Bin packing approximation algorithms: Survey and classification

[1]  G Galambos Parametric lower bound for on-line bin-packing , 1986 .

[2]  Richard J. Anderson,et al.  Parallel Approximation Algorithms for Bin Packing , 1988, Inf. Comput..

[3]  Hadas Shachnai,et al.  Tight bounds for online class-constrained packing , 2002, Theor. Comput. Sci..

[4]  Chak-Kuen Wong,et al.  Linear time-approximation algorithms for bin packing , 2000, Oper. Res. Lett..

[5]  Michael J. Magazine,et al.  Assembly line balancing as generalized bin packing , 1982, Oper. Res. Lett..

[6]  György Dósa,et al.  The Tight Bound of First Fit Decreasing Bin-Packing Algorithm Is FFD(I) <= 11/9OPT(I) + 6/9 , 2007, ESCAPE.

[7]  Hans Kellerer,et al.  On-Line Algorithms for Cardinality Constrained Bin Packing Problems , 2001, ISAAC.

[8]  Guochuan Zhang,et al.  Worst-Case analysis of the FFH algorithm for online variable-sized bin packing , 1996, Computing.

[9]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[10]  David R. Karger,et al.  A better algorithm for an ancient scheduling problem , 1994, SODA '94.

[11]  Zhen Liu,et al.  Bin-packing with fragile objects and frequency allocation in cellular networks , 2009, Wirel. Networks.

[12]  Ralph E. Gomory,et al.  A Linear Programming Approach to the Cutting Stock Problem---Part II , 1963 .

[13]  Leah Epstein,et al.  The maximum resource bin packing problem , 2006, Theor. Comput. Sci..

[14]  Guochuan Zhang,et al.  Tight performance bound ofAFBk bin packing , 1997 .

[15]  D. Eppstein Foreword to special issue on SODA 2002 , 2007, TALG.

[16]  Eduardo C. Xavier,et al.  The class constrained bin packing problem with applications to video-on-demand , 2008, Theor. Comput. Sci..

[17]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[18]  G. S. Lueker,et al.  Bin packing can be solved within 1 + ε in linear time , 1981 .

[19]  Guochuan Zhang,et al.  Bounded Space On-Line Variable-Sized Bin Packing , 1997, Acta Cybern..

[20]  André van Vliet On the Asymptotic Worst Case Behavior of Harmonic Fit , 1996, J. Algorithms.

[21]  Guochuan Zhang,et al.  Bin Packing of Selfish Items , 2008, WINE.

[22]  Hans Kellerer,et al.  A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem , 1999, RANDOM-APPROX.

[23]  Barun Chandra Does Randomization Help in On-Line Bin Packing? , 1992, Inf. Process. Lett..

[24]  Rongheng Li,et al.  The proof of FFD(L) < -OPT(L) + 7/9 , 1997 .

[25]  Gerhard J. Woeginger,et al.  Online Algorithms , 1998, Lecture Notes in Computer Science.

[26]  János Csirik,et al.  A Classification Scheme for Bin Packing Theory , 2007, Acta Cybern..

[27]  Hans Kellerer,et al.  Algorithms for on-line bin-packing problems with cardinality constraints , 2004, Discret. Appl. Math..

[28]  Leah Epstein,et al.  On Bin Packing with Conflicts , 2008, SIAM J. Optim..

[29]  Zhen Liu,et al.  Bin-Packing with Fragile Objects , 2002, IFIP TCS.

[30]  Amos Fiat,et al.  New algorithms for an ancient scheduling problem , 1992, STOC '92.

[31]  Jeffrey B. Sidney,et al.  Bin packing using semi-ordinal data , 1996, Oper. Res. Lett..

[32]  David S. Johnson,et al.  Near-optimal bin packing algorithms , 1973 .

[33]  Leah Epstein,et al.  Tight results for Next Fit and Worst Fit with resource augmentation , 2010, Theor. Comput. Sci..

[34]  Tami Tamir,et al.  Polynominal time approximation schemes for class-constrained packing problem , 2000, APPROX.

[35]  Frank D. Murgolo An Efficient Approximation Scheme for Variable-Sized Bin Packing , 1987, SIAM J. Comput..

[36]  Edward G. Coffman,et al.  Dynamic Bin Packing , 1983, SIAM J. Comput..

[37]  Luke Finlay,et al.  Online LIB problems: Heuristics for Bin Covering and lower bounds for Bin Packing , 2005, RAIRO Oper. Res..

[38]  D. T. Lee,et al.  A simple on-line bin-packing algorithm , 1985, JACM.

[39]  Hadas Shachnai,et al.  Approximation Schemes for Packing with Item Fragmentation , 2007, Theory of Computing Systems.

[40]  D. T. Lee,et al.  On-Line Bin Packing in Linear Time , 1989, J. Algorithms.

[41]  Michael E. Saks,et al.  An on-line graph coloring algorithm with sublinear performance ratio , 1989, Discret. Math..

[42]  J. B. G. Frenk,et al.  A Simple Proof of Liang's Lower Bound for On-Line bin Packing and the Extension to the Parametric Case , 1993, Discret. Appl. Math..

[43]  Guochuan Zhang,et al.  Online bin packing of fragile objects with application in cellular networks , 2007, J. Comb. Optim..

[44]  Joan Boyar,et al.  The Accommodating Function: A Generalization of the Competitive Ratio , 2001, SIAM J. Comput..

[45]  Gerhard J. Woeginger,et al.  Repacking helps in bounded space on-line bind-packing , 1993, Computing.

[46]  Brenda S. Baker,et al.  A New Proof for the First-Fit Decreasing Bin-Packing Algorithm , 1985, J. Algorithms.

[47]  Gregory Gutin,et al.  Batched bin packing , 2005, Discret. Optim..

[48]  Gerhard J. Woeginger,et al.  An On-Line Scheduling Heuristic With Better Worst Case Ratio Than Graham's List Scheduling , 1993, SIAM J. Comput..

[49]  L. Epstein,et al.  Approximation schemes for packing splittable items with cardinality constraints , 2007 .

[50]  Errol L. Lloyd,et al.  Partially Dynamic bin Packing can be Solved Within 1 + \varepsilon in (Amortized) Polylogarithmic Time , 1997, Inf. Process. Lett..

[51]  Joseph Y.-T. Leung,et al.  Combinatorial analysis of an efficient algorithm for processor and storage allocation , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[52]  György Turán,et al.  On the performance of on-line algorithms for partition problems , 1989, Acta Cybern..

[53]  Joan Boyar,et al.  The relative worst order ratio for online algorithms , 2007, TALG.

[54]  Hendrik W. Lenstra,et al.  Integer Programming with a Fixed Number of Variables , 1983, Math. Oper. Res..

[55]  J. Baewicz,et al.  A linear time algorithm for restricted bin packing and scheduling problems , 1983 .

[56]  José R. Correa,et al.  A fast asymptotic approximation scheme for bin packing with rejection , 2008, Theor. Comput. Sci..

[57]  Chak-Kuen Wong,et al.  Bin Packing with Geometric Constraints in Computer Network Design , 1978, Oper. Res..

[58]  Errol L. Lloyd,et al.  Fully Dynamic Algorithms for Bin Packing: Being (Mostly) Myopic Helps , 1993, SIAM J. Comput..

[59]  Hans Kellerer,et al.  A 5/4 Linear Time Bin Packing Algorithm , 2000, J. Comput. Syst. Sci..

[60]  Leah Epstein Bin Packing with Rejection Revisited , 2008, Algorithmica.

[61]  Gerhard J. Woeginger,et al.  On-line bin packing — A restricted survey , 1995, Math. Methods Oper. Res..

[62]  Leah Epstein Online Bin Packing with Cardinality Constraints , 2006, SIAM J. Discret. Math..

[63]  David S. Johnson The NP-Completeness Column: An Ongoing Guide , 1986, J. Algorithms.

[64]  David S. Johnson,et al.  Fast Algorithms for Bin Packing , 1974, J. Comput. Syst. Sci..

[65]  Yuval Rabani,et al.  A Better Lower Bound for On-Line Scheduling , 1994, Inf. Process. Lett..

[66]  Raphael Rom,et al.  Packet scheduling with fragmentation , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[67]  Sartaj Sahni,et al.  Algorithms for Scheduling Independent Tasks , 1976, J. ACM.

[68]  C. Kenyon Best-fit bin-packing with random order , 1996, SODA '96.

[69]  André van Vliet,et al.  An Improved Lower Bound for On-Line Bin Packing Algorithms , 1992, Inf. Process. Lett..

[70]  LEAH EPSTEIN,et al.  New Bounds for Variable-Sized Online Bin Packing , 2003, SIAM J. Comput..

[71]  Mihály Csaba Markót,et al.  Improved lower bounds for semi-online bin packing problems , 2008, Computing.

[72]  Leah Epstein,et al.  Class constrained bin packing revisited , 2010, Theor. Comput. Sci..

[73]  Jeffrey D. Ullman,et al.  Worst-Case Performance Bounds for Simple One-Dimensional Packing Algorithms , 1974, SIAM J. Comput..

[74]  Frank M. Liang A Lower Bound for On-Line Bin Packing , 1980, Inf. Process. Lett..

[75]  Klaus Jansen,et al.  An asymptotic fully polynomial time approximation scheme for bin covering , 2003, Theor. Comput. Sci..

[76]  D. Simchi-Levi New worst‐case results for the bin‐packing problem , 1994 .

[77]  Edward G. Coffman,et al.  Probabilistic analysis of packing and partitioning algorithms , 1991, Wiley-Interscience series in discrete mathematics and optimization.

[78]  Vittorio Bilò On the packing of selfish items , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[79]  David S. Johnson,et al.  Bounded Space On-Line Bin Packing: Best Is Better than First , 1991, SODA '91.

[80]  Leah Epstein,et al.  Selfish Bin Packing , 2008, Algorithmica.

[81]  János Csirik An on-line algorithm for variable-sized bin packing , 2004, Acta Informatica.

[82]  Jeffrey D. Ullman,et al.  Worst-case analysis of memory allocation algorithms , 1972, STOC.

[83]  Yossi Matias,et al.  Scheduling space-sharing for internet advertising , 2002, Journal of Scheduling.

[84]  David B. Shmoys,et al.  A packing problem you can almost solve by sitting on your suitcase , 1986 .

[85]  David S. Johnson,et al.  A 71/60 theorem for bin packing , 1985, J. Complex..

[86]  Edward G. Coffman,et al.  Bin packing with divisible item sizes , 1987, J. Complex..

[87]  Frank D. Murgolo Anomalous behavior in bin packing algorithms , 1988, Discret. Appl. Math..

[88]  Eugene L. Lawler,et al.  Sequencing and scheduling: algorithms and complexity , 1989 .

[89]  Raphael Rom,et al.  Bin Packing with Item Fragmentation , 2001, WADS.

[90]  Leah Epstein,et al.  Online bin packing with resource augmentation , 2007, Discret. Optim..

[91]  D. K. Friesen,et al.  Variable Sized Bin Packing , 1986, SIAM J. Comput..

[92]  Gyula Y. Katona Edge Disjoint Polyp Packing , 1997, Discret. Appl. Math..

[93]  Richard M. Karp,et al.  An efficient approximation scheme for the one-dimensional bin-packing problem , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[94]  Giorgio Gambosi,et al.  On-Line Maintenance of an Approximate Bin-Packing Solution , 1997, Nord. J. Comput..

[95]  David S. Johnson,et al.  Approximation Algorithms for Bin-Packing — An Updated Survey , 1984 .

[96]  Guochuan Zhang,et al.  A New Version of On-line Variable-sized Bin Packing , 1997, Discret. Appl. Math..

[97]  Edward G. Coffman,et al.  An Application of Bin-Packing to Multiprocessor Scheduling , 1978, SIAM J. Comput..

[98]  Yossi Azar,et al.  On-line bin-stretching , 1998, Theor. Comput. Sci..

[99]  Jérôme Monnot,et al.  Bridging gap between standard and differential polynomial approximation: The case of bin-packing , 1999 .

[100]  Claire Mathieu,et al.  Better approximation algorithms for bin covering , 2001, SODA '01.

[101]  Gerhard J. Woeginger Improved Space for Bounded-Space, On-Line Bin-Packing , 1993, SIAM J. Discret. Math..

[102]  Yong He,et al.  Bin packing problems with rejection penalties and their dual problems , 2006, Inf. Comput..

[103]  Charles U. Martel A linear time bin-packing algorithm , 1985 .

[104]  Eugene L. Lawler,et al.  Chapter 9 Sequencing and scheduling: Algorithms and complexity , 1993, Logistics of Production and Inventory.

[105]  David S. Johnson,et al.  Approximation Algorithms for Bin Packing Problems: A Survey , 1981 .

[106]  Vangelis Th. Paschos,et al.  Differential Approximation Algorithms for Some Combinatorial Optimization Problems , 1998, Theor. Comput. Sci..

[107]  Michael B. Richey,et al.  Improved bounds for harmonic-based bin packing algorithms , 1991, Discret. Appl. Math..

[108]  Herb Schwetman,et al.  Analysis of Several Task-Scheduling Algorithms for a Model of Multiprogramming Computer Systems , 1975, JACM.

[109]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[110]  Kaihong Xu,et al.  The Asymptotic Worst-Case Behavior of the FFD Heuristic for Small Items , 2000, J. Algorithms.

[111]  Weizhen Mao,et al.  Tight Worst-Case Performance Bounds for Next-k-Fit Bin Packing , 1993, SIAM J. Comput..

[112]  Hans Kellerer,et al.  Cardinality constrained bin‐packing problems , 1999, Ann. Oper. Res..

[113]  Noga Alon,et al.  Approximation schemes for scheduling , 1997, SODA '97.

[114]  Giorgio Gambosi,et al.  Algorithms for the Relaxed Online Bin-Packing Model , 2000, SIAM J. Comput..

[115]  József Békési,et al.  New lower bounds for certain classes of bin packing algorithms , 2010, Theor. Comput. Sci..

[116]  David S. Johnson,et al.  Fast Allocation Algorithms , 1972, SWAT.

[117]  Edward F. Grove Online bin packing with lookahead , 1995, SODA '95.

[118]  Leah Epstein,et al.  More on online bin packing with two item sizes , 2008, Discret. Optim..

[119]  Philippe Flajolet,et al.  Analysis of algorithms , 2000, Random Struct. Algorithms.

[120]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[121]  Gerhard J. Woeginger,et al.  New lower and upper bounds for on-line scheduling , 1994, Oper. Res. Lett..

[122]  Michael A. Langston,et al.  Online variable-sized bin packing , 1989, Discret. Appl. Math..

[123]  George L. Nemhauser,et al.  Handbooks in operations research and management science , 1989 .

[124]  Yossi Azar,et al.  Fair versus Unrestricted Bin Packing , 2002, Algorithmica.

[125]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[126]  C. Mandal,et al.  Complexity of fragmentable object bin packing and an application , 1998 .

[127]  Daniele Vigo,et al.  Bin Packing Approximation Algorithms: Combinatorial Analysis , 1999, Handbook of Combinatorial Optimization.

[128]  G. Young,et al.  A note on an open‐end bin packing problem , 2001 .

[129]  Jr. E. G. Coffman An Introduction to Combinatorial Models of Dynamic Storage Allocation , 1983 .

[130]  Donna J. Brown,et al.  A Lower Bound for On-Line One-Dimensional Bin Packing Algorithms. , 1979 .

[131]  Steven S. Seiden,et al.  On the online bin packing problem , 2001, JACM.

[132]  Donald K. Friesen,et al.  Tighter Bounds for the Multifit Processor Scheduling Algorithm , 1984, SIAM J. Comput..

[133]  Klaus Jansen,et al.  Approximation Algorithms for Time Constrained Scheduling , 1997, Inf. Comput..

[134]  Joseph Y.-T. Leung,et al.  Bin packing: Maximizing the number of pieces packed , 2004, Acta Informatica.

[135]  Susan Fera. Assmann Problems in discrete applied mathematics , 1983 .

[136]  Alberto Caprara,et al.  Worst-case analysis of the subset sum algorithm for bin packing , 2004, Oper. Res. Lett..

[137]  Ronald L. Graham,et al.  Bounds on multiprocessing anomalies and related packing algorithms , 1972, AFIPS '72 (Spring).

[138]  János Csirik,et al.  The Parametric Behavior of the First-Fit Decreasing Bin Packing Algorithm , 1993, J. Algorithms.

[139]  David C. Fisher Next-fit packs a list and its reverse into the same number of bins , 1988 .

[140]  Sanjeev Khanna,et al.  A Polynomial Time Approximation Scheme for the Multiple Knapsack Problem , 2005, SIAM J. Comput..

[141]  János Csirik,et al.  Resource augmentation for online bounded space bin packing , 2000, J. Algorithms.

[142]  Yossi Azar,et al.  Fair versus Unrestricted Bin Packing , 2000, SWAT.

[143]  Rudolf Berghammer,et al.  A linear approximation algorithm for bin packing with absolute approximation factor 3/2 , 2003, Sci. Comput. Program..

[144]  Michael A. Langston,et al.  Improved 0/1-interchange scheduling , 1982, BIT.

[145]  Leah Epstein,et al.  Resource augmented semi-online bounded space bin packing , 2009, Discret. Appl. Math..

[146]  Solomon W. Golomb,et al.  On Certain Nonlinear Recurring Sequences , 1963 .

[147]  Steven S. Seiden An Optimal Online Algorithm for Bounded Space Variable-Sized Bin Packing , 2001, SIAM J. Discret. Math..

[148]  Donald K. Friesen,et al.  Analysis of a Hybrid Algorithm for Packing Unequal Bins , 1988, SIAM J. Comput..

[149]  Edward G. Coffman,et al.  A Tight Asymptotic Bound for Next-Fit-Decreasing Bin-Packing , 1981 .

[150]  Andrew Chi-Chih Yao,et al.  Resource Constrained Scheduling as Generalized Bin Packing , 1976, J. Comb. Theory A.

[151]  W. Mao Besk-k-Fit bin packing , 2005, Computing.

[152]  Richard E. Ladner,et al.  Windows scheduling as a restricted version of bin packing , 2007, TALG.

[153]  Leah Epstein,et al.  On-Line Maximizing the Number of Items Packed in Variable-Sized Bins , 2002, Acta Cybern..

[154]  L. Epstein On online bin packing with LIB constraints , 2009 .

[155]  Prabhu Manyem,et al.  Approximation Lower Bounds in Online LIB Bin Packing and Covering , 2003, J. Autom. Lang. Comb..

[156]  J. J. Sylvester,et al.  On a Point in the Theory of Vulgar Fractions , 1880 .

[157]  Prudence W. H. Wong,et al.  On Dynamic Bin Packing: An Improved Lower Bound and Resource Augmentation Analysis , 2008, Algorithmica.

[158]  Gregory Gutin,et al.  On-line bin Packing with Two Item Sizes , 2006, Algorithmic Oper. Res..

[159]  Andrew Chi-Chih Yao,et al.  New Algorithms for Bin Packing , 1978, JACM.

[160]  Prudence W. H. Wong,et al.  Dynamic bin packing of unit fractions items , 2008, Theor. Comput. Sci..

[161]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[162]  Joseph Y.-T. Leung,et al.  On a Dual Version of the One-Dimensional Bin Packing Problem , 1984, J. Algorithms.

[163]  Hadas Shachnai,et al.  Fast Asymptotic FPTAS for Packing Fragmentable Items with Costs , 2007, FCT.

[164]  Sungsoo Park,et al.  Algorithms for the variable sized bin packing problem , 2003, Eur. J. Oper. Res..

[165]  R. Péter Mathematische Fassung der sogenannten "Entscheidungs-Tabellen" , 1973, Acta Cybern..

[166]  Michael A. Langston,et al.  Analysis of a Compound bin Packing Algorithm , 1991, SIAM J. Discret. Math..

[167]  M. Yue On the exact upper bound for the multifit processor scheduling algorithm , 1990 .