 
Summary: Strongly Polynomial Algorithms for the
Unsplittable Flow Problem
Yossi Azar 1 and Oded Regev 2
1 Dept. of Computer Science, TelAviv University, TelAviv, 69978, Israel.
azar@math.tau.ac.il
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2 Dept. of Computer Science, TelAviv University, TelAviv, 69978, Israel.
odedr@math.tau.ac.il
Abstract. We provide the rst strongly polynomial algorithms with
the best approximation ratio for all three variants of the unsplittable
ow problem (UFP ). In this problem we are given a (possibly directed)
capacitated graph with n vertices and m edges, and a set of terminal pairs
each with its own demand and prot. The objective is to connect a subset
of the terminal pairs each by a single
ow path as to maximize the total
prot of the satised terminal pairs subject to the capacity constraints.
Classical UFP , in which demands must be lower than edge capacities,
is known to have an O(
p
m) approximation algorithm. We provide the
same result with a strongly polynomial combinatorial algorithm. The
