Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension

Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to p...
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Autor*in:	Biró, Csaba [verfasserIn] Curbelo, Israel R

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	On-line algorithm Chain partitioning Poset dimension

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: Order - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984, 40(2023), 3 vom: 29. März, Seite 683-690
Übergeordnetes Werk:	volume:40 ; year:2023 ; number:3 ; day:29 ; month:03 ; pages:683-690

Links:	Volltext

DOI / URN:	10.1007/s11083-023-09629-7

Katalog-ID:	SPR053938100

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520			\|a Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d.
650		4	\|a On-line algorithm \|7 (dpeaa)DE-He213
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912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
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
912			\|a GBV_ILN_2044
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
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
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
912			\|a GBV_ILN_2148
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912			\|a GBV_ILN_2153
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912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
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912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
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912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
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912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
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allfields	10.1007/s11083-023-09629-7 doi (DE-627)SPR053938100 (SPR)s11083-023-09629-7-e DE-627 ger DE-627 rakwb eng Biró, Csaba verfasserin (orcid)0000-0002-8263-6787 aut Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. On-line algorithm (dpeaa)DE-He213 Chain partitioning (dpeaa)DE-He213 Poset dimension (dpeaa)DE-He213 Curbelo, Israel R aut Enthalten in Order Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 40(2023), 3 vom: 29. März, Seite 683-690 (DE-627)266883478 (DE-600)1468197-3 1572-9273 nnns volume:40 year:2023 number:3 day:29 month:03 pages:683-690 https://dx.doi.org/10.1007/s11083-023-09629-7 lizenzpflichtig 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_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 40 2023 3 29 03 683-690
spelling	10.1007/s11083-023-09629-7 doi (DE-627)SPR053938100 (SPR)s11083-023-09629-7-e DE-627 ger DE-627 rakwb eng Biró, Csaba verfasserin (orcid)0000-0002-8263-6787 aut Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. On-line algorithm (dpeaa)DE-He213 Chain partitioning (dpeaa)DE-He213 Poset dimension (dpeaa)DE-He213 Curbelo, Israel R aut Enthalten in Order Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 40(2023), 3 vom: 29. März, Seite 683-690 (DE-627)266883478 (DE-600)1468197-3 1572-9273 nnns volume:40 year:2023 number:3 day:29 month:03 pages:683-690 https://dx.doi.org/10.1007/s11083-023-09629-7 lizenzpflichtig 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_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 40 2023 3 29 03 683-690
allfields_unstemmed	10.1007/s11083-023-09629-7 doi (DE-627)SPR053938100 (SPR)s11083-023-09629-7-e DE-627 ger DE-627 rakwb eng Biró, Csaba verfasserin (orcid)0000-0002-8263-6787 aut Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. On-line algorithm (dpeaa)DE-He213 Chain partitioning (dpeaa)DE-He213 Poset dimension (dpeaa)DE-He213 Curbelo, Israel R aut Enthalten in Order Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 40(2023), 3 vom: 29. März, Seite 683-690 (DE-627)266883478 (DE-600)1468197-3 1572-9273 nnns volume:40 year:2023 number:3 day:29 month:03 pages:683-690 https://dx.doi.org/10.1007/s11083-023-09629-7 lizenzpflichtig 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_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 40 2023 3 29 03 683-690
allfieldsGer	10.1007/s11083-023-09629-7 doi (DE-627)SPR053938100 (SPR)s11083-023-09629-7-e DE-627 ger DE-627 rakwb eng Biró, Csaba verfasserin (orcid)0000-0002-8263-6787 aut Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. On-line algorithm (dpeaa)DE-He213 Chain partitioning (dpeaa)DE-He213 Poset dimension (dpeaa)DE-He213 Curbelo, Israel R aut Enthalten in Order Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 40(2023), 3 vom: 29. März, Seite 683-690 (DE-627)266883478 (DE-600)1468197-3 1572-9273 nnns volume:40 year:2023 number:3 day:29 month:03 pages:683-690 https://dx.doi.org/10.1007/s11083-023-09629-7 lizenzpflichtig 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_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 40 2023 3 29 03 683-690
allfieldsSound	10.1007/s11083-023-09629-7 doi (DE-627)SPR053938100 (SPR)s11083-023-09629-7-e DE-627 ger DE-627 rakwb eng Biró, Csaba verfasserin (orcid)0000-0002-8263-6787 aut Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. On-line algorithm (dpeaa)DE-He213 Chain partitioning (dpeaa)DE-He213 Poset dimension (dpeaa)DE-He213 Curbelo, Israel R aut Enthalten in Order Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984 40(2023), 3 vom: 29. März, Seite 683-690 (DE-627)266883478 (DE-600)1468197-3 1572-9273 nnns volume:40 year:2023 number:3 day:29 month:03 pages:683-690 https://dx.doi.org/10.1007/s11083-023-09629-7 lizenzpflichtig 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_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 40 2023 3 29 03 683-690
language	English
source	Enthalten in Order 40(2023), 3 vom: 29. März, Seite 683-690 volume:40 year:2023 number:3 day:29 month:03 pages:683-690
sourceStr	Enthalten in Order 40(2023), 3 vom: 29. März, Seite 683-690 volume:40 year:2023 number:3 day:29 month:03 pages:683-690
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	On-line algorithm Chain partitioning Poset dimension
isfreeaccess_bool	false
container_title	Order
authorswithroles_txt_mv	Biró, Csaba @@aut@@ Curbelo, Israel R @@aut@@
publishDateDaySort_date	2023-03-29T00:00:00Z
hierarchy_top_id	266883478
id	SPR053938100
language_de	englisch
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author	Biró, Csaba
spellingShingle	Biró, Csaba misc On-line algorithm misc Chain partitioning misc Poset dimension Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension
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topic_title	Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension On-line algorithm (dpeaa)DE-He213 Chain partitioning (dpeaa)DE-He213 Poset dimension (dpeaa)DE-He213
topic	misc On-line algorithm misc Chain partitioning misc Poset dimension
topic_unstemmed	misc On-line algorithm misc Chain partitioning misc Poset dimension
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title	Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension
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title_full	Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension
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author_browse	Biró, Csaba Curbelo, Israel R
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author-letter	Biró, Csaba
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title_sort	improved lower bounds on the on-line chain partitioning of posets of bounded dimension
title_auth	Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension
abstract	Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d. © The Author(s), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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title_short	Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension
url	https://dx.doi.org/10.1007/s11083-023-09629-7
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up_date	2024-07-03T23:01:50.149Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">SPR053938100</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20231202064637.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">231202s2023 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11083-023-09629-7</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR053938100</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s11083-023-09629-7-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">Biró, Csaba</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-8263-6787</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2023</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), under exclusive licence to Springer Nature B.V. 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemerédi proved that any on-line algorithm could be forced to use %$\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemerédi’s argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size d. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use %$(2-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a 2-dimensional poset of width w. Second, we prove that any on-line algorithm can be forced to use %$(2-\frac{1}{d-1}-o(1))\left( {\begin{array}{c}w+1\\ 2\end{array}}\right)%$ chains to partition a poset of width w presented via a realizer of size d.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">On-line algorithm</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Chain partitioning</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Poset dimension</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Curbelo, Israel R</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Order</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1984</subfield><subfield code="g">40(2023), 3 vom: 29. März, Seite 683-690</subfield><subfield code="w">(DE-627)266883478</subfield><subfield code="w">(DE-600)1468197-3</subfield><subfield code="x">1572-9273</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:40</subfield><subfield code="g">year:2023</subfield><subfield code="g">number:3</subfield><subfield code="g">day:29</subfield><subfield code="g">month:03</subfield><subfield code="g">pages:683-690</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s11083-023-09629-7</subfield><subfield code="z">lizenzpflichtig</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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Improved Lower Bounds on the On-line Chain Partitioning of Posets of Bounded Dimension

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