  We consider a routing problem which plays an important role in several
applications, primarily in communication network planning and VLSI layout
design. The original underlying graph algorithmic task is called Disjoint Paths
problem. In most applications, one can encounter its capacitated
generalization, which is known as the Unsplitting Flow problem. These
algorithmic tasks are very hard in general, but various efficient
(polynomial-time) approximate solutions are known. Nevertheless, the
approximations tend to be rather complicated, often rendering them impractical
in large, complex networks. Our goal is to present a solution that provides a
simple, efficient algorithm for the unsplittable flow problem in large directed
graphs. The simplicity is achieved by sacrificing a small part of the solution
space. This also represents a novel paradigm of approximation: rather than
giving up finding an exact solution, we restrict the solution space to its most
important subset and exclude those that are marginal in some sense. Then we
find the exact optimum efficiently within the subset. Specifically, the
sacrificed parts (i.e., the marginal instances) only contain scenarios where
some edges are very close to saturation. Therefore, the excluded part is not
significant, since the excluded almost saturated solutions are typically
undesired in practical applications, anyway.
