HPWL (half-perimeter wirelength)
Beginner
A quick guess of how long a wire will be: draw the smallest box around everything it connects, then add the box’s width and height.
Novice
A quick estimate of how much wire one connection needs: draw the smallest rectangle around all the pins it joins and add the rectangle’s width and height. Added up over every connection, it gives one number for the placer to shrink.
Expert
Width plus height of a net’s pin bounding box. It equals the shortest rectilinear route for a two-pin net and is a lower bound for nets with more pins, since any tree joining the pins spans the box in both directions. It is built from max and min, so it has no smooth gradient; analytical placers optimize smooth stand-ins (log-sum-exp, weighted-average) and report true HPWL.