Some Extensions of the Bottleneck Paths Problem

  • Tong-Wook Shinn
  • Tadao Takaoka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8344)


We extend the well known bottleneck paths problem in two directions for directed unweighted graphs with positive real edge capacities. Firstly we narrow the problem domain and compute the bottleneck of the entire network in O(mlogn) time, where m and n are the number of edges and vertices in the graph, respectively. Secondly we enlarge the domain and compute the shortest paths for all possible bottleneck amounts. We present a combinatorial algorithm to solve the Single Source Shortest Paths for All Flows (SSSP-AF) problem in O(mn) worst case time, followed by an algorithm to solve the All Pairs Shortest Paths for All Flows (APSP-AF) problem in \(O(\sqrt{t}n^{(\omega+9)/4})\) time, where t is the number of distinct edge capacities and O(n ω ) is the time taken to multiply two n-by-n matrices over a ring. We also discuss practical applications for these new problems.


Short Path Acceleration Phase Open Short Path First Edge Capacity Capacity Matrix 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tong-Wook Shinn
    • 1
  • Tadao Takaoka
    • 1
  1. 1.Department of Computer Science and Software EngineeringUniversity of CanterburyChristchurchNew Zealand

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