Conditional Constraint for Interger Linear Programming

Question

I'm working on a problem on Trees. I'm trying to write an ILP formulation. I have a tree T=(V,E) V are vertices E are edges. One of my constraints is about connectivity and i want to formulate my statement which is: if X[i,j] =1; then X[parent_i,i] = 1. X is binary variable indicating we select that node in solution if it's in solution 1 else 0. i,j are elements of V How can i formulate this?

Thanks in advance.

X[parent_i,i] >= X[i,j] – Falk Hüffner Oct 30 '14 at 09:44 — Falk Hüffner, Oct 30 '14 at 09:44

score 1 · Accepted Answer · answered Oct 30 '14 at 21:52

1

For A, B in {0, 1}, [A = 1 ⇒ B = 1] ⇔ [A ≤ B].

answered Oct 30 '14 at 21:52

Timothy Shields

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Thanks for your answer but it's not completely solve my problem. – Berkehan Oct 31 '14 at 18:40
Actually when i look it again this is the same thing with what i think thank you. – Berkehan Nov 04 '14 at 18:07

score 0 · Answer 2 · answered Oct 31 '14 at 18:47

I come with a solution i used parent relation with nodes. Solution is: X(parent[parent[i]],parent[i])-X(Parent[i],i)>=0. Lets say we have k-->i-->j hierachy there are 3 possibility: fisrtly k,i and i,j both may be 0, secondly both may be 1; at last k,i may be 1 and i,j may be 0. But k,i can't be 0 when i,j is 1. So (k,i) - (i,j) must be greater and equal to 0.

Conditional Constraint for Interger Linear Programming

2 Answers2