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In a binary search tree, all nodes except the nodes in the bottom of the tree have two nodes connected to the lower side of the node. These two nodes are called the children of the node above, and the node above is called the parent node of the two child nodes. Note that the root node does not have a parent node. Similarly, the nodes at the bottom of the tree do not have any children. These nodes are called leaves. One of the features of branch and bound is that the entire tree is not known from the beginning.

2. 2 is a so-called binary search tree, which is a special case of a general search tree and is the type of tree of interest for the MIQP problems considered in this text. The ellipses in the tree are called nodes. The rows of nodes in the tree are called levels. The top node is called the root node. In a binary search tree, all nodes except the nodes in the bottom of the tree have two nodes connected to the lower side of the node. These two nodes are called the children of the node above, and the node above is called the parent node of the two child nodes.

3, the upper and the lower bound for a node are indicated as a super- and a subindex respectively for the circle representing the node. The computation of the bounds for problem P over the set S gives an upper bound of 10 and a lower bound of 1. Problem P is split into two subproblems P0 and P1 over the sets S0 and S1 . The upper bound for P0 is 5 and the lower bound is 4. Further, the upper bound for P1 is 7 and the lower bound is 6. Since the best possible objective function value over S1 does not even reach the worst possible value over S0 , it is no use continuing working with P1 .

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