A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph

@article{Horton1987APA,
  title={A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph},
  author={J. Horton},
  journal={SIAM J. Comput.},
  year={1987},
  volume={16},
  pages={358-366}
}
  • J. Horton
  • Published 1987
  • Mathematics, Computer Science
  • SIAM J. Comput.
Define the length of a basis of the cycle space of a graph to be the sum of the lengths of all cycles in the basis. An algorithm is given that finds a cycle basis with the shortest possible length in $O(m^3 n)$ operations, where m is the number of edges and n is the number of vertices. This is the first known polynomial-time algorithm for this problem. Edges may be weighted or unweighted. Also, the shortest cycle basis is shown to have at most ${{3(n - 1)(n - 2)} / 2}$ edges for the unweighted… Expand

Figures and Topics from this paper

Paper Mentions

A Faster Algorithm for Minimum Cycle Basis of Graphs
An Õ(m2n) Randomized Algorithm to Compute a Minimum Cycle Basis of a Directed Graph
Finding Shorter Cycles in a Weighted Graph
Algorithms to Compute Minimum Cycle Basis in Directed Graphs
New Approximation Algorithms for Minimum Cycle Bases of Graphs
Minimum Cycle Basis and All-Pairs Min Cut of a Planar Graph in Subquadratic Time
Faster Algorithms for Minimum Cycle Basis in Directed Graphs
A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs
Union of all the Minimum Cycle Bases of a Graph
  • P. Vismara
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 1997
...
1
2
3
4
5
...

References

SHOWING 1-8 OF 8 REFERENCES
An Efficient Cycle Vector Space Algorithm for Listing all Cycles of a Planar Graph
  • M. Syslo
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1981
A Mechanical Analysis of the Cyclic Structure of Undirected Linear Graphs
An algorithm for the longest cycle problem
On cycle bases of a graph
  • M. Syslo
  • Mathematics, Computer Science
  • Networks
  • 1979
Algorithm 97: Shortest path
Numerical Processing of Horizontal Control Data- Economization by Automation
  • Numerical Processing of Horizontal Control Data- Economization by Automation
  • 1984
On a minimum cycle basis of a graph
Minimal Bases of Cycles of a Graph
  • Recent Advances in Graph Theory, Proceedings of the Symposium held in Praque
  • 1974