To solve this problem, notice that $E$ is the midpoint of $AC$ and $D$ is the midpoint of $BC$.

Therefore, quadrilateral $CEDB$ is a midsegment quadrilateral of triangle $ABC$. In a triangle, the segment joining the midpoints of any two sides is parallel to the third side and half its length (midsegment theorem).

Since $E$ and $D$ are midpoints:

• $ED$ is parallel to $AB$ and $ED = \frac{1}{2} \cdot AB$.

The line segment $s$ is parallel to $u$ and $s = \frac{1}{2} \cdot u$.

The expression that represents the value of $s$ is:

$s = \frac{1}{2}u$

So, the correct option is:

$\boxed{s = \frac{1}{2}u}$