Brief Announcement: Bridging the Theory-Practice Gap in Multi-commodity Flow Routing

In the concurrent multi-commodity flow problem, we are given a capacitated network G = (V,E) of switches V connected by links E, and a set of commodities K = {(si, ti, di)}. The objective is to maximize the minimum fraction λ of any demand di that is routed from source si to target ti. This problem has been studied extensively by the theory community in the sequential model (e.g., [4]) and in distributed models (e.g., [2, 3]). Solutions in the networking systems community also fall into these models (e.g., [1, 6, 5]), yet none of them use algorithms from the theory community. Why the gap between theory and practice? This work seeks to answer and resolve this question. We argue that existing theoretical models are ill-suited for real networks (§2) and propose a new distributed model that better captures their requirements (§3). We have developed optimal algorithms in this model for data center networks (§4); making these algorithms practical requires a novel use of programmable hardware switches. A solution for general networks poses an intriguing open problem.