An improved approximation algorithm for requirement cut

Anupam Gupta, Viswanath Nagarajan, R. Ravi

Abstract: This note presents improved approximation guarantees for the requirement cut problem: given an n -vertex edge-weighted graph G = ( V , E ) , and g groups of vertices X 1 , … , X g ⊆ V with each group X i having a requirement r i between 0 and | X i | , the goal is to find a minimum cost set of edges whose removal separates each group X i into at least r i disconnected components. We give a tight Θ ( log g ) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O ( log k ⋅ log g ) approximation ratio for general graphs, where k = | ∪ i = 1 g X i | ≤ n .