding 1 to each space gives width 32. Adding 1 to every glyph advance would generally produce a different layout, because there need not be one glyph per word or per stored character. Word spacing must therefore be applied to the intended separators rather than inferred from a count of glyphs.

In CSS, word-spacing: 1px specifies additional spacing at the relevant word separators; it does not set every interword gap to exactly one CSS pixel.^[ref]