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Online Algorithms pp 147–177Cite as

On-line packing and covering problems

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References

  1. M. Ajtai, J. Komlós, and G. Tusnády. On optimal matching. Combinatorica, 4:259–264, 1984.

    Google Scholar 

  2. N. Alon any Y. Azar, J. Csirik, L. Epstein, S. V. Sevastianov, A. P. A. Vestjens, and G. J. Woeginger. On-line and off-line approximation algorithms for vector covering problems. In Proc. 4th European Symposium on Algorithms, LNCS, pages 406–418. Springer, 1996. To appear in Algorithmica.

    Google Scholar 

  3. S. F. Assmann. Problems in Discrete Applied Mathematics. PhD thesis, MIT, Cambridge, MA, 1983.

    Google Scholar 

  4. S. F. Assmann, D. S. Johnson, D. J. Kleitman, and J. Y. T. Leung. On a dual version of the one-dimensional bin packing problem. J. Algorithms, 5:502–525, 1984.

    Google Scholar 

  5. Y. Azar and L. Epstein. On two dimensional packing. In Proc. 5th Scand. Workshop Alg. Theor., LNCS, pages 321–332. Springer, 1996.

    Google Scholar 

  6. B. S. Baker. A new proof for the First-Fit decreasing bin-packing algorithm. J. Algorithms, 6:49–70, 1985.

    Article  Google Scholar 

  7. B. S. Baker, D. J. Brown, and H. P. Katseff. A 5/4 algorithm for two-dimensional packing. J. Algorithms, 2:348–368, 1981.

    Google Scholar 

  8. B. S. Baker, D. J. Brown, and H. P. Katseff. Lower bounds for two-dimensional packing algorithms. Acta Informatica, 8:207–225, 1982.

    Google Scholar 

  9. B. S. Baker and E. G. Coffman. A tight asymptotic bound for Next-Fit-Decreasing bin-packing. SIAM J. Alg. Disc. Meth., 2:147–152, 1981.

    Google Scholar 

  10. B. S. Baker, E. G. Coffman, and R. L. Rivest. Orthogonal packings in two dimensions. SIAM J. Comput., 9:846–855, 1980.

    Google Scholar 

  11. B. S. Baker and J. S. Schwartz. Shelf algorithms for two-dimensional packing problems. SIAM J. Comput., 12:508–525, 1983.

    Article  Google Scholar 

  12. J. J. Bartholdi, J. H. vande Vate, and J. Zhang. Expected performance of the shelf heuristic for two-dimensional packing. Oper. Res. Lett., 8:11–16, 1989.

    Article  Google Scholar 

  13. J. L. Bentley, D. S. Johnson, F. T. Leighton, C. C. McGeoch, and L. A. McGeoch. Some unexpected expected behavior results for bin packing. In Proc. 16th Annual ACM Symp. Theory of Computing, pages 279–288, 1984.

    Google Scholar 

  14. D. Blitz, A. Van Vliet, and G. J. Woeginger. Lower bounds on the asymptotic worst-case ratio of on-line bin packing algorithms. Unpublished manuscript, 1996.

    Google Scholar 

  15. D. J. Brown. A lower bound for on-line one-dimensional bin packing algorithms. Technical Report R-864, Coordinated Sci. Lab., Urbana, Illinois, 1979.

    Google Scholar 

  16. J. Brzustowski. Can you win at Tetris? Master's thesis, The University of British Columbia, 1992.

    Google Scholar 

  17. H. Burgiel. How to lose at Tetris. Technical report, The Geometry Center, Minneapolis, MN, 1996.

    Google Scholar 

  18. B. Chandra. Does randomization help in on-line bin packing? Inform. Process. Lett., 43:15–19, 1992.

    Article  MathSciNet  Google Scholar 

  19. E. E. Chang, W. Wang, and M. S. Kankanhalli. Multidimensional on-line bin packing: An algorithm and its average-case analysis. Inform. Process. Lett., 48:121–125, 1993.

    Google Scholar 

  20. F. R. K. Chung, M. R. Garey, and D. S. Johnson. On packing two-dimensional bins. SIAM J. Alg. Disc. Meth., 3:66–76, 1982.

    Google Scholar 

  21. E. G. Coffman. An introduction to combinatorial models of dynamic storage allocation. SIAM Rev., 25:311–325, 1983.

    Google Scholar 

  22. E. G. Coffman, M. R. Garey, and D. S. Johnson. Dynamic bin packing. SIAM J. Comput., 12:227–258, 1983.

    Google Scholar 

  23. E. G. Coffman, M. R. Garey, and D. S. Johnson. Approximation algorithms for bin packing: a survey. In D. Hochbaum, editor, Approximation algorithms for NP-hard Problems, pages 46–93. PWS Publishing Company, 1997.

    Google Scholar 

  24. E. G. Coffman, D. S. Johnson, P. W. Shor, and R. R. Weber. Bin packing with discrete item sizes, part ii: average case behaviour of First Fit. Unpublished manuscript, 1996.

    Google Scholar 

  25. E. G. Coffman and G. S. Lueker. Probabilistic analysis of Packing and Partitioning Algorithms. John Wiley, New York, 1991.

    Google Scholar 

  26. E. G. Coffman, G. S. Lueker, and A. H. G. Rinnooy Kan. Asymptotic methods in the probabilistic analysis of sequencing and packing heuristics. Management Science, 34:266–290, 1988.

    Google Scholar 

  27. E. G. Coffman and P. W. Shor. Packing in two dimensions: asymptotic average-case analysis of algorithms. Algorithmica, 9:253–277, 1993.

    Google Scholar 

  28. E. G. Coffman, K. So, M. Hofri, and A. C. C. Yao. A stochastic model of bin packing. Information and Control, 44:105–115, 1980.

    Google Scholar 

  29. D. Coppersmith and P. Raghavan. Multidimensional on-line bin packing: Algorithms and worst case analysis. Oper. Res. Lett., 8:17–20, 1989.

    Google Scholar 

  30. J. Csirik. Bin-packing as a random walk: a note on Knoedels paper. Oper. Res. Lett., 5:161–163, 1986.

    Google Scholar 

  31. J. Csirik. An on-line algorithm for variable-sized bin packing. Acta Informatica, 26:697–709, 1989.

    Article  Google Scholar 

  32. J. Csirik. The parametric behaviour of the First Fit decreasing bin-packing algorithm. J. Algorithms, 15:1–28, 1993.

    Google Scholar 

  33. J. Csirik, J. B. G. Frenk, G. Galambos, and A. H. G. Rinnooy Kan. Probabilistic analysis of algorithms for dual bin packing problems. J. Algorithms, 12:189–203, 1991.

    Article  Google Scholar 

  34. J. Csirik, J. B. G. Frenk, and M. Labbe. Two dimensional rectangle packing: on line methods and results. Discr. Appl. Math., 45:197–204, 1993.

    Article  Google Scholar 

  35. J. Csirik and G. Galambos. An O(n) bin packing algorithm for uniformly distributed data. Computing, 36:313–319, 1986.

    Article  Google Scholar 

  36. J. Csirik, G. Galambos, and G. Turán. A lower bound on on-line algorithms for decreasing lists. In Proc. of EURO VI, 1984.

    Google Scholar 

  37. J. Csirik and B. Imreh. On the worst-case performance of the NkF bin packing heuristic. Acta Cybernetica, 9:89–105, 1989.

    Google Scholar 

  38. J. Csirik and D. S. Johnson. Bounded space on-line bin packing: best is better than first. In Proc. 2nd ACM-SIAM Symp. Discrete Algorithms, pages 309–319, 1991.

    Google Scholar 

  39. J. Csirik and E. Máté. The probabilistic behaviour of the NFD bin-packing heuristic. Acta Cybernetica, 7:241–246, 1986.

    Google Scholar 

  40. J. Csirik and V. Totik. On-line algorithms for a dual version of bin packing. Discr. Appl. Math., 21:163–167, 1988.

    Article  Google Scholar 

  41. J. Csirik and A. Van Vliet. An on-line algorithm for multidimensional bin packing. Oper. Res. Lett., 13:149–158, 1993.

    Article  Google Scholar 

  42. J. Csirik and G. J. Woeginger. Shelf algorithms for on-line strip packing. Inform. Process. Lett., 63:171–175, 1997.

    Article  Google Scholar 

  43. G. N. Frederickson. Probabilistic analysis for simple one-and two-dimensional bin packing algorithms. Inform. Process. Lett., 11:156–161, 1980.

    Article  Google Scholar 

  44. D. K. Friesen and M. A. Langston. Variable sized bin packing. SIAM J. Comput., 15:222–230, 1986.

    Article  Google Scholar 

  45. G. Galambos. Parametric lower bounds for on-line bin packing. SIAM J. Alg. Disc. Meth., 7:362–367, 1986.

    Google Scholar 

  46. G. Galambos. Notes on Lee's harmonic fit algorithm. Annales Univ. Sci. Budapest., Sect. Comp., 9:121–126, 1988.

    Google Scholar 

  47. G. Galambos. A 1.6 lower bound for the two-dimensional on-line rectangle bin packing. Acta Cybernetica, 10:21–24, 1991.

    MathSciNet  Google Scholar 

  48. G. Galambos and J. B. G. Frenk. A simple proof of Liang's lower bound for online bin packing and the extension to the parametric case. Discr. Appl. Math., 41:173–178, 1993.

    Article  Google Scholar 

  49. G. Galambos, H. Kellerer, and G. J. Woeginger. A lower bound for on-line vector packing algorithms. Acta Cybernetica, 11:23–34, 1994.

    Google Scholar 

  50. G. Galambos and A. Van Vliet. Lower bounds for 1-, 2-, and 3-dimensional online bin packing algorithms. Computing, 52:281–297, 1994.

    Article  Google Scholar 

  51. G. Galambos and G. J. Woeginger. Repacking helps in bounded space on-line bin packing. Computing, 49:329–338, 1993.

    Article  Google Scholar 

  52. G. Gambosi, A. Postiglione, and M. Talamo. New algorithms for on-line bin packing. In Proc. 1st Italian Conference on Algorithms and Complexity, 1990.

    Google Scholar 

  53. M. R. Garey, R. L. Graham, D. S. Johnson, and A. C. C. Yao. Resource constrained scheduling as generalized bin packing. J. Comb. Th. Ser. A., 21:257–298, 1976.

    Article  Google Scholar 

  54. M. R. Garey and D. S. Johnson. Computers and Intractability (A Guide to the theory of of NP-Completeness. W. H. Freeman and Company, San Francisco, 1979.

    Google Scholar 

  55. H. Groemer. Covering and packing properties of bounded sequences of convex sets. Mathematika, 29:18–31, 1982.

    Google Scholar 

  56. E. F. Grove. On-line binpacking with lookahead. In Proc. 6th ACM-SIAM Symp. Discrete Algorithms, pages 430–436, 1995.

    Google Scholar 

  57. U. Hoffman. A class of simple stochastic on-line bin packing algorithms. Computing, 29:227–239, 1982.

    Article  Google Scholar 

  58. M. Hofri. Two-dimensional packing: Expected performance of simple level algorithms. Information and Control, 45:1–17, 1980.

    Article  Google Scholar 

  59. M. Hofri. A probabilistic analysis of the Next-Fit bin packing algorithm. J. Algorithms, 5:547–556, 1984.

    Article  Google Scholar 

  60. M. Hofri. Probabilistic analysis of algorithms. Springer, New York, 1987.

    Google Scholar 

  61. M. Hofri and S. Kahmi. A stochastic analysis of the NFD bin packing algorithm. J. Algorithms, 7:489–509, 1986.

    Article  Google Scholar 

  62. Z. Ivkovic and E. Lloyd. Fully dynamic algorithms for bin packing: Being myopic helps. In Proc. 1st European Symposium on Algorithms, LNCS, pages 224–235. Springer, 1993.

    Google Scholar 

  63. Z. Ivkovic and E. Lloyd. A fundamental restriction on fully dynamic maintenance of bin packing. Inform. Process. Lett., 59:229–232, 1996.

    Article  Google Scholar 

  64. Z. Ivkovic and E. Lloyd. Partially dynamic bin packing can be solved within 1+eps in (amortized) polylogaritmic time. Inform. Process. Lett., 63:45–50, 1997.

    Article  Google Scholar 

  65. J. Januszewski and M. Lassak. On-line covering by boxes and by covex bodies. Bull. Pol. Acad. Math., 42:69–76, 1994.

    Google Scholar 

  66. J. Januszewski and M. Lassak. On-line covering the unit cube by cubes. Discrete Comput. Geom., 12:433–438, 1994.

    Google Scholar 

  67. J. Januszewski and M. Lassak. Efficient on-line covering of large cubes by convex bodies of at most unit diameters. Bull. Pol. Acad. Math., 43:305–315, 1995.

    Google Scholar 

  68. J. Januszewski and M. Lassak. On-line covering the unit square by squares and the three-dimensional unit cube by cubes. Demonstratio Math., 28:143–149, 1995.

    Google Scholar 

  69. J. Januszewski and M. Lassak. On-line packing the unit cube by cubes, unpublished manuscript, University of Bydgoszcz, Poland, 1996.

    Google Scholar 

  70. J. Januszewski, M. Lassak, G. Rote, and G. J. Woeginger. On-line q-adic covering by the method of the n-th segment and its application to on-line covering by cubes. Beitr. Algebra Geom., 37:94–100, 1996.

    Google Scholar 

  71. D. S. Johnson. Near-optimal bin packing algorithms. PhD thesis, MIT, Cambridge, MA, 1973.

    Google Scholar 

  72. D. S. Johnson. Fast algorithms for bin packing. J. Comput. System Sci., 8:272–314, 1974.

    Google Scholar 

  73. D. S. Johnson, A. Demers, J. D. Ullman, M. R. Garey, and R. L. Graham. Worst-case performance bounds for simple one-dimensional packing algorithms. SIAM J. Comput., 3:256–278, 1974.

    Article  Google Scholar 

  74. N. Karmarkar. Probabilistic analysis of some bin packing algorithms. In Proc. 23rd IEEE Symp. Found. Comp. Sci., pages 107–118, 1982.

    Google Scholar 

  75. R. M. Karp, M. Luby, and A. Marchetti-Spaccamela. Probabilistic analysis of multi-dimensional binpacking problems. In Proc. 16th Annual ACM Symp. Theory of Computing, pages 289–298, 1984.

    Google Scholar 

  76. N. G. Kinnersley and M. A. Langston. On-line variable-sized bin packing. Discr. Appl. Math., 22:143–148, 1988.

    Article  Google Scholar 

  77. W. Knoedel. A bin packing algorithm with complexity o(nlogn) and performance 1 in the stochastic limit. In J. Gruska and M. Chytil, editors, Proc. 10th Symp. Math. Found. Comp. Science, LNCS, pages 369–378. Springer, 1981.

    Google Scholar 

  78. W. Knoedel. Ueber das mittlere Verhalten von on-line Packungsalgorithmen. EIK, 19:427–433, 1983.

    Google Scholar 

  79. L. T. Kou and G. Markowsky. Multidimensional bin packing algorithms. IBM J. Research and Development, 21:443–448, 1977.

    Google Scholar 

  80. W. Kuperberg. On-line covering a cube by a sequence of cubes. Discrete Comput. Geom., 12:83–90, 1994.

    Google Scholar 

  81. M. Lassak. On-line covering a box by cubes. Beitr. Algebra Geom., 36:1–7, 1995.

    Google Scholar 

  82. M. Lassak and J. Zhang. An on-line potato-sack theorem. Discrete Comput. Geom., 6:1–7, 1991.

    Google Scholar 

  83. C. C. Lee and D. T. Lee. A simple on-line bin packing algorithm. J. Assoc. Comput. Mach., 32:562–572, 1985.

    Google Scholar 

  84. C. C. Lee and D. T. Lee. Robust on-line bin packing algorithms. Technical Report 83-03-FC-02, Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL, 1987.

    Google Scholar 

  85. F. T. Leighton and P. Shor. Tight bounds for minimax grid matching with applications to the average case analysis of algorithms. Combinatorica, 9:161–187, 1989.

    Article  Google Scholar 

  86. K. Li and K. H. Cheng. Heuristic algorithms for on-line packing in three dimensions. J. Algorithms, 13:589–605, 1992.

    Article  Google Scholar 

  87. F. M. Liang. A lower bound for on-line bin packing. Inform. Process. Lett., 10:76–79, 1980.

    Article  Google Scholar 

  88. G. S. Lueker. An average-case analysis of bin packing with uniformly distributed item sizes. Technical Report 181, Dept. Information and Computer Science, University of California at Irvine, 1982.

    Google Scholar 

  89. W. Mao. Best-k-Fit bin packing. Computing, 50:265–270, 1993.

    Article  Google Scholar 

  90. W. Mao. Tight worst-case performance bounds for Next-k-Fit bin packing. SIAM J. Comput., 22:46–56, 1993.

    Article  Google Scholar 

  91. A. Meir and L. Moser. On packing of squares and cubes. J. Combin. Theory, 5:126–134, 1968.

    Google Scholar 

  92. H. L. Ong, M. J. Magazine, and T. S. Wee. Probabilistic analysis of bin packing heuristics. Oper. Res., 5:983–998, 1984.

    MathSciNet  Google Scholar 

  93. P. Ramanan. Average case analysis of the Smart Next Fit algorithm. Inform. Process. Lett., 31:221–225, 1989.

    Article  Google Scholar 

  94. P. Ramanan, D. J. Brown, C. C. Lee, and D. T. Lee. On-line bin packing in linear time. J. Algorithms, 10:305–326, 1989.

    Article  Google Scholar 

  95. P. Ramanan and K. Tsuga. Average case analysis of the modified harmonic algorithm. Algorithrnica, 4:519–533, 1989.

    Article  Google Scholar 

  96. W. T. Rhee and M. Talagrand. The complete convergence of best fit decreasing. SIAM J. Comput., 18:909–918, 1989.

    Article  Google Scholar 

  97. W. T. Rhee and M. Talagrand. The complete convergence of first fit decreasing. SIAM J. Comput., 18:919–938, 1989.

    Article  Google Scholar 

  98. W. T. Rhee and M. Talagrand. Dual bin packing of items of random size. Math. Progr., 58:229–242, 1993.

    Article  Google Scholar 

  99. W. T. Rhee and M. Talagrand. On line bin packing with items of random size. Math. Oper. Res., 18:438–445, 1993.

    Google Scholar 

  100. W. T. Rhee and M. Talagrand. On line bin packing with items of random sizes — ii. SIAM J. Comput., 22:1252–1256, 1993.

    Article  Google Scholar 

  101. M. B. Richey. Improved bounds for harmonic-based bin packing algorithms. Discr. Appl. Math., 34:203–227, 1991.

    Article  Google Scholar 

  102. S. D. Shapiro. Performance of heuristic bin packing algorithms with segments of random length. Inf. and Cont., 35:146–148, 1977.

    Google Scholar 

  103. P. W. Shor. The average-case analysis of some on-line algorithms for bin packing. Combinatorica, 6:179–200, 1986.

    Google Scholar 

  104. P. W. Shor. How to pack better than Best-Fit: Tight bounds for average-case online bin packing. In Proc. 32nd IEEE Symp. Found. Comp. Sci., pages 752–759, 1991.

    Google Scholar 

  105. D. D. K. D. B. Sleator. A 2.5 times optimal algorithm for packing in two dimensions. Inform. Process. Lett., 10:37–40, 1976.

    Article  Google Scholar 

  106. A. Van Vliet. An improved lower bound for on-line bin packing algorithms. Inform. Process. Lett., 43:277–284, 1992.

    Article  Google Scholar 

  107. A. Van Vliet. Lower and upper bounds for on-line bin packing and scheduling heuristics. PhD thesis, Erasmus University, Rotterdam, The Netherlands, 1995.

    Google Scholar 

  108. A. Van Vliet. On the asymptotic worst case behaviour of harmonic fit. J. Algorithms, 20:113–136, 1996.

    Article  Google Scholar 

  109. G. J. Woeginger. Improved space for bounded-space on-line bin packing. SIAM J. Discr. Math., 6:575–581, 1993.

    Article  Google Scholar 

  110. G. J. Woeginger and G. Zhang. Optimal on-line algorithms for variable-sized bin covering. Technical Report Woe-022, TU Graz, Austria, 1998.

    Google Scholar 

  111. A. C. C. Yao. New algorithms for bin packing. J. Assoc. Comput. Mach., 27:207–227, 1980.

    Google Scholar 

  112. G. Zhang. A tight worst-case performance bound for AFB-k. Technical Report 015, Institute of Applied Mathematics, Academia Sinica, Beijing, China, 1994.

    Google Scholar 

  113. G. Zhang. Worst-case analysis of the FFH algorithm for on-line variable-sized bin packing. Computing, 56:165–172, 1996.

    Google Scholar 

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  1. János Csirik
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  2. Gerhard J. Woeginger
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Amos Fiat Gerhard J. Woeginger

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Csirik, J., Woeginger, G.J. (1998). On-line packing and covering problems. In: Fiat, A., Woeginger, G.J. (eds) Online Algorithms. Lecture Notes in Computer Science, vol 1442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029568

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