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A (k + 1)-Approximation Robust Network Flow Algorithm and a Tighter Heuristic Method Using Iterative Multiroute Flow

  • Jean-François Baffier
  • Vorapong Suppakitpaisarn
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)

Abstract

We consider two variants of a max-flow problem against k edge failures, each of which can be both approximated by a multiroute flow algorithm. The maximum k-robust flow problem is to find the minimum max-flow value among \({m\choose k}\) networks that can be obtained by deleting each set of k edges. The maximum k-balanced flow problem is to find a max-flow of the network such that the flow value is maximum against any set of k edge failures, when deleting the corresponding flow to those k edges in the original flow. We prove \(C_M \leqslant C_{M'} \leqslant C_B \leqslant C_R \leqslant (k + 1)\cdot C_M\), where C M is the max-(k + 1)-route flow value, C M is the effectiveness of the max-(k + 1)-route flow after k attacks, C B is the max-k-balanced flow value, and C R is the max-k-robust flow value. Also, we develop a polynomial-time heuristic algorithm for both cases, called the iterative multiroute flow. Our experimental results show that the average improvement made by our heuristic method can be up to 10% better than the multiroute flow algorithm. Compared to the optimal max-k-robust flow solutions – obtained by a brute-force algorithm – there is an average gap of 2% at most.

Keywords

Source Node Approximation Ratio Sink Node Disjoint Path Average Improvement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jean-François Baffier
    • 1
  • Vorapong Suppakitpaisarn
    • 2
  1. 1.Université Paris-Sud, JFLI, CNRSThe University of TokyoJapan
  2. 2.ERATO, Kawarabayashi Large Graph ProjectNII, JSTJapan

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