### Number of non-zeros in hines matrix ?

Posted:

**Tue Mar 08, 2016 12:29 am**I have following set of questions related to hines matrix.

[*]For a given matrix dimension N, does hines matrix always have (3*N-2) elements ?

[*]Does the number of non-zeros in hines matrix depend on branching in the model ?

[*]If I consider off-maindiagonal non-zero elements in upper triangle of hines matrix, do they form a maximal set ?

Consider a 2d point set S. If each pair of points p1,p2 from S satisfy following condition then set S is called maximal set.

(p1.x >= p2.x && p1.y <= p2.y) || (p1.x <= p2.x && p1.y >= p2.y)

[*]For a given matrix dimension N, does hines matrix always have (3*N-2) elements ?

[*]Does the number of non-zeros in hines matrix depend on branching in the model ?

[*]If I consider off-maindiagonal non-zero elements in upper triangle of hines matrix, do they form a maximal set ?

**Maximal set:**Consider a 2d point set S. If each pair of points p1,p2 from S satisfy following condition then set S is called maximal set.

(p1.x >= p2.x && p1.y <= p2.y) || (p1.x <= p2.x && p1.y >= p2.y)