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The Densest k Subgraph Problem in b-Outerplanar Graphs

  • Sean Gonzales
  • Theresa MiglerEmail author
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 881)

Abstract

We give an exact \(O(nk^2)\) algorithm for finding the densest k subgraph in outerplanar graphs. We extend this to an exact \(O(nk^2 8^b)\) algorithm for finding the densest k subgraph in b-outerplanar graphs. Often, when there is an exact polynomial time algorithm for a problem on b-outerplanar graphs, this algorithm can be extended to a polynomial time approximation scheme (PTAS) on planar graphs using Baker’s technique. We hypothesize that this is not possible for the densest k subgraph problem.

Keywords

Densest k subgraph problem Density Outerplanar graphs 

Notes

Acknowledgements

We would like to express our sincere thanks to Samuel Chase for his collaboration on our initial explorations of finding a PTAS for the densest k subgraph problem. We would like to thank our reviewer who pointed us to previous work on this problem [3].

Supplementary material

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.California Polytechnic State UniversitySan Luis ObispoUSA

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