{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,11,12]],"date-time":"2026-11-12T20:52:36Z","timestamp":1794516756214,"version":"4.9.1"},"publisher-location":"New York, NY","reference-count":14,"publisher":"Springer New York","isbn-type":[{"value":"9781493928637","type":"print"},{"value":"9781493928644","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-1-4939-2864-4_391","type":"book-chapter","created":{"date-parts":[[2016,4,21]],"date-time":"2016-04-21T20:03:20Z","timestamp":1461269000000},"page":"2047-2051","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sphere Packing Problem"],"prefix":"10.1007","author":[{"given":"Danny Z.","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,4,22]]},"reference":[{"key":"391_CR19585","unstructured":"Amato NM, Goodrich MT, Ramos EA (2000) Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling. In: Proceedings of the 11th annual ACM-SIAM symposium on discrete algorithms, pp 705\u2013706"},{"issue":"3","key":"391_CR19586","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s00453-001-0022-x","volume":"30","author":"C Baur","year":"2001","unstructured":"Baur C, Fekete SP (2001) Approximation of geometric dispersion problems. Algorithmica 30(3):451\u2013470","journal-title":"Algorithmica"},{"key":"391_CR19587","doi-asserted-by":"crossref","unstructured":"Bourland JD, Wu QR (1996) Use of shape for automated, optimized 3D radiosurgical treatment planning. In: Proceedings of the SPIE international symposium on medical imaging, pp 553\u2013558","DOI":"10.1007\/BFb0046998"},{"key":"391_CR19588","doi-asserted-by":"crossref","unstructured":"Chen DZ, Hu X, Huang Y, Li Y, Xu J (2001) Algorithms for congruent sphere packing and applications. In: Proceedings of the 17th annual ACM symposium on computational geometry, pp 212\u2013221","DOI":"10.1145\/378583.378672"},{"key":"391_CR19589","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2016-7","volume-title":"Sphere packings, lattices and groups","author":"JH Conway","year":"1988","unstructured":"Conway JH, Sloane NJA (1988) Sphere packings, lattices and groups. Springer, New York"},{"key":"391_CR19590","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/0304-3975(92)90319-B","volume":"92","author":"H Edelsbrunner","year":"1992","unstructured":"Edelsbrunner H, Guibas LJ, Pach J, Pollack R, Seidel R, Sharir M (1992) Arrangements of curves in the plane: topology, combinatorics, and algorithms. Theor Comput Sci 92:319\u2013336","journal-title":"Theor Comput Sci"},{"issue":"3","key":"391_CR19591","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1016\/0020-0190(81)90111-3","volume":"12","author":"RJ Fowler","year":"1981","unstructured":"Fowler RJ, Paterson MS, Tanimoto SL (1981) Optimal packing and covering in the plane are NP-complete. Inf Process Lett 12(3):133\u2013137","journal-title":"Inf Process Lett"},{"issue":"1","key":"391_CR19592","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1145\/2455.214106","volume":"32","author":"DS Hochbaum","year":"1985","unstructured":"Hochbaum DS, Maass W (1985) Approximation schemes for covering and packing problems in image processing and VLSI. J ACM 32(1):130\u2013136","journal-title":"J ACM"},{"issue":"1\u20132","key":"391_CR19593","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1002\/1097-0207(20000910\/20)49:1\/2<61::AID-NME923>3.0.CO;2-Y","volume":"49","author":"XY Li","year":"2000","unstructured":"Li XY, Teng SH, \u00dcng\u00f6r A (2000) Biting: advancing front meets sphere packing. Int J Numer Methods Eng 49(1\u20132):61\u201381","journal-title":"Int J Numer Methods Eng"},{"key":"391_CR19594","doi-asserted-by":"crossref","unstructured":"Milenkovic VJ (2000) Densest translational lattice packing of nonconvex polygons. In: Proceedings of the 16th ACM annual symposium on computational geometry, pp 280\u2013289","DOI":"10.1145\/336154.336214"},{"issue":"12","key":"391_CR19595","doi-asserted-by":"publisher","first-page":"2748","DOI":"10.1118\/1.1328080","volume":"27","author":"DM Shepard","year":"2000","unstructured":"Shepard DM, Ferris MC, Ove R, Ma L (2000) Inverse treatment planning for Gamma Knife radiosurgery. Med Phys 27(12):2748\u20132756","journal-title":"Med Phys"},{"issue":"3","key":"391_CR19596","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1023\/A:1016083231326","volume":"114","author":"A Sutou","year":"2002","unstructured":"Sutou A, Dai Y (2002) Global optimization approach to unequal sphere packing problems in 3D. J Optim Theory Appl 114(3):671\u2013694","journal-title":"J Optim Theory Appl"},{"key":"391_CR19597","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1023\/A:1009831621621","volume":"3","author":"J Wang","year":"1999","unstructured":"Wang J (1999) Medial axis and optimal locations for min-max sphere packing. J Comb Optim 3:453\u2013463","journal-title":"J Comb Optim"},{"key":"391_CR19598","unstructured":"Wu QR (1996) Treatment planning optimization for Gamma unit radiosurgery. Ph.D. thesis, The Mayo Graduate School"}],"container-title":["Encyclopedia of Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-1-4939-2864-4_391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T23:53:38Z","timestamp":1792108418000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/chapter\/10.1007\/978-1-4939-2864-4_391"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9781493928637","9781493928644"],"references-count":14,"URL":"https:\/\/doi.org\/10.1007\/978-1-4939-2864-4_391","relation":{"is-part-of":[{"id-type":"doi","id":"https:\/\/doi.org\/10.1007\/978-1-4939-2864-4","asserted-by":"object"}]},"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"22 April 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}