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An Approximation Algorithm based on First-fit Strategy for Template Packing Problem

First-fit 전략을 사용하는 템플럿 패킹 문제를 위한 근사 알고리즘

  • Song, Ha-Joo (Dept. of IT Convergence and Application, Pukyong National University) ;
  • Kwon, Oh-Heum (Dept. of IT Convergence and Application, Pukyong National University)
  • Received : 2016.01.22
  • Accepted : 2016.02.03
  • Published : 2016.02.28

Abstract

This paper deals with a kind of packing problem of which the goal is to compose one or more templates which will be used to produce the items of different types. Each template consists of a fixed number of slots which are assigned to the different types of items and the production of the items is accomplished by printing the template repeatedly. The objective is to minimize the total number of produced items. This problem is known to be NP-hard. We present a polynomial time approximation algorithm which has a constant approximation ratio. The proposed algorithm is based on the well-known first-fit strategy.

Keywords

References

  1. R. Cohen, L. Katzir, and D. Raz, "An Efficient Approximation for the Generalized Assignment Problem," Information Processing Letters, Vol. 100, No. 4, pp. 162-166, 2006. https://doi.org/10.1016/j.ipl.2006.06.003
  2. J. Du and J.Y. Leung, "Complexity of Scheduling Parallel Task Systems," SIAM Journal of Discrete Mathematics, Vol. 2, No. 4, pp. 473-487, 1989. https://doi.org/10.1137/0402042
  3. L. Fleischer, M.X. Goemans, V.S. Mirrokni, and M. Sviridenko, "Tight Approximation Algorithms for Maximum General Assignment Problems," Proceedings of Symposium on Discrete Algorithms, pp. 611-620, 2006.
  4. M. Garey and D.S. Johnson, Computers and Intractability: A Guide to the NP-Completeness, W.H. Freemac and Company, New York, 1979.
  5. A. Lodi, S. Martello, and D. Vigo, "Recent Advances on Two-dimensional Bin Packing Problems," Discrete Applied Mathematics, Vol. 123, No. 3, pp. 379-396, 2002. https://doi.org/10.1016/S0166-218X(01)00347-X
  6. O.H. Kwon and H.J. Song, “Improved Approximation Algorithm Based on Branch-and-Bound Technique for Label Packing Problem,“ Journal of Korean Institute of Next Generation Computing, Vol. 10, No. 10, pp. 13-24, 2014.
  7. H.M. Kwon, “Two Level Bin-Packing Algorithm for Data Allocation on Multiple Broadcast Channels,“ Journal of Korea Multimedia Society, Vol. 14, No. 9, pp. 1165-1174, 2011. https://doi.org/10.9717/kmms.2011.14.9.1165

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