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...
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Autor*in:	Balogh, János [verfasserIn] Dósa, György Hvattum, Lars Magnus Olaj, Tomas Tuza, Zsolt

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Square packing Guillotine cut Asymptotic analysis Gardner’s problem Square the square Recursive algorithm

Anmerkung:	© The Author(s) 2022

Übergeordnetes Werk:	Enthalten in: Optimization letters - Berlin : Springer, 2007, 16(2022), 9 vom: 19. März, Seite 2775-2785
Übergeordnetes Werk:	volume:16 ; year:2022 ; number:9 ; day:19 ; month:03 ; pages:2775-2785

Links:	Volltext

DOI / URN:	10.1007/s11590-022-01858-w

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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773	1	8	\|g volume:16 \|g year:2022 \|g number:9 \|g day:19 \|g month:03 \|g pages:2775-2785
856	4	0	\|u https://dx.doi.org/10.1007/s11590-022-01858-w \|z kostenfrei \|3 Volltext
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912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
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912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
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912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
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912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
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912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
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912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
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912			\|a GBV_ILN_2470
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912			\|a GBV_ILN_2548
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912			\|a GBV_ILN_4333
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allfields	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
allfields_unstemmed	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
allfieldsGer	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
allfieldsSound	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
language	English
source	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
sourceStr	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
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Square packing Guillotine cut Asymptotic analysis Gardner’s problem Square the square Recursive algorithm
isfreeaccess_bool	true
container_title	Optimization letters
authorswithroles_txt_mv	Balogh, János @@aut@@ Dósa, György @@aut@@ Hvattum, Lars Magnus @@aut@@ Olaj, Tomas @@aut@@ Tuza, Zsolt @@aut@@
publishDateDaySort_date	2022-03-19T00:00:00Z
hierarchy_top_id	534676499
id	SPR048474088
language_de	englisch
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author	Balogh, János
spellingShingle	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
authorStr	Balogh, János
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topic_title	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
topic	misc Square packing misc Guillotine cut misc Asymptotic analysis misc Gardner’s problem misc Square the square misc Recursive algorithm
topic_unstemmed	misc Square packing misc Guillotine cut misc Asymptotic analysis misc Gardner’s problem misc Square the square misc Recursive algorithm
topic_browse	misc Square packing misc Guillotine cut misc Asymptotic analysis misc Gardner’s problem misc Square the square misc Recursive algorithm
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Guillotine cutting is asymptotically optimal for packing consecutive squares
ctrlnum	(DE-627)SPR048474088 (SPR)s11590-022-01858-w-e
title_full	Guillotine cutting is asymptotically optimal for packing consecutive squares
author_sort	Balogh, János
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author_browse	Balogh, János Dósa, György Hvattum, Lars Magnus Olaj, Tomas Tuza, Zsolt
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format_se	Elektronische Aufsätze
author-letter	Balogh, János
doi_str_mv	10.1007/s11590-022-01858-w
title_sort	guillotine cutting is asymptotically optimal for packing consecutive squares
title_auth	Guillotine cutting is asymptotically optimal for packing consecutive squares
abstract	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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container_issue	9
title_short	Guillotine cutting is asymptotically optimal for packing consecutive squares
url	https://dx.doi.org/10.1007/s11590-022-01858-w
remote_bool	true
author2	Dósa, György Hvattum, Lars Magnus Olaj, Tomas Tuza, Zsolt
author2Str	Dósa, György Hvattum, Lars Magnus Olaj, Tomas Tuza, Zsolt
ppnlink	534676499
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doi_str	10.1007/s11590-022-01858-w
up_date	2024-07-03T19:27:04.384Z
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Guillotine cutting is asymptotically optimal for packing consecutive squares

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