{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,15]],"date-time":"2025-06-15T13:40:18Z","timestamp":1749994818015},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2018,3,4]],"date-time":"2018-03-04T00:00:00Z","timestamp":1520121600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Eur. J. Appl. Math"],"published-print":{"date-parts":[[2019,4]]},"abstract":"<jats:p>During the 125th European Study Group with Industry held in Limassol, Cyprus, 5\u20139 December 2016, one of the participating companies, Engino.net Ltd, posed a very interesting challenge to the members of the study group. Engino.net Ltd is a Cypriot company, founded in 2004, that produces a series of toy sets \u2013 the Engino\u00ae toy sets \u2013 consisting of a number of building blocks, which can be assembled by pupils to compose toy models. Depending on the contents of a particular toy set, the company has developed a number of models that can be built utilizing the blocks present in the set; however, the production of a step-by-step assembly manual for each model could only be done manually. The goal of the challenge posed by the company was to implement a procedure to automatically generate the assembly instructions for a given toy. In the present paper, we propose a graph-theoretic approach to model the problem and provide a series of results to solve it by employing modified versions of well-established algorithms in graph theory. An algorithmic procedure to obtain a hierarchical, physically feasible decomposition of a given toy model, from which a series of step-by-step assembly instructions can be recovered, is proposed.<\/jats:p>","DOI":"10.1017\/s0956792518000086","type":"journal-article","created":{"date-parts":[[2018,3,4]],"date-time":"2018-03-04T14:15:28Z","timestamp":1520172928000},"page":"278-297","source":"Crossref","is-referenced-by-count":2,"title":["Physically feasible decomposition of Engino\u00ae toy models: A graph-theoretic approach"],"prefix":"10.1017","volume":"30","author":[{"given":"E. N.","family":"ANTONIOU","sequence":"first","affiliation":[]},{"given":"A.","family":"ARA\u00daJO","sequence":"additional","affiliation":[]},{"given":"M. D.","family":"BUSTAMANTE","sequence":"additional","affiliation":[]},{"given":"A.","family":"GIBALI","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,3,4]]},"reference":[{"key":"S0956792518000086_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(94)90048-5"},{"key":"S0956792518000086_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574386"},{"key":"S0956792518000086_ref11","unstructured":"Peysakhov M. , Galinskaya V. & Regli W. C. (2000) Representation and evolution of lego-based assemblies. In: Proceedings of the AAAI\/IAAI, p. 1089."},{"key":"S0956792518000086_ref10","doi-asserted-by":"publisher","DOI":"10.1145\/73393.73424"},{"key":"S0956792518000086_ref8","doi-asserted-by":"publisher","DOI":"10.1080\/0020754031000120078"},{"key":"S0956792518000086_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-010-3093-5"},{"key":"S0956792518000086_ref9","doi-asserted-by":"crossref","unstructured":"Li W. , Agrawala M. , Curless B. & Salesin D. (2008) Automated generation of interactive 3D exploded view diagrams. 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