Guillotine cutting is asymptotically optimal for packing consecutive squares
Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summin...
Ausführliche Beschreibung
Autor*in: |
Balogh, János [verfasserIn] |
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E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2022 |
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Schlagwörter: |
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Anmerkung: |
© The Author(s) 2022 |
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Übergeordnetes Werk: |
Enthalten in: Optimization letters - Berlin : Springer, 2007, 16(2022), 9 vom: 19. März, Seite 2775-2785 |
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Übergeordnetes Werk: |
volume:16 ; year:2022 ; number:9 ; day:19 ; month:03 ; pages:2775-2785 |
Links: |
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DOI / URN: |
10.1007/s11590-022-01858-w |
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Katalog-ID: |
SPR048474088 |
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245 | 1 | 0 | |a Guillotine cutting is asymptotically optimal for packing consecutive squares |
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520 | |a Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. | ||
650 | 4 | |a Square packing |7 (dpeaa)DE-He213 | |
650 | 4 | |a Guillotine cut |7 (dpeaa)DE-He213 | |
650 | 4 | |a Asymptotic analysis |7 (dpeaa)DE-He213 | |
650 | 4 | |a Gardner’s problem |7 (dpeaa)DE-He213 | |
650 | 4 | |a Square the square |7 (dpeaa)DE-He213 | |
650 | 4 | |a Recursive algorithm |7 (dpeaa)DE-He213 | |
700 | 1 | |a Dósa, György |4 aut | |
700 | 1 | |a Hvattum, Lars Magnus |4 aut | |
700 | 1 | |a Olaj, Tomas |4 aut | |
700 | 1 | |a Tuza, Zsolt |4 aut | |
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10.1007/s11590-022-01858-w doi (DE-627)SPR048474088 (SPR)s11590-022-01858-w-e DE-627 ger DE-627 rakwb eng Balogh, János verfasserin aut Guillotine cutting is asymptotically optimal for packing consecutive squares 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Square packing (dpeaa)DE-He213 Guillotine cut (dpeaa)DE-He213 Asymptotic analysis (dpeaa)DE-He213 Gardner’s problem (dpeaa)DE-He213 Square the square (dpeaa)DE-He213 Recursive algorithm (dpeaa)DE-He213 Dósa, György aut Hvattum, Lars Magnus aut Olaj, Tomas aut Tuza, Zsolt aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2022), 9 vom: 19. März, Seite 2775-2785 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2022 number:9 day:19 month:03 pages:2775-2785 https://dx.doi.org/10.1007/s11590-022-01858-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2022 9 19 03 2775-2785 |
spelling |
10.1007/s11590-022-01858-w doi (DE-627)SPR048474088 (SPR)s11590-022-01858-w-e DE-627 ger DE-627 rakwb eng Balogh, János verfasserin aut Guillotine cutting is asymptotically optimal for packing consecutive squares 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Square packing (dpeaa)DE-He213 Guillotine cut (dpeaa)DE-He213 Asymptotic analysis (dpeaa)DE-He213 Gardner’s problem (dpeaa)DE-He213 Square the square (dpeaa)DE-He213 Recursive algorithm (dpeaa)DE-He213 Dósa, György aut Hvattum, Lars Magnus aut Olaj, Tomas aut Tuza, Zsolt aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2022), 9 vom: 19. März, Seite 2775-2785 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2022 number:9 day:19 month:03 pages:2775-2785 https://dx.doi.org/10.1007/s11590-022-01858-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2022 9 19 03 2775-2785 |
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10.1007/s11590-022-01858-w doi (DE-627)SPR048474088 (SPR)s11590-022-01858-w-e DE-627 ger DE-627 rakwb eng Balogh, János verfasserin aut Guillotine cutting is asymptotically optimal for packing consecutive squares 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Square packing (dpeaa)DE-He213 Guillotine cut (dpeaa)DE-He213 Asymptotic analysis (dpeaa)DE-He213 Gardner’s problem (dpeaa)DE-He213 Square the square (dpeaa)DE-He213 Recursive algorithm (dpeaa)DE-He213 Dósa, György aut Hvattum, Lars Magnus aut Olaj, Tomas aut Tuza, Zsolt aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2022), 9 vom: 19. März, Seite 2775-2785 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2022 number:9 day:19 month:03 pages:2775-2785 https://dx.doi.org/10.1007/s11590-022-01858-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2022 9 19 03 2775-2785 |
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10.1007/s11590-022-01858-w doi (DE-627)SPR048474088 (SPR)s11590-022-01858-w-e DE-627 ger DE-627 rakwb eng Balogh, János verfasserin aut Guillotine cutting is asymptotically optimal for packing consecutive squares 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Square packing (dpeaa)DE-He213 Guillotine cut (dpeaa)DE-He213 Asymptotic analysis (dpeaa)DE-He213 Gardner’s problem (dpeaa)DE-He213 Square the square (dpeaa)DE-He213 Recursive algorithm (dpeaa)DE-He213 Dósa, György aut Hvattum, Lars Magnus aut Olaj, Tomas aut Tuza, Zsolt aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2022), 9 vom: 19. März, Seite 2775-2785 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2022 number:9 day:19 month:03 pages:2775-2785 https://dx.doi.org/10.1007/s11590-022-01858-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2022 9 19 03 2775-2785 |
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10.1007/s11590-022-01858-w doi (DE-627)SPR048474088 (SPR)s11590-022-01858-w-e DE-627 ger DE-627 rakwb eng Balogh, János verfasserin aut Guillotine cutting is asymptotically optimal for packing consecutive squares 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. Square packing (dpeaa)DE-He213 Guillotine cut (dpeaa)DE-He213 Asymptotic analysis (dpeaa)DE-He213 Gardner’s problem (dpeaa)DE-He213 Square the square (dpeaa)DE-He213 Recursive algorithm (dpeaa)DE-He213 Dósa, György aut Hvattum, Lars Magnus aut Olaj, Tomas aut Tuza, Zsolt aut Enthalten in Optimization letters Berlin : Springer, 2007 16(2022), 9 vom: 19. März, Seite 2775-2785 (DE-627)534676499 (DE-600)2374345-1 1862-4480 nnns volume:16 year:2022 number:9 day:19 month:03 pages:2775-2785 https://dx.doi.org/10.1007/s11590-022-01858-w kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2022 9 19 03 2775-2785 |
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Enthalten in Optimization letters 16(2022), 9 vom: 19. März, Seite 2775-2785 volume:16 year:2022 number:9 day:19 month:03 pages:2775-2785 |
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Square packing Guillotine cut Asymptotic analysis Gardner’s problem Square the square Recursive algorithm |
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Balogh, János @@aut@@ Dósa, György @@aut@@ Hvattum, Lars Magnus @@aut@@ Olaj, Tomas @@aut@@ Tuza, Zsolt @@aut@@ |
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Balogh, János |
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Balogh, János misc Square packing misc Guillotine cut misc Asymptotic analysis misc Gardner’s problem misc Square the square misc Recursive algorithm Guillotine cutting is asymptotically optimal for packing consecutive squares |
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Guillotine cutting is asymptotically optimal for packing consecutive squares Square packing (dpeaa)DE-He213 Guillotine cut (dpeaa)DE-He213 Asymptotic analysis (dpeaa)DE-He213 Gardner’s problem (dpeaa)DE-He213 Square the square (dpeaa)DE-He213 Recursive algorithm (dpeaa)DE-He213 |
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misc Square packing misc Guillotine cut misc Asymptotic analysis misc Gardner’s problem misc Square the square misc Recursive algorithm |
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guillotine cutting is asymptotically optimal for packing consecutive squares |
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Guillotine cutting is asymptotically optimal for packing consecutive squares |
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Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. © The Author(s) 2022 |
abstractGer |
Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. © The Author(s) 2022 |
abstract_unstemmed |
Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped. © The Author(s) 2022 |
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Guillotine cutting is asymptotically optimal for packing consecutive squares |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR048474088</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230509114739.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">221028s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11590-022-01858-w</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR048474088</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11590-022-01858-w-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Balogh, János</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Guillotine cutting is asymptotically optimal for packing consecutive squares</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract More than half a century ago Martin Gardner popularized a question leading to the benchmark problem of determining the minimum side length of a square into which the squares of sizes %$1,2,\dots ,n%$ can be packed without overlap. Constructions are known for a certain range of n, and summing up the areas yields that a packing in a square of size smaller than %$N:= \!\sqrt{n(n+1)(2n+1)/6)} %$ is not possible. Here we prove that an asymptotically minimal packing exists in a square of size %$N+cn+O(\!\sqrt{n})%$ with %$c<1%$, and such a packing is achievable with guillotine-cuts. An improved construction is also given for the case where the constraint of guillotine cutting is dropped.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Square packing</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Guillotine cut</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Asymptotic analysis</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gardner’s problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Square the square</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Recursive algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dósa, György</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hvattum, Lars Magnus</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Olaj, Tomas</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tuza, Zsolt</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Optimization letters</subfield><subfield code="d">Berlin : Springer, 2007</subfield><subfield code="g">16(2022), 9 vom: 19. März, Seite 2775-2785</subfield><subfield code="w">(DE-627)534676499</subfield><subfield code="w">(DE-600)2374345-1</subfield><subfield code="x">1862-4480</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:16</subfield><subfield code="g">year:2022</subfield><subfield code="g">number:9</subfield><subfield code="g">day:19</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:2775-2785</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s11590-022-01858-w</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" 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