Unsplittable Multicommodity Flows in Outerplanar Graphs

TL;DR

This paper investigates the unsplittable multicommodity flow problem in outerplanar graphs, demonstrating that demands satisfying the cut-condition can be routed with limited capacity violation, advancing understanding of routing constraints in such graphs.

Contribution

It proves that in outerplanar graphs, demands meeting the cut-condition can be routed along single paths with bounded capacity violation, extending prior results on splittable flows.

Findings

Routing demands with cut-condition satisfaction requires at most 3.6 times maximum demand capacity violation.

The result applies specifically to outerplanar graphs, a subclass of planar graphs.

Provides a bound on capacity violation for unsplittable multicommodity flows in this graph class.

Abstract

We consider the problem of multicommodity flows in outerplanar graphs. Okamura and Seymour showed that the cut-condition is sufficient for routing demands in outerplanar graphs. We consider the unsplittable version of the problem and prove that if the cut-condition is satisfied, then we can route each demand along a single path by exceeding the capacity of an edge by no more than $\frac{18}{5} \cdot d_{max}$, where $d_{max}$ is the value of the maximum demand.