2.1 Randomized Rounding 12.1.1 Min Congestion Routing Problem

xie ≥ 0 ∀i,∀e The sets δ+(v) and δ−(v) correspond to the incoming and outgoing flow, respectively, for vertex v. The summation constraints then enforce flow conservation, and source/sink assignments. Since the objective function is to minimize t, which is constrained to be an upper bound for the flow across any edge, t will give us the (possibly fractional) congestion for a solution point of this LP. In order to recover an integral/unsplittable flow solution from the LP solution, we will consider an equivalent formulation of the LP.