External-Memory Breadth-First Search with Sublinear I/O

  • Kurt Mehlhorn
  • Ulrich Meyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2461)


Breadth-first search (BFS) is a basic graph exploration technique. We give the first external memory algorithm for sparse undirected graphs with sublinear I/O. The best previous algorithm requires \( \Theta \left( {n + \tfrac{{n + m}} {{D \cdot B}} \cdot \log _{M/B} \tfrac{{n + m}} {B}} \right) \) I/Os on a graph with n nodes and m edges and a machine with main-memory of size M, D parallel disks, and block size B. We present a new approach which requires only \( \mathcal{O}(\sqrt {\tfrac{{n \cdot (n + m)}} {{D \cdot B}} + } \tfrac{{n + m}} {{D \cdot B}} \cdot \log _{M/B} \tfrac{{n + m}} {B}) \) I/Os. Hence, for \( \Omega \sqrt {D \cdot B} \) and all realistic values of \( m = \mathcal{O}(n) \), it improves upon the I/O-performance of the best previous algorithm by a factor \( \log _{M/B} \tfrac{{n + m}} {B}) \). Our approach is fairly simple and we conjecture it to be practical. We also give improved algorithms for undirected single-source shortest-paths with small integer edge weights and for semi-external BFS on directed Eulerian graphs.


Source Node Undirected Graph External Memory Master Node Outerplanar Graph 
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-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Kurt Mehlhorn
    • 1
  • Ulrich Meyer
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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