1. PBQP Problem

1.1 Topology

1.2 Cost Vectors

1.3 Cost Matrices

2. Remove Trivial Nodes

Following nodes have cost vectors of length one:

• n4

2.1 New Topology

2.2 New Cost Vectors

3. Simplification of Cost Matrices

3.1. New Vectors/Matrices

3.2.1 Simplification of Edge n0-n2

Input:

Output:

edge has been eliminated

3.2.2 Simplification of Edge n0-n1

Input:

Output:

3.2.3 Simplification of Edge n1-n3

Input:

Output:

3.2.4 Simplification of Edge n1-n2

Input:

Output:

3.2.5 Simplification of Edge n2-n3

Input:

Output:

3.2. New Topology

4. Reductions

4.1 RI-Reduction of Node n0

Before reduction:

Input:

Output:

4.2 RII-Reduction of Node n1

Before reduction:

Input:

Output:

Simplified:

4.3 RI-Reduction of Node n2

Before reduction:

Input:

Output:

5. Determine Solution/Minimum

5.1. Trivial Solution

• node n3 is set to 2
  
• node n4 is set to 1
  

5.2. Minimum

Minimum is equal to 49.

5.3. Back Propagation

• node n2 is set to 3
• node n1 is set to 1
• node n0 is set to 2