Mathematical Programming Computation

, Volume 10, Issue 2, pp 143–185 | Cite as

Detecting almost symmetries of graphs

  • Ben Knueven
  • Jim Ostrowski
  • Sebastian Pokutta
Full Length Paper


We present a branch-and-bound framework to solve the following problem: Given a graph G and an integer k, find a subgraph of G formed by removing no more than k edges that minimizes the number of vertex orbits. We call the symmetries on such a subgraph “almost symmetries” of G. We implement our branch-and-bound framework in PEBBL to allow for parallel enumeration and demonstrate good scaling up to 16 cores. We show that the presented branching strategy is much better than a random branching strategy on the tested graphs. Finally, we consider the presented strategy as a heuristic for quickly finding almost symmetries of a graph G. The software that was reviewed as part of this submission has been issued the Digital Object Identifier DOI: 10.5281/zenodo.840558.


Almost symmetries Graph automorphism Branch-and-bound 

Mathematics Subject Classification

05C60 05C85 90C27 



The research reported in this paper was funded in part by NSF Award Number 1332662 and NSF Award Number 1333789.


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Copyright information

© Springer-Verlag GmbH Germany and The Mathematical Programming Society 2017

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringUniversity of TennesseeKnoxvilleUSA
  2. 2.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA

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