Computing the Degeneracy of Large Graphs

  • Martín Farach-Colton
  • Meng-Tsung Tsai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8392)


Any ordering of the nodes of an n-node, m-edge simple undirected graph G defines an acyclic orientation of the edges in which each edge is oriented from the earlier node in the ordering to the later. The degeneracy on an ordering is the maximum outdegree it induces, and the degeneracy of a graph is smallest degeneracy of any node ordering. Small-degeneracy orderings have many applications.

We give an algorithm for generating an ordering whose degeneracy approximates the minimum possible, that is, it approximates the degeneracy of the graph. Although the optimal ordering itself can be computed in \(\mathcal{O}(m)\) time and \(\mathcal{O}(m)\) space, such algorithms are infeasible for large graphs. Our approximation algorithm is semi-streaming: it uses less space, can achieve a constant approximation ratio, and accesses the graph in logarithmic read-only passes.


Greedy Algorithm Approximation Factor Large Graph Candidate Node Sequential Pass 
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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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Martín Farach-Colton
    • 1
  • Meng-Tsung Tsai
    • 1
  1. 1.Rutgers UniversityNew BrunswickUSA

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