Towards (1 + ε)-Approximate flow sparsifiers

Abstract

A useful approach to "compress" a large network G is to represent it with a flow-sparsifier, i.e., a small network H that supports the same flows as G, up to a factor q ≥ 1 called the quality of sparsifier. Specifically, we assume the network G contains a set of k terminals T, shared with the network H, i.e., T ⊆V(G) ∩V(H), and we want H to preserve all multicommodity flows that can be routed between the terminals T. The challenge is to construct H that is small. These questions have received a lot of attention in recent years, leading to some known tradeoffs between the sparsifier's quality q and its size \V(H)\. Nevertheless, it remains an outstanding question whether every G admits a flow-sparsifier H with quality q = 1 + ε, or even q = O(1), and size |V(H)|