1 research outputs found
A Combinatorial -time Algorithm for the Min-Cost Flow Problem
We present a combinatorial method for the min-cost flow problem and prove
that its expected running time is bounded by . This matches
the best known bounds, which previously have only been achieved by numerical
algorithms or for special cases. Our contribution contains three parts that
might be interesting in their own right: (1) We provide a construction of an
equivalent auxiliary network and interior primal and dual points with potential
in linear time. (2) We present a combinatorial
potential reduction algorithm that transforms initial solutions of potential
to ones with duality gap below in \tilde O(P_0\cdot
\mbox{CEF}(n,m,\epsilon)) time, where and
\mbox{CEF}(n,m,\epsilon) denotes the running time of any combinatorial
algorithm that computes an -approximate electrical flow. (3) We show
that solutions with duality gap less than suffice to compute optimal
integral potentials in time with our novel crossover procedure.
All in all, using a variant of a state-of-the-art -electrical flow
solver, we obtain an algorithm for the min-cost flow problem running in