"1" the shortest way how to build a diagram? The
Differential constraint system is a collection of {di-dj<=u},
considering Di-dj<=u to Dj+u>=di,
∴ node I to satisfy all dj+u>=di of node J,
then must take at least min (dj+ u), if it gets bigger, it will be contradictory.
This allows the shortest path to be built and a set of values to be obtained.
"2" What does this set of values mean?
It is obtained by the shortest circuit. The
just satisfies all the conditions and is most tightly constrained.
that is, it is not unique, and any di may be smaller and the relative difference will become larger.
"2" a property of this set of values: You can translate the
Brief proof: ∵dj+u>=di, set DJ ' =dj+a,∴dj+a+u>=di+a that DJ ' +u>=di '.
The maximum number of
"3" slack operations is n-1.
Descriptive proof: The shortest path has a maximum of n-1 edges. The iterative relaxation operation is actually the process of generating the shortest path tree by the level of the vertex distance s, and the shortest path tree is up to n-1 layer.
"4" node initial value
Set virtual node 0, from 0 to any node I connected one edge, set its weight of 0, and then do the shortest way.
Now the question is: Why is this set up?
What information to find on the Internet is not accurate, directly to the practice. The
now actually gives the N group D0+0>=di inequality, to prove that the existence of so many groups and the absence of these solutions is not subject to change. The contradiction of the
∵ can only be the negative power loop appears. The
∴ proves that a negative-weight loop is present through the addition of 0 nodes.
because 0 only to go out, do not even come back, ∴ negative right loop must not have 0 nodes.
∴ If there is now a negative power loop, then there must be a negative power loop.
Note, however, that by adding a 0 limit, the resulting solution is not necessarily the optimal solution.
For example, for differential constrained system d1-d2>=-3. The
first establishes nodes 1, 2, and builds edges (all-in-one). The
then establishes node 0, connection (0,1,0), (0,2,0). The value calculated by the
is d1=d2=0.
"5" How to find a set of minimum positive integer solutions (nonnegative integer solutions, etc)
each Unicom block is bound to each other. The
uses and checks the set to seek the Unicom block, then translates each block.
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Some understandings of differential constrained systems
