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We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.<\/jats:p>","DOI":"10.1088\/2632-2153\/ab94c5","type":"journal-article","created":{"date-parts":[[2020,5,20]],"date-time":"2020-05-20T22:15:24Z","timestamp":1590012924000},"page":"035001","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":8,"title":["Algorithms for tensor network contraction ordering"],"prefix":"10.1088","volume":"1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8113-0998","authenticated-orcid":false,"given":"Frank","family":"Schindler","sequence":"first","affiliation":[]},{"given":"Adam S","family":"Jermyn","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,7,2]]},"reference":[{"key":"mlstab94c5bib1","doi-asserted-by":"publisher","first-page":"2863","DOI":"10.1103\/PhysRevLett.69.2863","volume":"69","author":"White","year":"1992","journal-title":"Phys. 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