Deliver one signal to a million flip-flops at almost the same instant, on the wire that toggles every cycle and burns a big slice of the power budget. The algorithms run from geometric symmetry through provably zero-skew tree construction to deliberately redundant meshes.
Build a tree whose root-to-leaf delays match. Four algorithms, in rising order of sophistication: symmetry, recursive geometric balance, exact delay balance, and provably minimal-wire zero skew.
Route the clock as a recursively nested H: every leaf is geometrically equidistant from the root, so skew is zero by construction, as long as loads are uniform.
Recursively split the actual sink set by the median coordinate and route from the region's center of mass to each half's center: geometric balance for arbitrary sink placements.
Merge subtrees bottom-up, computing from the Elmore delay model the exact tapping point on the connecting wire that equalizes both sides' delays, adding wire length only when geometry demands it.
Do not commit merge points early: propagate, bottom-up, the entire segment of feasible zero-skew locations, and only embed exact positions on the way back down. Minimal wire, zero skew, and the algorithm real tools descend from.
Zero skew is neither free nor always right. These methods buffer real trees against real loads, and spend skew deliberately where it buys timing.
Real trees insert buffers level by level to meet slew and load limits, cluster sinks under capacitance budgets, and balance the buffered structure, the practical layer over the geometric algorithms.
Zero skew is not optimal: deliberately arriving early at some flops and late at others steals time from fast paths for slow ones. Formulated as an optimization over arrival offsets, solvable exactly.
When variation is the enemy, add wire: meshes and hybrid schemes trade power for robustness by shorting many paths together.
Short a whole grid of clock wire together and drive it from many points: local skew collapses because neighboring sinks share metal, at a steep cost in wire, buffers, and power.
A balanced top structure delivers the clock to many regional tap drivers; below them, ordinary local trees serve the flops. Mesh-like robustness where it matters, tree-like power where it does not.