In this paper, we propose an efficient algorithm to decompose a directed acyclic graph (DAG) into chains, which has a lot of applications in computer science and engineering. Especially, it can be used to store transitive closures of directed graphs in an economical way. For a DAG G with n nodes, our algorithm needs O\((n^{2} + bn \sqrt{b} )\) time to find a minimized set of disjoint chains, where b is G′s width, defined to be the largest node subset U of G such that for every pair of nodes u, v ∈̣U, there does not exist a path from u to v or from v to u. Accordingly, the transitive closure of G can be stored in O(bn) space, and the reachability can be checked in O(logb) time. The method can also be extended to handle cyclic directed graphs.


Bipartite Graph Child Node Edge Incident Transitive Closure Maximum Match 
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 2007

Authors and Affiliations

  • Yangjun Chen
    • 1
  1. 1.Department of Applied Computer Science, University of Winnipeg, Winnipeg, Manitoba, R3B 2E9Canada

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