What question did this study set out to answer?

The research aims to establish a comprehensive framework for understanding the computational complexity of tensor network contractions.

Exponential time complexity for contracting tensor networks

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This article demonstrates efficient tensor network contraction algorithms, indicating advancements in computational complexity analysis.

The research aims to establish a comprehensive framework for understanding the computational complexity of tensor network contractions.
Developed edge separator theorems for specific graph classes.
Presented sub-exponential contraction algorithms for finite element and H-minor-free graphs.
Transformed high-dimensional tensors into low-dimensional series using two methods: the adder gadget and CANDECOMP/PARAFAC decomposition.
Proved lower bounds under #ETH for algorithm optimality.
Introduced a treewidth-parameterized contraction algorithm.
Established a near-optimal framework for tensor network contractions using edge separators.
Achieved sub-exponential time complexity for specific graph classes.
Provided a fine-grained dichotomy for tensor network contraction based on Hadwiger number.
Demonstrated algorithm efficiency through innovative tensor transformations.

Liu et al. (2025) studied this question.

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