We study the problem of finding contraction orderings on tensor networks for physical simulations using a syncretic abstract data type, the contraction-tree, and explain its connection to temporal and spatial measures of tensor contraction computational complexity (nodes express time; arcs express space). We have implemented the Ratcatcher of Seymour and Thomas for determining the carving-width of planar networks, in order to offer experimental evidence that this measure of spatial complexity makes a generally effective heuristic for limiting their total contraction time.
@article{arxiv.1908.11034,
title = {Carving-width and contraction trees for tensor networks},
author = {J. Jakes-Schauer and D. Anekstein and P. Wocjan},
journal= {arXiv preprint arXiv:1908.11034},
year = {2019}
}