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To segment a graph properly, weights are assigned to each edge ei ¡ô E, considering factors such as available bandwidth, entanglement fidelity, and classical time delay. These weights help in determining the cost of distributing graph states through the network.
For example, the weight W(ei) is calculated using parameters like Cei (available bandwidth), fei (entanglement fidelity), and dei (classical time delay), providing a measure of the cost associated with each edge in the graph.
The Normalized Cut technique is used for graph segmentation, aiming to minimize the cut cost while considering the size of each subset. This technique involves calculating the degree matrix D, the weight matrix W, and the Laplacian matrix L, followed by eigenvalue decomposition and K- means clustering to segment the graph into different regions.
For example, after obtaining the segmentation, the maximum bit consumption per node, the estimated time required for distribution, and the expected number of quantum gates used are calculated to ensure that the nodes have sufficient resources and the operation time is within acceptable limits.
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IEEE/ICACT20250011 Slide.13
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