 Conditional expectation cut formula

For any partial assignment $P$, let $f(P)$ count edges whose two endpoints are already fixed on opposite sides, and let $u(P)$ count edges with at least one unassigned endpoint. Under the remaining independent fair bits,An edge with fixed equal labels contributes zero; fixed unequal labels contribute one. If one endpoint is unassigned, its fair bit disagrees with the fixed label with probability $1/2$. If both endpoints are unassigned, their independent fair bits disagree with probability $1/2$ as well. Count each unresolved edge once, even when both endpoints are unassigned.

Process vertices in a fixed order. Evaluate the conditional expectation cut formula after setting the next label to zero and after setting it to one; retain the larger value, choosing zero on ties. The conditional expectation choice invariant ensures the final cut of a graph has size at least $m/2$. This is a deterministic approximation algorithm for maximum cut.^[ref]