On Linear Programming Relaxations for Unsplittable Flow in Trees

We study some linear programming relaxations for the Unsplittable Flow problem on trees (UFPtree). Inspired by results obtained by Chekuri, Ene, and Korula for Unsplittable Flow on paths (UFP-path), we present a relaxation with polynomially many constraints that has an integrality gap bound of O(log n·min{log m, log n}) where n denotes the number of tasks and m denotes the number of edges in the tree. This matches the approximation guarantee of their combinatorial algorithm and is the first demonstration of an efficiently-solvable relaxation for UFP-tree with a sub-linear integrality gap. The new constraints in our LP relaxation are just a few of the (exponentially many) rank constraints that can be added to strengthen the natural relaxation. A side effect of how we prove our upper bound is an efficient O(1)-approximation for solving the rank LP. We also show that our techniques can be used to prove integrality gap bounds for similar LP relaxations for packing demand-weighted subtr...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Zachary Friggstad, Zhihan Gao
• Keywords: Algorithms, APPROX 2015