 
Summary: The Price of Routing Unsplittable Flow
Baruch Awerbuch # Yossi Azar + Amir Epstein #
Abstract
The essence of the routing problem in real networks is that the traffic demand from a source
to destination must be satisfied by choosing a single path between source and destination. The
splittable version of this problem is when demand can be satisfied by many paths, namely a flow
from source to destination. The unsplittable, or discrete version of the problem is more realistic yet
is more complex from the algorithmic point of view; in some settings optimizing such unsplittable
traffic flow is computationally intractable.
In this paper, we assume this more realistic unsplittable model, and investigate the ''price
of anarchy'', or deterioration of network performance measured in total traffic latency under the
selfish user behavior. We show that for linear edge latency functions the price of anarchy is exactly
2.618 for weighted demand and exactly 2.5 for unweighted demand. These results are easily
extended to (weighted or unweighted) atomic ''congestion games'', where paths are replaced by
general subsets. We also show that for polynomials of degree d edge latency functions the price
of anarchy is d #(d) . Our results hold also for mixed strategies.
Previous results of Roughgarden and Tardos showed that for linear edge latency functions
the price of anarchy is exactly 4
3
under the assumption that each user controls only a negligible
