#18871: MILP formulation for cutwidth
-------------------------+-------------------------------------------------
Reporter: | Owner:
dcoudert | Status: needs_work
Type: | Milestone: sage-6.8
enhancement | Resolution:
Priority: major | Merged in:
Component: graph | Reviewers: Nathann Cohen
theory | Work issues:
Keywords: | Commit:
cutwidth, MILP | 1d4194a9f98ac9678f1bae0c94c533ed30f47fdf
Authors: David | Stopgaps:
Coudert |
Report Upstream: N/A |
Branch: |
public/18871 |
Dependencies: |
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Changes (by ncohen):
* status: needs_review => needs_work
* reviewer: => Nathann Cohen
Comment:
Hellooooooo David,
Some comments:
- Module's doc, documentation of MILP variable `z`: at the end of the line
there
is a `y^y`. Shouldn't it be `y^k`?
- Constraints: the third constraint is missing one side of the inequality.
- But I am not sure that I understand the system: why wouldn't you say
that:
a) `x_v^k <= x_v^{k+1}` (the values can only increase)
b) `\sum_v x_v^k == k` (for every k)
- About y: what about only having those two constraints:
- `y_{uv}^k >= x_v^k - x_u^k`
- `y_{uv}^k >= x_u^k - x_v^k`
It seems to me that they are sufficient to express `y_{uv}^k >= x_u^k
XOR
x_v^k`. And you do not really need to say that `y` has to be *equal* to
the
XOR, the `>=` should be enough given that you minimize the cost of a
cut.
- If you see a better way to name the `x,y`, and `z`... `:-P`
- When building the documentation, the references toward the number of the
constraints do not appear correctly. Neither does the 'xor'.
- You call `set_binary` on a variable that you already defined as binary.
- Is there any reason why you catch the `MIPSolverException`?
- You do not have to int+round the value of `z['z']`. The solver should
give you
an integer value as you defined the variable as integral: if it does
not,
that's a bug that should be fixed.
Nathann
--
Ticket URL: <http://trac.sagemath.org/ticket/18871#comment:4>
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