By Ivanyi A. (ed.)

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**Extra resources for Algorithms of informatics, vol. 3**

**Sample text**

All elements of A and b are rationals. e. it is the set conv(P ∩ Z n ) . 2. Thus the description of the integer hull as a polyhedral set is the inequality system: x1 ≥ 0, x1 + x2 ≤ 3, x1 ≤ 1, x1 − x2 ≤ 0 . Under the conditions of the definition the integer hull is a polyhedral set, too. It is a non-trivial statement and in the case of irrational coefficients it can be not true. e. a set of linear inequalities defining exactly the integer hull polyhedral set is known, then the integer programming problem can be reduced to a linear programming problem.

The optimal solution is the intersection point the lines determined by the equations 3x1 − 5x2 = 0 and 3x1 + 5x2 = 15 . If the branching is based on variable x1 then they are defined by the inequalities x1 ≤ 2 and x1 ≥ 3 . 5. In the next subsection the problem is revisited. Then this fact will be observed from the simplex tableaux. Variable x2 would create the branches x2 ≤ 1 and x2 ≥ 2 . 3. 5), and the optimal level of . the objective function represented by the line 2x1 + x2 = 13 2 None of them is empty.

The last element has no next element, therefore the value of suc is none in this case. The procedure of changing all elements is somewhat similar to the Branch Reconstruction procedure. e. suc. suc 2 while Node=none 3 ... suc 5 return Node The loop runs until there is no next element. The necessary operations are executed in row 4. The variable Node becomes the next element of the list in row 5. To insert a new branch into the list is easy. Assume that it is NewNode of type Branch and it is to be inserted after Node which is in the list.