. . . "deBruijnsTheorem"@en . . . . . . . . . . . . . . . "Packing problems"@en . . . . . . . . . "213003"^^ . "\uCC44\uC6B0\uAE30 \uBB38\uC81C"@ko . "\uCC44\uC6B0\uAE30 \uBB38\uC81C(\uC601\uC5B4: packing problems)\uB294 \uBB3C\uCCB4\uB97C \uC6A9\uAE30\uC5D0 \uCC44\uC6B0\uB294 \uC218\uD559\uC758 \uCD5C\uC801\uD654 \uBB38\uC81C\uC774\uB2E4. \uBAA9\uD45C\uB294 \uD558\uB098\uC758 \uC6A9\uAE30\uC5D0 \uBB3C\uCCB4\uB97C \uAC00\uB2A5\uD55C \uD55C \uBE7D\uBE7D\uD558\uAC8C \uCC44\uC6B0\uAC70\uB098 \uBAA8\uB4E0 \uBB3C\uCCB4\uB97C \uAC00\uB2A5\uD55C \uD55C \uC801\uC740 \uC6A9\uAE30\uC5D0 \uCC44\uC6B0\uB294 \uAC83\uC774\uB2E4. \uC774 \uBB38\uC81C\uC758 \uB300\uBD80\uBD84\uC740 \uC2E4\uC0DD\uD65C\uC5D0 \uD3EC\uC7A5, \uC800\uC7A5 \uADF8\uB9AC\uACE0 \uC218\uC1A1 \uBB38\uC81C\uC640 \uAD00\uACC4\uC9C0\uC744 \uC218 \uC788\uB2E4. \uAC01 \uCC44\uC6B0\uAE30 \uBB38\uC81C\uB294 \uC774\uC911 \uAC00 \uC788\uB2E4. \uC774\uAC83\uC740 \uACB9\uCE58\uB294 \uAC83\uC744 \uD5C8\uC6A9\uD558\uC5EC \uC6A9\uAE30\uC758 \uBAA8\uB4E0 \uC601\uC5ED\uC744 \uB3D9\uC77C\uD55C \uBB3C\uCCB4\uB85C \uC644\uC804\uD788 \uB36E\uB294\uB370 \uBA87 \uAC1C\uAC00 \uB4E4\uC5B4\uAC00\uB294\uC9C0\uB97C \uAD6C\uD558\uB294 \uBB38\uC81C\uC774\uB2E4. \uB294 \uB2E4\uC74C\uC774 \uC8FC\uC5B4\uC9C4\uB2E4: \n* '\uC6A9\uAE30' (\uBCF4\uD1B5 \uB2E8\uC77C 2 \uB610\uB294 3\uCC28\uC6D0 \uBCFC\uB85D\uD55C \uC601\uC5ED\uC774\uB098 \uBB34\uD55C\uD55C \uACF5\uAC04\uC774\uB2E4) \n* \uC77C\uBD80 \uB610\uB294 \uBAA8\uB450\uAC00 \uD558\uB098 \uC774\uC0C1\uC758 \uC6A9\uAE30\uC5D0 \uB4E4\uC5B4\uAC00\uC57C \uD558\uB294 '\uBB3C\uCCB4'\uC758 \uC9D1\uD569. \uC9D1\uD569\uC740 \uD06C\uAE30\uAC00 \uC815\uD574\uC9C4 \uB2E4\uB978 \uBB3C\uCCB4 \uB610\uB294 \uBC18\uBCF5\uD574\uC11C \uC0AC\uC6A9\uD560 \uC218 \uC788\uB294 \uC720\uC77C\uD55C \uACE0\uC815\uB41C \uCC28\uC6D0\uC758 \uBB3C\uCCB4\uB97C \uD3EC\uD568\uD55C\uB2E4. \uBCF4\uD1B5 \uCC44\uC6B0\uAE30\uB294 \uBB3C\uAC74\uACFC \uB2E4\uB978 \uBB3C\uAC74 \uC0AC\uC774\uB098 \uC6A9\uAE30 \uBCBD \uC0AC\uC774\uC5D0 \uACB9\uCE58\uB294 \uC77C\uC774 \uC5C6\uC5B4\uC57C \uD55C\uB2E4. \uC77C\uBD80 \uBCC0\uD615\uC5D0\uC11C \uCD08\uC810\uC740 \uC6A9\uAE30\uC5D0 \uCD5C\uB300 \uBC00\uB3C4\uB85C \uCC44\uC6B0\uB294 \uAD6C\uC131\uC744 \uCC3E\uB294 \uAC83\uC774\uB2E4. \uB354 \uC77C\uBC18\uC801\uC73C\uB85C \uBAA9\uD45C\uB294 \uAC00\uB2A5\uD55C \uC801\uC740 \uC6A9\uAE30\uC5D0 \uBAA8\uB4E0 \uBB3C\uCCB4\uB97C \uB2F4\uB294 \uAC83\uC774\uB2E4. \uC5B4\uB5A4 \uBCC0\uD615\uC5D0\uC11C (\uBB3C\uCCB4\uC640 \uBB3C\uCCB4\uAC04 \uADF8\uB9AC\uACE0/\uB610\uB294 \uC6A9\uAE30\uC758 \uACBD\uACC4\uC5D0\uC11C) \uACB9\uCE58\uB294 \uAC83\uC740 \uD5C8\uB77D\uB418\uC9C0\uB9CC \uCD5C\uC18C\uD654\uB418\uC5B4\uC57C \uD55C\uB2E4."@ko . . . . . . . . . . . . "Pakadaj problemoj estas speco de problemoj en matematiko. En pakada problemo estas donitaj: \n* unu a\u016D pli multaj (kutime du-dimensiaj a\u016D tri-dimensiaj) konteneroj; \n* kelkaj 'varoj', iuj a\u016D \u0109iuj el kiuj devas esti pakitaj en \u0109i tiujn kontenerojn. Kutime la problemoj enga\u011Das trovadon de la maksimuma kvanto de certaj formoj kiuj povas esti pakitaj, a\u016D trovadon de la minimuma amplekso de la kontenero. E\u0109 se iu pakado estas la plej densa ebla, iam okazas ke iu el la pakitaj eroj havas liberecon de movo en iu regiono."@eo . . . . "Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, you are given: \n* A container, usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. \n* A set of objects, some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packing must be without overlaps between goods and other goods or the container walls. In some variants, the aim is to find the configuration that packs a single container with the maximal packing density. More commonly, the aim is to pack all the objects into as few containers as possible. In some variants the overlapping (of objects with each other and/or with the boundary of the container) is allowed but should be minimized."@en . . . . . . . . . . . . . . . . . . . . . "\u0417\u0430\u0434\u0430\u0447\u0438 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u2014 \u044D\u0442\u043E \u043A\u043B\u0430\u0441\u0441 \u0437\u0430\u0434\u0430\u0447 \u043E\u043F\u0442\u0438\u043C\u0438\u0437\u0430\u0446\u0438\u0438 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435, \u0432 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043F\u044B\u0442\u0430\u044E\u0442\u0441\u044F \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u0442\u044C \u043E\u0431\u044A\u0435\u043A\u0442\u044B \u0432 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u044B. \u0426\u0435\u043B\u044C \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u2014 \u043B\u0438\u0431\u043E \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u0442\u044C \u043E\u0442\u0434\u0435\u043B\u044C\u043D\u044B\u0439 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440 \u043A\u0430\u043A \u043C\u043E\u0436\u043D\u043E \u043F\u043B\u043E\u0442\u043D\u0435\u0435, \u043B\u0438\u0431\u043E \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u0442\u044C \u0432\u0441\u0435 \u043E\u0431\u044A\u0435\u043A\u0442\u044B, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u0432 \u043A\u0430\u043A \u043C\u043E\u0436\u043D\u043E \u043C\u0435\u043D\u044C\u0448\u0435 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u043E\u0432. \u041C\u043D\u043E\u0433\u0438\u0435 \u0438\u0437 \u0442\u0430\u043A\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u043C\u043E\u0433\u0443\u0442 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u044C\u0441\u044F \u043A \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0435 \u043F\u0440\u0435\u0434\u043C\u0435\u0442\u043E\u0432 \u0432 \u0440\u0435\u0430\u043B\u044C\u043D\u043E\u0439 \u0436\u0438\u0437\u043D\u0438, \u0432\u043E\u043F\u0440\u043E\u0441\u0430\u043C \u0441\u043A\u043B\u0430\u0434\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u044F \u0438 \u0442\u0440\u0430\u043D\u0441\u043F\u043E\u0440\u0442\u0438\u0440\u043E\u0432\u043A\u0438. \u041A\u0430\u0436\u0434\u0430\u044F \u0437\u0430\u0434\u0430\u0447\u0430 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u0438\u043C\u0435\u0435\u0442 \u0434\u0432\u043E\u0439\u0441\u0442\u0432\u0435\u043D\u043D\u0443\u044E , \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0441\u043F\u0440\u0430\u0448\u0438\u0432\u0430\u0435\u0442\u0441\u044F, \u043A\u0430\u043A \u043C\u043D\u043E\u0433\u043E \u0442\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043F\u0440\u0435\u0434\u043C\u0435\u0442\u043E\u0432, \u0447\u0442\u043E\u0431\u044B \u043F\u043E\u043B\u043D\u043E\u0441\u0442\u044C\u044E \u043F\u043E\u043A\u0440\u044B\u0442\u044C \u0432\u0441\u0435 \u043E\u0431\u043B\u0430\u0441\u0442\u0438 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u0430, \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u043F\u0440\u0435\u0434\u043C\u0435\u0442\u044B \u043C\u043E\u0433\u0443\u0442 \u043D\u0430\u043A\u043B\u0430\u0434\u044B\u0432\u0430\u0442\u044C\u0441\u044F. \u0412 \u0437\u0430\u0434\u0430\u0447\u0435 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u0437\u0430\u0434\u0430\u043D\u043E: \n* \u00AB\u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u044B\u00BB (\u043E\u0431\u044B\u0447\u043D\u043E \u043E\u0434\u043D\u0430 \u0434\u0432\u0443\u043C\u0435\u0440\u043D\u0430\u044F \u0438\u043B\u0438 \u0442\u0440\u0451\u0445\u043C\u0435\u0440\u043D\u0430\u044F \u0432\u044B\u043F\u0443\u043A\u043B\u0430\u044F \u043E\u0431\u043B\u0430\u0441\u0442\u044C \u0438\u043B\u0438 \u0431\u0435\u0441\u043A\u043E\u043D\u0435\u0447\u043D\u0430\u044F \u043E\u0431\u043B\u0430\u0441\u0442\u044C) \n* \u043C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u00AB\u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432\u00BB, \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0435 \u0438\u0437 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0438\u043B\u0438 \u0432\u0441\u0435 \u0434\u043E\u043B\u0436\u043D\u044B \u0431\u044B\u0442\u044C \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u043D\u044B \u0432 \u043E\u0434\u0438\u043D \u0438\u043B\u0438 \u043D\u0435\u0441\u043A\u043E\u043B\u044C\u043A\u043E \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u043E\u0432. \u041C\u043D\u043E\u0436\u0435\u0441\u0442\u0432\u043E \u043C\u043E\u0436\u0435\u0442 \u0441\u043E\u0434\u0435\u0440\u0436\u0430\u0442\u044C \u0440\u0430\u0437\u043B\u0438\u0447\u043D\u044B\u0435 \u043E\u0431\u044A\u0435\u043A\u0442\u044B \u0441 \u0437\u0430\u0434\u0430\u043D\u043D\u044B\u043C\u0438 \u0440\u0430\u0437\u043C\u0435\u0440\u0430\u043C\u0438, \u0438\u043B\u0438 \u043E\u0434\u0438\u043D \u043E\u0431\u044A\u0435\u043A\u0442 \u0444\u0438\u043A\u0441\u0438\u0440\u043E\u0432\u0430\u043D\u043D\u044B\u0445 \u0440\u0430\u0437\u043C\u0435\u0440\u043E\u0432, \u043A\u043E\u0442\u043E\u0440\u044B\u0439 \u043C\u043E\u0436\u0435\u0442 \u0431\u044B\u0442\u044C \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u043D \u043D\u0435\u0441\u043A\u043E\u043B\u044C\u043A\u043E \u0440\u0430\u0437. \u041E\u0431\u044B\u0447\u043D\u043E \u0432 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0435 \u043E\u0431\u044A\u0435\u043A\u0442\u044B \u043D\u0435 \u0434\u043E\u043B\u0436\u043D\u044B \u043F\u0435\u0440\u0435\u0441\u0435\u043A\u0430\u0442\u044C\u0441\u044F \u0438 \u043E\u0431\u044A\u0435\u043A\u0442\u044B \u043D\u0435 \u0434\u043E\u043B\u0436\u043D\u044B \u043F\u0435\u0440\u0435\u0441\u0435\u043A\u0430\u0442\u044C \u0441\u0442\u0435\u043D\u044B \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u0430. \u0412 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0432\u0430\u0440\u0438\u0430\u043D\u0442\u0430\u0445 \u0446\u0435\u043B\u044C \u0437\u0430\u043A\u043B\u044E\u0447\u0430\u0435\u0442\u0441\u044F \u0432 \u043D\u0430\u0445\u043E\u0436\u0434\u0435\u043D\u0438\u0438 \u043A\u043E\u043D\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u0438, \u043A\u043E\u0442\u043E\u0440\u0430\u044F \u0443\u043F\u0430\u043A\u043E\u0432\u044B\u0432\u0430\u0435\u0442 \u043E\u0434\u0438\u043D \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440 \u0441 \u043C\u0430\u043A\u0441\u0438\u043C\u0430\u043B\u044C\u043D\u043E\u0439 \u043F\u043B\u043E\u0442\u043D\u043E\u0441\u0442\u044C\u044E. \u0412 \u0431\u043E\u043B\u0435\u0435 \u043E\u0431\u0449\u0435\u043C \u0432\u0438\u0434\u0435 \u0446\u0435\u043B\u044C\u044E \u044F\u0432\u043B\u044F\u0435\u0442\u0441\u044F \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0430 \u0432\u0441\u0435\u0445 \u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432 \u0432 \u043A\u0430\u043A \u043C\u043E\u0436\u043D\u043E \u043C\u0435\u043D\u044C\u0448\u0435 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u043E\u0432. \u0412 \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u0432\u0430\u0440\u0438\u0430\u043D\u0442\u0430\u0445 \u043D\u0430\u043B\u043E\u0436\u0435\u043D\u0438\u0435 (\u043E\u0431\u044A\u0435\u043A\u0442\u043E\u0432 \u0434\u0440\u0443\u0433 \u043D\u0430 \u0434\u0440\u0443\u0433\u0430 \u0438/\u0438\u043B\u0438 \u043D\u0430 \u0433\u0440\u0430\u043D\u0438\u0446\u044B \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u0430) \u0440\u0430\u0437\u0440\u0435\u0448\u0430\u0435\u0442\u0441\u044F, \u043D\u043E \u044D\u0442\u043E \u043D\u0430\u043B\u043E\u0436\u0435\u043D\u0438\u0435 \u0434\u043E\u043B\u0436\u043D\u043E \u0431\u044B\u0442\u044C \u043C\u0438\u043D\u0438\u043C\u0438\u0437\u0438\u0440\u043E\u0432\u0430\u043D\u043E."@ru . . . "de Bruijn's Theorem"@en . "Klarner's Theorem"@en . . "\u30D1\u30C3\u30AD\u30F3\u30B0\u554F\u984C\uFF08\u82F1: Packing problems\uFF09\u306F\u3001\u6570\u5B66\u30D1\u30BA\u30EB\u306E\u4E00\u7A2E\u3002\u3042\u308B\u7269\u4F53\u306B\u3001\u5225\u306E\u3042\u308B\u7269\u4F53\uFF08\u3059\u3079\u3066\u540C\u3058\u5927\u304D\u3055\u3068\u3044\u3046\u6761\u4EF6\u3092\u6307\u5B9A\u3059\u308B\u3053\u3068\u3082\u3042\u308B\uFF09\u3092\u6700\u5927\u9762\u7A4D\u30FB\u6700\u5927\u4F53\u7A4D\u3067\u8A70\u3081\u8FBC\u3080\u3053\u3068\u3092\u3001\u7814\u7A76\u3059\u308B\u3082\u306E\u3002\u300C\u6700\u5BC6\u5186\u30D1\u30C3\u30AD\u30F3\u30B0\u300D\u306A\u3069\u304C\u3042\u308B\u3002"@ja . . . . . . . . . . "KlarnersTheorem"@en . . . . . . "\u30D1\u30C3\u30AD\u30F3\u30B0\u554F\u984C\uFF08\u82F1: Packing problems\uFF09\u306F\u3001\u6570\u5B66\u30D1\u30BA\u30EB\u306E\u4E00\u7A2E\u3002\u3042\u308B\u7269\u4F53\u306B\u3001\u5225\u306E\u3042\u308B\u7269\u4F53\uFF08\u3059\u3079\u3066\u540C\u3058\u5927\u304D\u3055\u3068\u3044\u3046\u6761\u4EF6\u3092\u6307\u5B9A\u3059\u308B\u3053\u3068\u3082\u3042\u308B\uFF09\u3092\u6700\u5927\u9762\u7A4D\u30FB\u6700\u5927\u4F53\u7A4D\u3067\u8A70\u3081\u8FBC\u3080\u3053\u3068\u3092\u3001\u7814\u7A76\u3059\u308B\u3082\u306E\u3002\u300C\u6700\u5BC6\u5186\u30D1\u30C3\u30AD\u30F3\u30B0\u300D\u306A\u3069\u304C\u3042\u308B\u3002"@ja . . . . . . "Pakadaj problemoj estas speco de problemoj en matematiko. En pakada problemo estas donitaj: \n* unu a\u016D pli multaj (kutime du-dimensiaj a\u016D tri-dimensiaj) konteneroj; \n* kelkaj 'varoj', iuj a\u016D \u0109iuj el kiuj devas esti pakitaj en \u0109i tiujn kontenerojn. Kutime la pakado devas esti sen bre\u0109oj a\u016D interkovroj, sed en iuj pakadaj problemoj la interkovroj (de varoj unu la alian a\u016D kun la rando de la kontenero estas permesita sed devus esti farita kiel eblas pli malgranda. En la aliaj, bre\u0109oj estas permesitaj, sed interkovroj estas ne permesitaj, kutime la tuteca areo de bre\u0109oj devus esti farita kiel eblas pli malgranda. Kutime la problemoj enga\u011Das trovadon de la maksimuma kvanto de certaj formoj kiuj povas esti pakitaj, a\u016D trovadon de la minimuma amplekso de la kontenero. E\u0109 se iu pakado estas la plej densa ebla, iam okazas ke iu el la pakitaj eroj havas liberecon de movo en iu regiono."@eo . . . . . "1123757126"^^ . . . "22017"^^ . . "\u0417\u0430\u0434\u0430\u0447\u0438 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438"@ru . . "Los problemas de empaquetado son una clase de problemas de optimizaci\u00F3n en matem\u00E1ticas que implican intentar empaquetar objetos en contenedores. El objetivo es empaquetar un solo contenedor lo m\u00E1s densamente posible o empaquetar todos los objetos usando la menor cantidad de contenedores posible. Muchos de estos problemas pueden estar relacionados con cuestiones reales de embalaje, almacenamiento y transporte. Cada problema de empaque tiene un problema de doble cobertura, que pregunta cu\u00E1ntos de los mismos objetos se requieren para cubrir completamente cada regi\u00F3n del contenedor, donde los objetos pueden superponerse."@es . "\u0417\u0430\u0434\u0430\u0447\u0438 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u2014 \u044D\u0442\u043E \u043A\u043B\u0430\u0441\u0441 \u0437\u0430\u0434\u0430\u0447 \u043E\u043F\u0442\u0438\u043C\u0438\u0437\u0430\u0446\u0438\u0438 \u0432 \u043C\u0430\u0442\u0435\u043C\u0430\u0442\u0438\u043A\u0435, \u0432 \u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043F\u044B\u0442\u0430\u044E\u0442\u0441\u044F \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u0442\u044C \u043E\u0431\u044A\u0435\u043A\u0442\u044B \u0432 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u044B. \u0426\u0435\u043B\u044C \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u2014 \u043B\u0438\u0431\u043E \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u0442\u044C \u043E\u0442\u0434\u0435\u043B\u044C\u043D\u044B\u0439 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440 \u043A\u0430\u043A \u043C\u043E\u0436\u043D\u043E \u043F\u043B\u043E\u0442\u043D\u0435\u0435, \u043B\u0438\u0431\u043E \u0443\u043F\u0430\u043A\u043E\u0432\u0430\u0442\u044C \u0432\u0441\u0435 \u043E\u0431\u044A\u0435\u043A\u0442\u044B, \u0438\u0441\u043F\u043E\u043B\u044C\u0437\u043E\u0432\u0430\u0432 \u043A\u0430\u043A \u043C\u043E\u0436\u043D\u043E \u043C\u0435\u043D\u044C\u0448\u0435 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u043E\u0432. \u041C\u043D\u043E\u0433\u0438\u0435 \u0438\u0437 \u0442\u0430\u043A\u0438\u0445 \u0437\u0430\u0434\u0430\u0447 \u043C\u043E\u0433\u0443\u0442 \u043E\u0442\u043D\u043E\u0441\u0438\u0442\u044C\u0441\u044F \u043A \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0435 \u043F\u0440\u0435\u0434\u043C\u0435\u0442\u043E\u0432 \u0432 \u0440\u0435\u0430\u043B\u044C\u043D\u043E\u0439 \u0436\u0438\u0437\u043D\u0438, \u0432\u043E\u043F\u0440\u043E\u0441\u0430\u043C \u0441\u043A\u043B\u0430\u0434\u0438\u0440\u043E\u0432\u0430\u043D\u0438\u044F \u0438 \u0442\u0440\u0430\u043D\u0441\u043F\u043E\u0440\u0442\u0438\u0440\u043E\u0432\u043A\u0438. \u041A\u0430\u0436\u0434\u0430\u044F \u0437\u0430\u0434\u0430\u0447\u0430 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u0438\u043C\u0435\u0435\u0442 \u0434\u0432\u043E\u0439\u0441\u0442\u0432\u0435\u043D\u043D\u0443\u044E , \u0432 \u043A\u043E\u0442\u043E\u0440\u043E\u0439 \u0441\u043F\u0440\u0430\u0448\u0438\u0432\u0430\u0435\u0442\u0441\u044F, \u043A\u0430\u043A \u043C\u043D\u043E\u0433\u043E \u0442\u0440\u0435\u0431\u0443\u0435\u0442\u0441\u044F \u043D\u0435\u043A\u043E\u0442\u043E\u0440\u044B\u0445 \u043F\u0440\u0435\u0434\u043C\u0435\u0442\u043E\u0432, \u0447\u0442\u043E\u0431\u044B \u043F\u043E\u043B\u043D\u043E\u0441\u0442\u044C\u044E \u043F\u043E\u043A\u0440\u044B\u0442\u044C \u0432\u0441\u0435 \u043E\u0431\u043B\u0430\u0441\u0442\u0438 \u043A\u043E\u043D\u0442\u0435\u0439\u043D\u0435\u0440\u0430, \u043F\u0440\u0438 \u044D\u0442\u043E\u043C \u043F\u0440\u0435\u0434\u043C\u0435\u0442\u044B \u043C\u043E\u0433\u0443\u0442 \u043D\u0430\u043A\u043B\u0430\u0434\u044B\u0432\u0430\u0442\u044C\u0441\u044F. \u0412 \u0437\u0430\u0434\u0430\u0447\u0435 \u0443\u043F\u0430\u043A\u043E\u0432\u043A\u0438 \u0437\u0430\u0434\u0430\u043D\u043E:"@ru . . . "\uCC44\uC6B0\uAE30 \uBB38\uC81C(\uC601\uC5B4: packing problems)\uB294 \uBB3C\uCCB4\uB97C \uC6A9\uAE30\uC5D0 \uCC44\uC6B0\uB294 \uC218\uD559\uC758 \uCD5C\uC801\uD654 \uBB38\uC81C\uC774\uB2E4. \uBAA9\uD45C\uB294 \uD558\uB098\uC758 \uC6A9\uAE30\uC5D0 \uBB3C\uCCB4\uB97C \uAC00\uB2A5\uD55C \uD55C \uBE7D\uBE7D\uD558\uAC8C \uCC44\uC6B0\uAC70\uB098 \uBAA8\uB4E0 \uBB3C\uCCB4\uB97C \uAC00\uB2A5\uD55C \uD55C \uC801\uC740 \uC6A9\uAE30\uC5D0 \uCC44\uC6B0\uB294 \uAC83\uC774\uB2E4. \uC774 \uBB38\uC81C\uC758 \uB300\uBD80\uBD84\uC740 \uC2E4\uC0DD\uD65C\uC5D0 \uD3EC\uC7A5, \uC800\uC7A5 \uADF8\uB9AC\uACE0 \uC218\uC1A1 \uBB38\uC81C\uC640 \uAD00\uACC4\uC9C0\uC744 \uC218 \uC788\uB2E4. \uAC01 \uCC44\uC6B0\uAE30 \uBB38\uC81C\uB294 \uC774\uC911 \uAC00 \uC788\uB2E4. \uC774\uAC83\uC740 \uACB9\uCE58\uB294 \uAC83\uC744 \uD5C8\uC6A9\uD558\uC5EC \uC6A9\uAE30\uC758 \uBAA8\uB4E0 \uC601\uC5ED\uC744 \uB3D9\uC77C\uD55C \uBB3C\uCCB4\uB85C \uC644\uC804\uD788 \uB36E\uB294\uB370 \uBA87 \uAC1C\uAC00 \uB4E4\uC5B4\uAC00\uB294\uC9C0\uB97C \uAD6C\uD558\uB294 \uBB38\uC81C\uC774\uB2E4. \uB294 \uB2E4\uC74C\uC774 \uC8FC\uC5B4\uC9C4\uB2E4: \n* '\uC6A9\uAE30' (\uBCF4\uD1B5 \uB2E8\uC77C 2 \uB610\uB294 3\uCC28\uC6D0 \uBCFC\uB85D\uD55C \uC601\uC5ED\uC774\uB098 \uBB34\uD55C\uD55C \uACF5\uAC04\uC774\uB2E4) \n* \uC77C\uBD80 \uB610\uB294 \uBAA8\uB450\uAC00 \uD558\uB098 \uC774\uC0C1\uC758 \uC6A9\uAE30\uC5D0 \uB4E4\uC5B4\uAC00\uC57C \uD558\uB294 '\uBB3C\uCCB4'\uC758 \uC9D1\uD569. \uC9D1\uD569\uC740 \uD06C\uAE30\uAC00 \uC815\uD574\uC9C4 \uB2E4\uB978 \uBB3C\uCCB4 \uB610\uB294 \uBC18\uBCF5\uD574\uC11C \uC0AC\uC6A9\uD560 \uC218 \uC788\uB294 \uC720\uC77C\uD55C \uACE0\uC815\uB41C \uCC28\uC6D0\uC758 \uBB3C\uCCB4\uB97C \uD3EC\uD568\uD55C\uB2E4. \uBCF4\uD1B5 \uCC44\uC6B0\uAE30\uB294 \uBB3C\uAC74\uACFC \uB2E4\uB978 \uBB3C\uAC74 \uC0AC\uC774\uB098 \uC6A9\uAE30 \uBCBD \uC0AC\uC774\uC5D0 \uACB9\uCE58\uB294 \uC77C\uC774 \uC5C6\uC5B4\uC57C \uD55C\uB2E4. \uC77C\uBD80 \uBCC0\uD615\uC5D0\uC11C \uCD08\uC810\uC740 \uC6A9\uAE30\uC5D0 \uCD5C\uB300 \uBC00\uB3C4\uB85C \uCC44\uC6B0\uB294 \uAD6C\uC131\uC744 \uCC3E\uB294 \uAC83\uC774\uB2E4. \uB354 \uC77C\uBC18\uC801\uC73C\uB85C \uBAA9\uD45C\uB294 \uAC00\uB2A5\uD55C \uC801\uC740 \uC6A9\uAE30\uC5D0 \uBAA8\uB4E0 \uBB3C\uCCB4\uB97C \uB2F4\uB294 \uAC83\uC774\uB2E4. \uC5B4\uB5A4 \uBCC0\uD615\uC5D0\uC11C (\uBB3C\uCCB4\uC640 \uBB3C\uCCB4\uAC04 \uADF8\uB9AC\uACE0/\uB610\uB294 \uC6A9\uAE30\uC758 \uACBD\uACC4\uC5D0\uC11C) \uACB9\uCE58\uB294 \uAC83\uC740 \uD5C8\uB77D\uB418\uC9C0\uB9CC \uCD5C\uC18C\uD654\uB418\uC5B4\uC57C \uD55C\uB2E4."@ko . . . . . . . . . "Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, you are given:"@en . . . . . . . . . . . . . . . "Los problemas de empaquetado son una clase de problemas de optimizaci\u00F3n en matem\u00E1ticas que implican intentar empaquetar objetos en contenedores. El objetivo es empaquetar un solo contenedor lo m\u00E1s densamente posible o empaquetar todos los objetos usando la menor cantidad de contenedores posible. Muchos de estos problemas pueden estar relacionados con cuestiones reales de embalaje, almacenamiento y transporte. Cada problema de empaque tiene un problema de doble cobertura, que pregunta cu\u00E1ntos de los mismos objetos se requieren para cubrir completamente cada regi\u00F3n del contenedor, donde los objetos pueden superponerse. En un problema de embalaje en contenedores, se proporciona: \n* 'contenedores' (generalmente una sola regi\u00F3n convexa bidimensional o tridimensional, o un espacio infinito) \n* Un conjunto de 'objetos' algunos o todos los cuales deben empaquetarse en uno o m\u00E1s contenedores. El conjunto puede contener diferentes objetos con sus tama\u00F1os especificados, o un solo objeto de una dimensi\u00F3n fija que se puede utilizar repetidamente. Por lo general, el embalaje no debe tener superposiciones entre las mercanc\u00EDas y otras mercanc\u00EDas o las paredes del contenedor. En algunas variantes, el objetivo es encontrar la configuraci\u00F3n que empaqueta un solo contenedor con la m\u00E1xima densidad. M\u00E1s com\u00FAnmente, el objetivo es empaquetar todos los objetos en la menor cantidad de contenedores posible.\u200B En algunas variantes, la superposici\u00F3n (de objetos entre s\u00ED y/o con el l\u00EDmite del contenedor) est\u00E1 permitida, pero debe minimizarse."@es . . . . . . . . . . . "\u30D1\u30C3\u30AD\u30F3\u30B0\u554F\u984C"@ja . . . . . . "Problema de empaquetado"@es . . . . . . . . . . "Pakada problemo"@eo . . . . . . . . .