{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T08:01:16Z","timestamp":1761897676490,"version":"3.41.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T00:00:00Z","timestamp":1644883200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2022,2,15]]},"abstract":"<jats:p> Crystal Structure Prediction (CSP) is one of the central and most challenging problems in materials science and computational chemistry. In CSP, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as \u201cNP-Hard and very challenging\u201d without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of CSP with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the CSP removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of CSP. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space. <\/jats:p>","DOI":"10.3233\/fi-2021-2096","type":"journal-article","created":{"date-parts":[[2022,2,15]],"date-time":"2022-02-15T17:35:23Z","timestamp":1644946523000},"page":"181-203","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["On the Hardness of Energy Minimisation for Crystal Structure Prediction"],"prefix":"10.1177","volume":"184","author":[{"given":"Duncan","family":"Adamson","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool, UK."}]},{"given":"Argyrios","family":"Deligkas","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Royal Holloway University of London, London, UK."}]},{"given":"Vladimir","family":"Gusev","sequence":"additional","affiliation":[{"name":"Leverhulme Research Centre for Functional Materials Design, University of Liverpool, Liverpool, UK."}]},{"given":"Igor","family":"Potapov","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Liverpool, Liverpool, UK."}]}],"member":"179","published-online":{"date-parts":[[2022,2,15]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2021-2096","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2021-2096","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:55:18Z","timestamp":1751367318000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2021-2096"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,15]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,2,15]]}},"alternative-id":["10.3233\/FI-2021-2096"],"URL":"https:\/\/doi.org\/10.3233\/fi-2021-2096","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2022,2,15]]}}}