Minimum Cycle Bases for Network Graphs

@article{Berger2004MinimumCB,
  title={Minimum Cycle Bases for Network Graphs},
  author={F. Berger and P. Gritzmann and S. D. Vries},
  journal={Algorithmica},
  year={2004},
  volume={40},
  pages={51-62}
}
Abstract The minimum cycle basis problem in a graph G = (V,E) is the task to construct a minimum length basis of its cycle vector space. A well-known algorithm by Horton of 1987 needs running time O(|V||E|2.376). We present a new combinatorial approach which generates minimum cycle bases in time O(\max{|E|3,|E||V|2log |V|}) with a space requirement of Θ(|E|2). This method is especially suitable for large sparse graphs of electric engineering applications since there, typically, |E| is close to… Expand
63 Citations
New Approximation Algorithms for Minimum Cycle Bases of Graphs
New Approximation Algorithms for Minimum Cycle Bases of Graphs
Minimum path bases and relevant paths
Algorithms to Compute Minimum Cycle Basis in Directed Graphs
Length bounds for cycle bases of graphs
Minimum Cycle Bases in Graphs Algorithms and Applications
A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 28 REFERENCES
A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph
  • J. Horton
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1987
On Finding a Cycle Basis with a Shortest Maximal Cycle
A Polynomial Time Algorithm to Find the Minimum Cycle Basis of a Regular Matroid
The All-Pairs Min Cut Problem and the Minimum Cycle Basis Problem on Planar Graphs
An algorithm for finding a fundamental set of cycles of a graph
  • K. Paton
  • Mathematics, Computer Science
  • CACM
  • 1969
Cycle bases of graphs for sparse flexibility matrices
Minimum cycle bases of Halin graphs
Depth-First Search and Linear Graph Algorithms
  • R. Tarjan
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1972
Matrices and Matroids for Systems Analysis
Combinatorial relaxation algorithm for mixed polynomial matrices
...
1
2
3
...