Improved Throughput for All-or-Nothing Multicommodity Flows with Arbitrary Demands

Throughput is a main performance objective in
communication networks. This paper considers a fundamental
maximum throughput routing problem — the all-or-nothing
multicommodity flow (ANF) problem — in arbitrary directed
graphs and in the practically relevant but challenging setting
where demands can be (much) larger than the edge capacities.
Formally, the input for the ANF problem is an edge-capacitated
directed graph where we have a given number of source-
destination node-pairs with their respective demands and strictly
positive weights. The goal is to route a maximum weight subset
of the given pairs (i.e., the weighted throughput), respecting the
edge capacities: A commodity is routed if all of its demand is
routed from its respective source to destination (this is the all-
or-nothing aspect); splitting flows is allowed (i.e., flows may not
follow a single path). We present a polynomial-time bi-criteria
approximation randomized rounding framework for this NP-
hard problem that yields an arbitrarily good approximation
on the weighted throughput while violating the edge capacity
constraints by at most a sublogarithmic multiplicative factor.
We present two non-trivial linear programming relaxations that
can be used in the framework; the first uses a novel edge-
flow formulation and the second uses a packing formulation.
We demonstrate the “equivalence” of these formulations and
then highlight the advantages of each of the two approaches.
We complement our theoretical results with a proof-of-concept
empirical evaluation, considering a variety of network scenarios.