Colored Bin Packing: Online Algorithms and Lower Bounds
Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Böhm, Martin [verfasserIn] Dósa, György [verfasserIn] Epstein, Leah [verfasserIn] Sgall, Jiří [verfasserIn] Veselý, Pavel [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Algorithmica - New York, NY : Springer, 1986, 80(2016), 1 vom: 17. Nov., Seite 155-184 |
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| Übergeordnetes Werk: |
volume:80 ; year:2016 ; number:1 ; day:17 ; month:11 ; pages:155-184 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00453-016-0248-2 |
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| Katalog-ID: |
SPR006180124 |
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| 520 | |a Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. | ||
| 650 | 4 | |a Online algorithms |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Bin packing |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Worst-case analysis |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Colored bin packing |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Black and white bin packing |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Dósa, György |e verfasserin |4 aut | |
| 700 | 1 | |a Epstein, Leah |e verfasserin |4 aut | |
| 700 | 1 | |a Sgall, Jiří |e verfasserin |4 aut | |
| 700 | 1 | |a Veselý, Pavel |e verfasserin |4 aut | |
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10.1007/s00453-016-0248-2 doi (DE-627)SPR006180124 (SPR)s00453-016-0248-2-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Böhm, Martin verfasserin aut Colored Bin Packing: Online Algorithms and Lower Bounds 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. Online algorithms (dpeaa)DE-He213 Bin packing (dpeaa)DE-He213 Worst-case analysis (dpeaa)DE-He213 Colored bin packing (dpeaa)DE-He213 Black and white bin packing (dpeaa)DE-He213 Dósa, György verfasserin aut Epstein, Leah verfasserin aut Sgall, Jiří verfasserin aut Veselý, Pavel verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 80(2016), 1 vom: 17. Nov., Seite 155-184 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:80 year:2016 number:1 day:17 month:11 pages:155-184 https://dx.doi.org/10.1007/s00453-016-0248-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 54.00 ASE AR 80 2016 1 17 11 155-184 |
| spelling |
10.1007/s00453-016-0248-2 doi (DE-627)SPR006180124 (SPR)s00453-016-0248-2-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Böhm, Martin verfasserin aut Colored Bin Packing: Online Algorithms and Lower Bounds 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. Online algorithms (dpeaa)DE-He213 Bin packing (dpeaa)DE-He213 Worst-case analysis (dpeaa)DE-He213 Colored bin packing (dpeaa)DE-He213 Black and white bin packing (dpeaa)DE-He213 Dósa, György verfasserin aut Epstein, Leah verfasserin aut Sgall, Jiří verfasserin aut Veselý, Pavel verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 80(2016), 1 vom: 17. Nov., Seite 155-184 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:80 year:2016 number:1 day:17 month:11 pages:155-184 https://dx.doi.org/10.1007/s00453-016-0248-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 54.00 ASE AR 80 2016 1 17 11 155-184 |
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10.1007/s00453-016-0248-2 doi (DE-627)SPR006180124 (SPR)s00453-016-0248-2-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Böhm, Martin verfasserin aut Colored Bin Packing: Online Algorithms and Lower Bounds 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. Online algorithms (dpeaa)DE-He213 Bin packing (dpeaa)DE-He213 Worst-case analysis (dpeaa)DE-He213 Colored bin packing (dpeaa)DE-He213 Black and white bin packing (dpeaa)DE-He213 Dósa, György verfasserin aut Epstein, Leah verfasserin aut Sgall, Jiří verfasserin aut Veselý, Pavel verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 80(2016), 1 vom: 17. Nov., Seite 155-184 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:80 year:2016 number:1 day:17 month:11 pages:155-184 https://dx.doi.org/10.1007/s00453-016-0248-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 54.00 ASE AR 80 2016 1 17 11 155-184 |
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10.1007/s00453-016-0248-2 doi (DE-627)SPR006180124 (SPR)s00453-016-0248-2-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Böhm, Martin verfasserin aut Colored Bin Packing: Online Algorithms and Lower Bounds 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. Online algorithms (dpeaa)DE-He213 Bin packing (dpeaa)DE-He213 Worst-case analysis (dpeaa)DE-He213 Colored bin packing (dpeaa)DE-He213 Black and white bin packing (dpeaa)DE-He213 Dósa, György verfasserin aut Epstein, Leah verfasserin aut Sgall, Jiří verfasserin aut Veselý, Pavel verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 80(2016), 1 vom: 17. Nov., Seite 155-184 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:80 year:2016 number:1 day:17 month:11 pages:155-184 https://dx.doi.org/10.1007/s00453-016-0248-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 54.00 ASE AR 80 2016 1 17 11 155-184 |
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10.1007/s00453-016-0248-2 doi (DE-627)SPR006180124 (SPR)s00453-016-0248-2-e DE-627 ger DE-627 rakwb eng 004 ASE 510 004 ASE 54.00 bkl Böhm, Martin verfasserin aut Colored Bin Packing: Online Algorithms and Lower Bounds 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. Online algorithms (dpeaa)DE-He213 Bin packing (dpeaa)DE-He213 Worst-case analysis (dpeaa)DE-He213 Colored bin packing (dpeaa)DE-He213 Black and white bin packing (dpeaa)DE-He213 Dósa, György verfasserin aut Epstein, Leah verfasserin aut Sgall, Jiří verfasserin aut Veselý, Pavel verfasserin aut Enthalten in Algorithmica New York, NY : Springer, 1986 80(2016), 1 vom: 17. Nov., Seite 155-184 (DE-627)253389704 (DE-600)1458414-1 1432-0541 nnns volume:80 year:2016 number:1 day:17 month:11 pages:155-184 https://dx.doi.org/10.1007/s00453-016-0248-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-ASE 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_101 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_267 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_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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_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 54.00 ASE AR 80 2016 1 17 11 155-184 |
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Enthalten in Algorithmica 80(2016), 1 vom: 17. Nov., Seite 155-184 volume:80 year:2016 number:1 day:17 month:11 pages:155-184 |
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Online algorithms Bin packing Worst-case analysis Colored bin packing Black and white bin packing |
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Böhm, Martin @@aut@@ Dósa, György @@aut@@ Epstein, Leah @@aut@@ Sgall, Jiří @@aut@@ Veselý, Pavel @@aut@@ |
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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">SPR006180124</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20220110185406.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201002s2016 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00453-016-0248-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006180124</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00453-016-0248-2-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="082" ind1="0" ind2="4"><subfield code="a">004</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="a">004</subfield><subfield code="q">ASE</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">54.00</subfield><subfield code="2">bkl</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Böhm, Martin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Colored Bin Packing: Online Algorithms and Lower Bounds</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</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="520" ind1=" " ind2=" "><subfield code="a">Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Online algorithms</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bin packing</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Worst-case analysis</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Colored bin packing</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Black and white bin packing</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Dósa, György</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Epstein, Leah</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sgall, Jiří</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Veselý, Pavel</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Algorithmica</subfield><subfield code="d">New York, NY : Springer, 1986</subfield><subfield code="g">80(2016), 1 vom: 17. 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Böhm, Martin |
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Böhm, Martin |
| doi_str_mv |
10.1007/s00453-016-0248-2 |
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004 510 |
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verfasserin |
| title_sort |
colored bin packing: online algorithms and lower bounds |
| title_auth |
Colored Bin Packing: Online Algorithms and Lower Bounds |
| abstract |
Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. |
| abstractGer |
Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. |
| abstract_unstemmed |
Abstract In the Colored Bin Packing problem a sequence of items of sizes up to 1 arrives to be packed into bins of unit capacity. Each item has one of at least two colors and an additional constraint is that we cannot pack two items of the same color next to each other in the same bin. The objective is to minimize the number of bins. In the important special case when all items have size zero, we characterize the optimal value to be equal to color discrepancy. As our main result, we give an (asymptotically) 1.5-competitive algorithm which is optimal. In fact, the algorithm always uses at most %$\lceil 1.5\cdot OPT \rceil %$ bins and we can force any deterministic online algorithm to use at least %$\lceil 1.5\cdot OPT \rceil %$ bins while the offline optimum is %$ OPT %$ for any value of %$ OPT \ge 2%$. In particular, the absolute competitive ratio of our algorithm is 5 / 3 and this is optimal. For items of arbitrary size we give a lower bound of 2.5 on the asymptotic competitive ratio of any online algorithm and an absolutely 3.5-competitive algorithm. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ the asymptotic competitive ratio of our algorithm is %$1.5+d/(d-1)%$. We also show that classical algorithms First Fit, Best Fit and Worst Fit are not constant competitive, which holds already for three colors and small items. In the case of two colors—the Black and White Bin Packing problem—we give a lower bound of 2 on the asymptotic competitive ratio of any online algorithm when items have arbitrary size. We also prove that all Any Fit algorithms have the absolute competitive ratio 3. When the items have sizes of at most 1 / d for a real %$d \ge 2%$ we show that the Worst Fit algorithm is absolutely %$(1+d/(d-1))%$-competitive. |
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Colored Bin Packing: Online Algorithms and Lower Bounds |
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Dósa, György Epstein, Leah Sgall, Jiří Veselý, Pavel |
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2024-07-03T21:22:33.798Z |
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| score |
7.4009285 |