Why it matters

LP rounding is core approximation technique. Understanding shapes design.

Advertisement

The architecture

Formulate ILP.

Relax to LP.

Solve LP.

Round: threshold, random, or dependent.

LP rounding flowLP relaxationsolve fractionalRound strategythreshold / randomFeasible integerwith bounded lossDifferent rounding schemes give different approximation ratios
LP rounding.
Advertisement

How it works end to end

Threshold rounding: if x_i > 0.5, take 1.

Randomized rounding: take 1 with prob x_i.

Dependent rounding: preserve constraints.