#19985: Add is_partial_cube
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Reporter: jaanos | Owner:
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-7.1
Component: graph theory | Resolution:
Keywords: graphs partial | Merged in:
cubes | Reviewers:
Authors: Janoš Vidali | Work issues:
Report Upstream: N/A | Commit:
Branch: | 618ab7378d84a24d2c572f58e4d7df23586ba80a
u/jaanos/add_is_partial_cube | Stopgaps:
Dependencies: |
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Comment (by jaanos):
Hi!
> This being said, isn't this of complexity `nm` already?
>
> {{{
> + for v, w in contracted.edge_iterator(labels = False):
> + diff = bitvec[v]^bitvec[w]
> }}}
The paper assumes that a machine word can store `log(n)` bits, so bitwise
operations can be done in `O(d/log(n))` time, where `d` is the degree of
the root (these sum up to at most `n-1` over all iterations of the
contraction loop). Since the number of edges is checked to be `O(n
log(n))`, the total time needed for bitwise operations is `O(n^2)`. Of
course, failing this assumption, the time complexity here is indeed `O(nm)
= O(n^2 log(n))`.
> Another small thing: `len(contracted[v])` should be
`contracted.out_degree(v)` (does not build the list of neighbors).
Will take care of that.
Janoš
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Ticket URL: <http://trac.sagemath.org/ticket/19985#comment:27>
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