New Approximation Algorithms for Minimum Cycle Bases of Graphs

@article{Kavitha2009NewAA,
  title={New Approximation Algorithms for Minimum Cycle Bases of Graphs},
  author={T. Kavitha and K. Mehlhorn and D. Michail},
  journal={Algorithmica},
  year={2009},
  volume={59},
  pages={471-488}
}
AbstractWe consider the problem of computing an approximate minimum cycle basis of an undirected non-negative edge-weighted graph G with m edges and n vertices; the extension to directed graphs is also discussed. In this problem, a {0,1} incidence vector is associated with each cycle and the vector space over $\mathbb{F}_{2}$ generated by these vectors is the cycle space of G. A set of cycles is called a cycle basis of G if it forms a basis for its cycle space. A cycle basis where the sum of… Expand
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References

SHOWING 1-10 OF 59 REFERENCES
New Approximation Algorithms for Minimum Cycle Bases of Graphs
An Õ(mn) Algorithm for Minimum Cycle Basis of Graphs∗
Algorithms to Compute Minimum Cycle Basis in Directed Graphs
A Faster Deterministic Algorithm for Minimum Cycle Bases in Directed Graphs
An Õ(m2n) Randomized Algorithm to Compute a Minimum Cycle Basis of a Directed Graph
A Polynomial-Time Algorithm to Find the Shortest Cycle Basis of a Graph
  • J. Horton
  • Mathematics, Computer Science
  • SIAM J. Comput.
  • 1987
When Do Short Cycles Generate the Cycle Space?
Minimum Cycle Bases for Network Graphs
...
1
2
3
4
5
...