Approximation Algorithms for the Unsplittable Flow Problem

  • Amit Chakrabarti
  • Chandra Chekuri
  • Anuptam Gupta
  • Amit Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2462)

Abstract

We present approximation algorithms for the unsplittableflow problem (UFP) on undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum capacity. We focus on the non-uniform capacity case in which the edge capacities can vary arbitrarily over the graph. Our results are:
  • - For undirected graphs we obtain a O(Δα-1 log2n) approximation ratio, where n is the number of vertices, Δ the maximum degree, and α the expansion of the graph. Our ratio is capacity independent and improves upon the earlier O(Δα-1(cmax/cmin) log n) bound [15] for large values of cmax/cmin. Furthermore, if we specialize to the case where all edges have the same capacity, our algorithm gives an O(Δα-1 log n) approximation, which matches the performance of the best-known algorithm [15] for this special case.

  • - For certain strong constant-degree expanders considered by Frieze [10] we obtain an O(√log n) approximation for the uniform capacity case, improving upon the current O(log n) approximation.

  • - For UFP on the line and the ring, we give the first constant-factor approximation algorithms. Previous results addressed only the uniform capacity case.

  • - All of the above results improve if the maximum demand is bounded away from the minimum capacity.

Our results are based on randomized rounding followed by greedy alteration and are inspired by the use of this idea in recent work [21,9].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Amit Chakrabarti
    • 1
  • Chandra Chekuri
    • 2
  • Anuptam Gupta
    • 2
  • Amit Kumar
    • 3
  1. 1.Computer Science Dept.Princeton UniversityPrinceton
  2. 2.Bell LabsLucent Tech.USA
  3. 3.Computer Science Dept.Cornell UniversityUSA

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