Improved Balanced Flow Computation Using Parametric Flow

TL;DR

This paper introduces a more efficient algorithm for computing balanced flows in market equilibrium networks, reducing the number of maxflow computations needed and improving overall runtime performance.

Contribution

The authors develop a novel algorithm that requires only one parametric flow computation, significantly enhancing efficiency over previous methods.

Findings

Requires only a single parametric flow computation

Reduces the number of maxflow computations from O(n) to 1

Improves overall runtime by almost a factor of n

Abstract

We present a new algorithm for computing balanced flows in equality networks arising in market equilibrium computations. The current best time bound for computing balanced flows in such networks requires $O(n)$ maxflow computations, where $n$ is the number of nodes in the network [Devanur et al. 2008]. Our algorithm requires only a single parametric flow computation. The best algorithm for computing parametric flows [Gallo et al. 1989] is only by a logarithmic factor slower than the best algorithms for computing maxflows. Hence, the running time of the algorithms in [Devanur et al. 2008] and [Duan and Mehlhorn 2015] for computing market equilibria in linear Fisher and Arrow-Debreu markets improve by almost a factor of $n$.