The authors formalize tensor-network contraction orders as contraction trees, link the space and time bottlenecks to carving-width and treewidth, and show experimentally that a Ratcatcher-based planner produces near-optimal orders on planar grid networks.
Weighted Treewidth: Algorithmic Techniques and Results
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Carving-width and contraction trees for tensor networks
The authors formalize tensor-network contraction orders as contraction trees, link the space and time bottlenecks to carving-width and treewidth, and show experimentally that a Ratcatcher-based planner produces near-optimal orders on planar grid networks.