A Survey of Dependent Rounding
summary
Algorithms round fractional edge/node variables to 0/1 while preserving marginals and forcing per-constraint sums to the integer value, using a simple pairwise randomized rounding step that picks two variables, perturbs them by ±ε with carefully chosen probabilities, and repeats in polynomial time. Resulting negative-dependence guarantees (the negative cylinder property and stronger negative association in matroids) give Chernoff-style tails for nonnegative linear forms, let multipath routing match classical congestion bounds, enable a 1/4 approximation for stochastic matching, and improve a 3/2 scheduling bound after scaling down by a (1−γ) factor.
AI-written summary · about