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Faster and Simpler Algorithms for Multicommodity Flow and Other Fractional Packing Problems (1997) [187 citations — 4 self]

by Naveen Garg ,  Jochen Könemann
In Proceedings of the 39th Annual Symposium on Foundations of Computer Science
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Abstract:

This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We provide a different approach to these problems which yields faster and much simpler algorithms. Our approach also allows us to substitute shortest path computations for min-cost flow computations in computing maximum concurrent flow and min-cost multicommodity flow; this yields much faster algorithms when the number of commodities is large. 1. Introduction Consider the problem of computing a maximum s-t flow in a graph with unit edge capacities. While there are many different algorithms known for this problem we discuss one which views the problem purely as one of packing s-t paths so that constraints imposed by edge-capacities are not violated. The algorithm associates a length with each edge and at any step it routes a unit flow along the shortest s-t path. It then multiplies the length of every edge on this path by 1 + ffl for ...

Citations

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4 Approximation algorithms for NPhard problems, chapter Cut problems and their application to divide and conquer – Shmoys - 1997
1 An exponential function reduction method for block angular convex programs – Grigoriadis, Khachiyan - 1993
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