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)


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.


Source Node Approximation Ratio Sink Node Disjoint Path Average Improvement 
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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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