Finding Min-Sum Disjoint Shortest Paths from a Single Source to All Pairs of Destinations

  • Bing Yang
  • S. Q. Zheng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)


Given a graph G = (V, E) with |V| = n, |E| = m, and a source node s, we consider the problem of finding two disjoint paths from s to two destination nodes t 1 and t 2 with minimum total length, for every pair nodes t 1, t 2V–{s}. One efficient solution is to transform this problem into the problem of finding shortest pairs of disjoint paths, and use the Suurablle-Tarjan algorithm to solve the new problem in O(n 2 log n) time and O(n 2) space. We present an algorithm that solves this problem in O(n 2) time and O(n 2) space, with the solution paths are implicitly represented. Given such a representation, the time necessary to explicitly construct all the solution paths is O(1) for each edge on the paths. Based on this algorithm, we present another algorithm that solves this problem in O(m log 1 + m/n )n time and O(m) space, with the compromise of longer searching time on solution paths.


network routing reliability graph survival shortest path disjoint paths algorithm complexity 


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  1. Dijkstra, E.W.: A note on two problems in connexion with graphs. Numerische Mathematik 1, 269–271 (1959)zbMATHCrossRefMathSciNetGoogle Scholar
  2. Bellman, R.: On a routing problem. Quarterly of Applied Mathematics 16(1), 87–90 (1958)zbMATHMathSciNetGoogle Scholar
  3. Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton (1962)Google Scholar
  4. Floyd, R.W.: Algorithm 97 (SHORTEST PATH). Communications of the ACM 5(6), 345 (1962)CrossRefGoogle Scholar
  5. Warshall, S.: A theorem on boolean matrices. Journal of the ACM 9(1), 11–22 (1962)zbMATHCrossRefMathSciNetGoogle Scholar
  6. Suurballe, J.W.: Disjoint Paths in a Network. Networks 4, 125–145 (1974)zbMATHCrossRefMathSciNetGoogle Scholar
  7. Suurballe, J.W., Tarjan, R.E.: A Quick Method for Finding Shortest Pairs of Disjoint Paths. Networks 14, 325–336 (1984)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bing Yang
    • 1
  • S. Q. Zheng
    • 2
  1. 1.Cisco SystemsRichardsonUSA
  2. 2.Department of Computer ScienceUniversity of Texas at DallasRichardsonUSA

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