{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,12,30]],"date-time":"2022-12-30T19:49:14Z","timestamp":1672429754061},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2012,7]]},"DOI":"10.1007\/s00454-012-9422-8","type":"journal-article","created":{"date-parts":[[2012,3,7]],"date-time":"2012-03-07T09:30:29Z","timestamp":1331112629000},"page":"53-64","source":"Crossref","is-referenced-by-count":4,"title":["Unions of Fat Convex Polytopes Have Short Skeletons"],"prefix":"10.1007","volume":"48","author":[{"given":"Boris","family":"Aronov","sequence":"first","affiliation":[]},{"given":"Mark","family":"de Berg","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,3,8]]},"reference":[{"key":"9422_CR1","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1090\/conm\/453\/08794","volume-title":"Surveys on Discrete and Computational Geometry: Twenty Years Later","author":"P.K. Agarwal","year":"2008","unstructured":"Agarwal, P.K., Pach, J., Sharir, M.: State of the union (of geometric objects): A review. In: Goodman, J., Pach, J., Pollack, R. (eds.) Surveys on Discrete and Computational Geometry: Twenty Years Later, pp. 9\u201348. Am. Math. Soc., Providence (2008)"},{"key":"9422_CR2","unstructured":"Aronov, B., de Berg, M., Ezra, E., Sharir, M.: Improved bound for the union of locally fat objects in the plane. Manuscript"},{"key":"9422_CR3","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1007\/PL00009366","volume":"19","author":"J.-D. Boissonnat","year":"1998","unstructured":"Boissonnat, J.-D., Sharir, M., Tagansky, B., Yvinec, M.: Voronoi diagrams in higher dimensions under certain polyhedral distance functions. Discrete Comput. Geom. 19, 485\u2013519 (1998)","journal-title":"Discrete Comput. Geom."},{"key":"9422_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-93014-0","volume-title":"Theorie der konvexen K\u00f6rper","author":"T. Bonnesen","year":"1974","unstructured":"Bonnesen, T., Fenchel, W.: Theorie der konvexen K\u00f6rper. Springer, Berlin (1974)"},{"key":"9422_CR5","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s00454-007-9029-7","volume":"40","author":"M. Berg de","year":"2008","unstructured":"de Berg, M.: Improved bounds on the union complexity of fat objects. Discrete Comput. Geom. 40, 127\u2013140 (2008)","journal-title":"Discrete Comput. Geom."},{"key":"9422_CR6","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1137\/060672261","volume":"38","author":"M. Berg de","year":"2008","unstructured":"de Berg, M., Gray, C.: Vertical ray shooting and computing depth orders for fat objects. SIAM J. Comput. 38, 257\u2013275 (2008)","journal-title":"SIAM J. Comput."},{"issue":"1","key":"9422_CR7","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1145\/1613676.1613678","volume":"57","author":"E. Ezra","year":"2009","unstructured":"Ezra, E., Sharir, M.: Almost tight bound for the union of fat tetrahedra in three dimensions. J. ACM 57(1), 2 (2009)","journal-title":"J. ACM"},{"key":"9422_CR8","doi-asserted-by":"crossref","first-page":"1778","DOI":"10.1137\/1.9781611973082.136","volume-title":"Proc. Annual ACM-SIAM Symp. Discr. Algorithms","author":"E. Ezra","year":"2011","unstructured":"Ezra, E., Aronov, B., Sharir, M.: Improved bound for the union of fat triangles. In: Proc. Annual ACM-SIAM Symp. Discr. Algorithms, pp. 1778\u20131785 (2011)"},{"key":"9422_CR9","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1017\/S0305004100026542","volume":"47","author":"A.M. Macbeath","year":"1951","unstructured":"Macbeath, A.M.: An extremal property of the hypersphere. Proc. Camb. Philos. Soc. 47, 245\u2013247 (1951)","journal-title":"Proc. Camb. Philos. Soc."},{"key":"9422_CR10","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1137\/S009753979018330X","volume":"23","author":"J. Matou\u0161ek","year":"1994","unstructured":"Matou\u0161ek, J., Pach, J., Sharir, M., Sifrony, S., Welzl, E.: Fat triangles determine linearly many holes. SIAM J. Comput. 23, 154\u2013169 (1994)","journal-title":"SIAM J. Comput."},{"key":"9422_CR11","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1137\/S0097539700382169","volume":"31","author":"J. Pach","year":"2002","unstructured":"Pach, J., Tardos, G.: On the boundary complexity of the union of fat triangles. SIAM J. Comput. 31, 1745\u20131760 (2002)","journal-title":"SIAM J. Comput."},{"key":"9422_CR12","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/s00454-003-2928-3","volume":"30","author":"J. Pach","year":"2003","unstructured":"Pach, J., Safruti, I., Sharir, M.: The union of congruent cubes in three dimensions. Discrete Comput. Geom. 30, 133\u2013160 (2003)","journal-title":"Discrete Comput. Geom."},{"key":"9422_CR13","first-page":"370","volume-title":"Proc. 27th Annu. Symp. Comput. Geometry","author":"S. Pettie","year":"2011","unstructured":"Pettie, S.: On the structure and composition of forbidden sequences, with geometric applications. In: Proc. 27th Annu. Symp. Comput. Geometry, pp. 370\u2013379 (2011)"},{"key":"9422_CR14","volume-title":"Davenport\u2013Schinzel Sequences and Their Geometric Applications","author":"M. Sharir","year":"1996","unstructured":"Sharir, M., Agarwal, P.K.: Davenport\u2013Schinzel Sequences and Their Geometric Applications. Cambridge University Press, New York (1996)"},{"key":"9422_CR15","doi-asserted-by":"crossref","unstructured":"van\u00a0der Stappen, A.F.: Motion planning amidst fat obstacles. Ph.D. thesis, Utrecht University, Utrecht, the Netherlands (1994)","DOI":"10.1145\/177424.177453"},{"key":"9422_CR16","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1016\/0925-7721(93)90007-S","volume":"3","author":"A.F. Stappen van\u00a0der","year":"1993","unstructured":"van\u00a0der Stappen, A.F., Halperin, D., Overmars, M.H.: The complexity of the free space for a robot moving amidst fat obstacles. Comput. Geom., Theory Appl. 3, 353\u2013373 (1993)","journal-title":"Comput. Geom., Theory Appl."},{"key":"9422_CR17","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/BF02187894","volume":"3","author":"A. Wiernik","year":"1988","unstructured":"Wiernik, A., Sharir, M.: Planar realization of nonlinear Davenport\u2013Schinzel sequences by segments. Discrete Comput. Geom. 3, 15\u201347 (1988)","journal-title":"Discrete Comput. Geom."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-012-9422-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,24]],"date-time":"2019-06-24T21:42:29Z","timestamp":1561412549000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-012-9422-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,8]]},"references-count":17,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["9422"],"URL":"https:\/\/doi.org\/10.1007\/s00454-012-9422-8","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,3,8]]}}}