#9698: Hamiltonian cycles in undirected graphs - backtracking algorithm.
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Reporter: fidelbarrera | Owner: jason, ncohen, rlm
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-4.6
Component: graph theory | Keywords:
Author: Fidel Barrera-Cruz | Upstream: N/A
Reviewer: Nathann Cohen | Merged:
Work_issues: |
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Description changed by ncohen:
Old description:
> Randomized backtracking for finding hamiltonian cycles.
>
> A path P is maintained during the execution of the algorithm. Initially
> the path will contain an edge of the graph. Every 10 iterations the path
> is reversed. Every ``reset_bound`` iterations the path will be cleared
> and procedure is restarted. Every ``backtrack_bound`` steps we discard
> the last five vertices and continue with the procedure. The total number
> of steps in the algorithm is controlled by ``max_iter``. If a hamiltonian
> cycle is found it is returned. If the number of steps reaches
> ``max_iter``
> then a longest path is returned. See OUTPUT for more details.
New description:
Randomized backtracking for finding hamiltonian cycles.
A path P is maintained during the execution of the algorithm. Initially
the path will contain an edge of the graph. Every 10 iterations the path
is reversed. Every ``reset_bound`` iterations the path will be cleared and
procedure is restarted. Every ``backtrack_bound`` steps we discard the
last five vertices and continue with the procedure. The total number of
steps in the algorithm is controlled by ``max_iter``. If a hamiltonian
cycle is found it is returned. If the number of steps reaches ``max_iter``
then a longest path is returned. See OUTPUT for more details.
Apply first :
* #10043
* #10101
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9698#comment:19>
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