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Article: Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing
| Title | Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing |
|---|---|
| Authors | |
| Keywords | 1-space bounded Bin packing Multi dimensional Online algorithms |
| Issue Date | 2013 |
| Publisher | Springer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1382-6905 |
| Citation | Journal Of Combinatorial Optimization, 2013, v. 26 n. 2, p. 223-236 How to Cite? |
| Abstract | In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P ij. When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90 {ring operator}-rotation on any plane P ij is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For d-dimensional bin packing, an online algorithm with competitive ratio 4 d is given. Moreover, we consider d-dimensional hypercube packing, and give a 2 d+1-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing. © 2012 The Author(s). |
| Persistent Identifier | http://hdl.handle.net/10722/147128 |
| ISSN | 2021 Impact Factor: 1.262 2020 SCImago Journal Rankings: 0.538 |
| ISI Accession Number ID | |
| References | Bansal N, Correa JR, Kenyon C, Sviridenko M (2006a) Bin packing in multiple dimensions: in-approximability results and approximation schemes. Math Oper Res 31(1):31–49 doi: 10.1287/moor.1050.0168 Chung FRK, Garey MR, Johnson DS (1982) On packing two-dimensional bins. SIAM J Algebr Discrete Methods 3(1):66–76 doi: 10.1137/0603007 Coppersmith D, Raghavan P (1989) Multidimensional on-line bin packing: algorithms and worst case analysis. Oper Res Lett 8:17–20 doi: 10.1016/0167-6377(89)90027-8 Csirik J, Johnson DS (2001) Bounded space on-line bin packing: best is better than first. Algorithmica 31:115–138 doi: 10.1007/s00453-001-0041-7 Csirik J, Frenk J, Labbe M (1993) Two-dimensional rectangle packing: on-line methods and results. Discrete Appl Math 45(3):197–204 doi: 10.1016/0166-218X(93)90009-D Epstein L, van Stee R (2005a) Online square and cube packing. Acta Inform 41(9):595–606 doi: 10.1007/s00236-005-0169-z Epstein L, van Stee R (2005b) Optimal online algorithms for multidimensional packing problems. SIAM J Comput 35(2):431–448 doi: 10.1137/S0097539705446895 Epstein L, van Stee R (2007) Bounds for online bounded space hypercube packing. Discrete Optim 4:185–197 doi: 10.1016/j.disopt.2006.11.005 Fujita S (2003) On-line grid-packing with a single active grid. Inf Process Lett 85:199–204 doi: 10.1016/S0020-0190(02)00373-3 Han X, Iwama K, Zhang G (2008) Online removable square packing. Theory Comput Syst 43(1):38–55 doi: 10.1007/s00224-007-9039-0 Han X, Chin F, Ting H-F, Zhang G, Zhang Y (2011) A new upper bound 2.5545 on 2D online bin packing. ACM Trans Algorithms 7(4):50 doi: 10.1145/2000807.2000818 Januszewski J, Lassak M (1997) On-line packing sequences of cubes in the unit cube. Geom Dedic 67:285–293 doi: 10.1023/A:1004953109743 Johnson DS, Garey MR (1985) A 71/60 theorem for bin-packing. J Complex 1:65–106 doi: 10.1016/0885-064X(85)90022-6 Johnson DS, Demers AJ, Ullman JD, Garey MR, Graham RL (1974) Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J Comput 3(4):299–325 doi: 10.1137/0203025 Kohayakawa Y, Miyazawa FK, Raghavan P, Wakabayashi Y (2004) Multidimensionalcube packing. Algorithmica 40(3):173–187 doi: 10.1007/s00453-004-1102-5 Lee CC, Lee DT (1985) A simple on-line bin packing algorithm. J Assoc Comput Mach 32:562–572 doi: 10.1145/3828.3833 Leung JY-T, Tam TW, Wong CS, Young GH, Chin FYL (1990) Packing squares into a square. J Parallel Distrib Comput 10:271–275 doi: 10.1016/0743-7315(90)90019-L Meir A, Moser L (1968) On packing of squares and cubes. J Comb Theory 5:126–134 doi: 10.1016/S0021-9800(68)80047-X Ramanan PV, Brown DJ, Lee CC, Lee DT (1989) On-line bin packing in linear time. J Algorithms 10:305–326 doi: 10.1016/0196-6774(89)90031-X Seiden SS (2002) On the online bin packing problem. J ACM 49:640–671 doi: 10.1145/585265.585269 Seiden S, van Stee R (2003) New bounds for multi-dimensional packing. Algorithmica 36:261–293 doi: 10.1007/s00453-003-1016-7 Simchi-Levi D (1994) New worst-case results for the bin-packing problem. Nav Res Logist 41:579–585 doi: 10.1002/1520-6750(199406)41:4%3C579::AID-NAV3220410409%3E3.0.CO;2-G van Vliet A (1992) An improved lower bound for on-line bin packing algorithms. Inf Process Lett 43:277–284 doi: 10.1016/0020-0190(92)90223-I Yao AC-C (1980) New algorithms for bin packing. J ACM 27:207–227 doi: 10.1145/322186.322187 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Zhang, Y | en_HK |
| dc.contributor.author | Chin, FYL | en_HK |
| dc.contributor.author | Ting, HF | en_HK |
| dc.contributor.author | Han, X | en_HK |
| dc.date.accessioned | 2012-05-28T08:19:43Z | - |
| dc.date.available | 2012-05-28T08:19:43Z | - |
| dc.date.issued | 2013 | en_HK |
| dc.identifier.citation | Journal Of Combinatorial Optimization, 2013, v. 26 n. 2, p. 223-236 | en_HK |
| dc.identifier.issn | 1382-6905 | en_HK |
| dc.identifier.uri | http://hdl.handle.net/10722/147128 | - |
| dc.description.abstract | In this paper, we study 1-space bounded multi-dimensional bin packing and hypercube packing. A sequence of items arrive over time, each item is a d-dimensional hyperbox (in bin packing) or hypercube (in hypercube packing), and the length of each side is no more than 1. These items must be packed without overlapping into d-dimensional hypercubes with unit length on each side. In d-dimensional space, any two dimensions i and j define a space P ij. When an item arrives, we must pack it into an active bin immediately without any knowledge of the future items, and 90 {ring operator}-rotation on any plane P ij is allowed. The objective is to minimize the total number of bins used for packing all these items in the sequence. In the 1-space bounded variant, there is only one active bin for packing the current item. If the active bin does not have enough space to pack the item, it must be closed and a new active bin is opened. For d-dimensional bin packing, an online algorithm with competitive ratio 4 d is given. Moreover, we consider d-dimensional hypercube packing, and give a 2 d+1-competitive algorithm. These two results are the first study on 1-space bounded multi dimensional bin packing and hypercube packing. © 2012 The Author(s). | en_HK |
| dc.language | eng | en_US |
| dc.publisher | Springer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=1382-6905 | en_HK |
| dc.relation.ispartof | Journal of Combinatorial Optimization | en_HK |
| dc.rights | The Author(s) | en_US |
| dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | en_US |
| dc.subject | 1-space bounded | en_HK |
| dc.subject | Bin packing | en_HK |
| dc.subject | Multi dimensional | en_HK |
| dc.subject | Online algorithms | en_HK |
| dc.title | Online algorithms for 1-space bounded multi dimensional bin packing and hypercube packing | en_HK |
| dc.type | Article | en_HK |
| dc.identifier.openurl | http://www.springerlink.com/link-out/?id=2104&code=02757VP772851072&MUD=MP | en_US |
| dc.identifier.email | Chin, FYL:chin@cs.hku.hk | en_HK |
| dc.identifier.email | Ting, HF:hfting@cs.hku.hk | en_HK |
| dc.identifier.authority | Chin, FYL=rp00105 | en_HK |
| dc.identifier.authority | Ting, HF=rp00177 | en_HK |
| dc.description.nature | published_or_final_version | en_US |
| dc.identifier.doi | 10.1007/s10878-012-9457-z | en_HK |
| dc.identifier.scopus | eid_2-s2.0-84879883028 | en_HK |
| dc.identifier.hkuros | 208020 | - |
| dc.identifier.hkuros | 215789 | - |
| dc.relation.references | Bansal N, Correa JR, Kenyon C, Sviridenko M (2006a) Bin packing in multiple dimensions: in-approximability results and approximation schemes. Math Oper Res 31(1):31–49 | en_US |
| dc.relation.references | doi: 10.1287/moor.1050.0168 | en_US |
| dc.relation.references | Chung FRK, Garey MR, Johnson DS (1982) On packing two-dimensional bins. SIAM J Algebr Discrete Methods 3(1):66–76 | en_US |
| dc.relation.references | doi: 10.1137/0603007 | en_US |
| dc.relation.references | Coppersmith D, Raghavan P (1989) Multidimensional on-line bin packing: algorithms and worst case analysis. Oper Res Lett 8:17–20 | en_US |
| dc.relation.references | doi: 10.1016/0167-6377(89)90027-8 | en_US |
| dc.relation.references | Csirik J, Johnson DS (2001) Bounded space on-line bin packing: best is better than first. Algorithmica 31:115–138 | en_US |
| dc.relation.references | doi: 10.1007/s00453-001-0041-7 | en_US |
| dc.relation.references | Csirik J, Frenk J, Labbe M (1993) Two-dimensional rectangle packing: on-line methods and results. Discrete Appl Math 45(3):197–204 | en_US |
| dc.relation.references | doi: 10.1016/0166-218X(93)90009-D | en_US |
| dc.relation.references | Epstein L, van Stee R (2005a) Online square and cube packing. Acta Inform 41(9):595–606 | en_US |
| dc.relation.references | doi: 10.1007/s00236-005-0169-z | en_US |
| dc.relation.references | Epstein L, van Stee R (2005b) Optimal online algorithms for multidimensional packing problems. SIAM J Comput 35(2):431–448 | en_US |
| dc.relation.references | doi: 10.1137/S0097539705446895 | en_US |
| dc.relation.references | Epstein L, van Stee R (2007) Bounds for online bounded space hypercube packing. Discrete Optim 4:185–197 | en_US |
| dc.relation.references | doi: 10.1016/j.disopt.2006.11.005 | en_US |
| dc.relation.references | Fujita S (2003) On-line grid-packing with a single active grid. Inf Process Lett 85:199–204 | en_US |
| dc.relation.references | doi: 10.1016/S0020-0190(02)00373-3 | en_US |
| dc.relation.references | Han X, Iwama K, Zhang G (2008) Online removable square packing. Theory Comput Syst 43(1):38–55 | en_US |
| dc.relation.references | doi: 10.1007/s00224-007-9039-0 | en_US |
| dc.relation.references | Han X, Chin F, Ting H-F, Zhang G, Zhang Y (2011) A new upper bound 2.5545 on 2D online bin packing. ACM Trans Algorithms 7(4):50 | en_US |
| dc.relation.references | doi: 10.1145/2000807.2000818 | en_US |
| dc.relation.references | Januszewski J, Lassak M (1997) On-line packing sequences of cubes in the unit cube. Geom Dedic 67:285–293 | en_US |
| dc.relation.references | doi: 10.1023/A:1004953109743 | en_US |
| dc.relation.references | Johnson DS, Garey MR (1985) A 71/60 theorem for bin-packing. J Complex 1:65–106 | en_US |
| dc.relation.references | doi: 10.1016/0885-064X(85)90022-6 | en_US |
| dc.relation.references | Johnson DS, Demers AJ, Ullman JD, Garey MR, Graham RL (1974) Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J Comput 3(4):299–325 | en_US |
| dc.relation.references | doi: 10.1137/0203025 | en_US |
| dc.relation.references | Kohayakawa Y, Miyazawa FK, Raghavan P, Wakabayashi Y (2004) Multidimensionalcube packing. Algorithmica 40(3):173–187 | en_US |
| dc.relation.references | doi: 10.1007/s00453-004-1102-5 | en_US |
| dc.relation.references | Lee CC, Lee DT (1985) A simple on-line bin packing algorithm. J Assoc Comput Mach 32:562–572 | en_US |
| dc.relation.references | doi: 10.1145/3828.3833 | en_US |
| dc.relation.references | Leung JY-T, Tam TW, Wong CS, Young GH, Chin FYL (1990) Packing squares into a square. J Parallel Distrib Comput 10:271–275 | en_US |
| dc.relation.references | doi: 10.1016/0743-7315(90)90019-L | en_US |
| dc.relation.references | Meir A, Moser L (1968) On packing of squares and cubes. J Comb Theory 5:126–134 | en_US |
| dc.relation.references | doi: 10.1016/S0021-9800(68)80047-X | en_US |
| dc.relation.references | Ramanan PV, Brown DJ, Lee CC, Lee DT (1989) On-line bin packing in linear time. J Algorithms 10:305–326 | en_US |
| dc.relation.references | doi: 10.1016/0196-6774(89)90031-X | en_US |
| dc.relation.references | Seiden SS (2002) On the online bin packing problem. J ACM 49:640–671 | en_US |
| dc.relation.references | doi: 10.1145/585265.585269 | en_US |
| dc.relation.references | Seiden S, van Stee R (2003) New bounds for multi-dimensional packing. Algorithmica 36:261–293 | en_US |
| dc.relation.references | doi: 10.1007/s00453-003-1016-7 | en_US |
| dc.relation.references | Simchi-Levi D (1994) New worst-case results for the bin-packing problem. Nav Res Logist 41:579–585 | en_US |
| dc.relation.references | doi: 10.1002/1520-6750(199406)41:4%3C579::AID-NAV3220410409%3E3.0.CO;2-G | en_US |
| dc.relation.references | van Vliet A (1992) An improved lower bound for on-line bin packing algorithms. Inf Process Lett 43:277–284 | en_US |
| dc.relation.references | doi: 10.1016/0020-0190(92)90223-I | en_US |
| dc.relation.references | Yao AC-C (1980) New algorithms for bin packing. J ACM 27:207–227 | en_US |
| dc.relation.references | doi: 10.1145/322186.322187 | en_US |
| dc.relation.references | Bansal N, Caprara A, Sviridenko M (2006b) Improved approximation algorithm for multidimensional bin packing problems. In: FOCS 2006, pp 697–708 | en_US |
| dc.relation.references | Blitz D, van Vliet A, Woeginger GJ (1996) Lower bounds on the asymptotic worst-case ratio of on-line bin packing algorithms. Unpublished manuscript | en_US |
| dc.relation.references | Caprara A (2002) Packing 2-dimensional bins in harmony. In FOCS 2002, pp 490–499 | en_US |
| dc.relation.references | Chin FYL, Ting H-F, Zhang Y (2012) 1-space bounded algorithms for 2-dimensional bin packing. Int J Found Comput Sci (to appear) | en_US |
| dc.relation.references | Ferreira CE, Miyazawa EK, Wakabayashi Y (1999) Packing squares into squares. Pesqui Oper 19:223–237 | en_US |
| dc.relation.references | Garey MR, Johnson DS (1979) Computers and intractability: a guide for the theory of NP-completeness. Freeman, San Francisco | en_US |
| dc.relation.references | Han X, Fujita S, Guo H (2001) A two-dimensional harmonic algorithm with performance ratio 2.7834. IPSJ SIG Not 93:43–50 | en_US |
| dc.relation.references | Karmarkar N, Karp RM (1982) An efficient approximation scheme for the one-dimensional bin packing problem. In: Proc 23rd ann IEEE symp on foundations of comput sci. IEEE Computer Society, Los Alamitos, pp 312–320 | en_US |
| dc.relation.references | Zhang Y, Chen J, Chin FYL, Han X, Ting H-F, Tsin YH (2010) Improved online algorithms for 1-space bounded 2-dimensional bin packing. In: Proc of the 21th annual international symposium on algorithms and computation (ISAAC 2010). LNCS, vol 6507. Springer, Berlin, pp 242–253 | en_US |
| dc.identifier.spage | 223 | en_HK |
| dc.identifier.epage | 236 | en_HK |
| dc.identifier.eissn | 1573-2886 | en_US |
| dc.identifier.isi | WOS:000321062500001 | - |
| dc.publisher.place | Netherlands | en_HK |
| dc.description.other | Springer Open Choice, 28 May 2012 | en_US |
| dc.identifier.scopusauthorid | Zhang, Y=35114314500 | en_HK |
| dc.identifier.scopusauthorid | Chin, FYL=7005101915 | en_HK |
| dc.identifier.scopusauthorid | Ting, HF=7005654198 | en_HK |
| dc.identifier.scopusauthorid | Han, X=34872071800 | en_HK |
| dc.identifier.citeulike | 10385009 | - |
| dc.identifier.issnl | 1382-6905 | - |