한국인터넷방송통신학회논문지 (The Journal of the Institute of Internet, Broadcasting and Communication)

  • 제13권6호
  • /
  • Pages.211-220
  • /
  • 2013
  • /
  • 2289-0238(pISSN)
  • /
  • 2289-0246(eISSN)
한국인터넷방송통신학회 (The Institute of Internet, Broadcasting and Communication)
권호 표지
DOI QR코드

DOI QR Code

선형 병목할당 문제의 역-삭제 알고리즘

Linear Bottleneck Assignment Problem Based on Reverse-delete Algorithm

  • 이상운 (강릉원주대학교 과학기술대학 멀티미디어공학과)
  • Lee, Sang-Un (Dept. of Multimedia Eng., Gangneung-Wonju National University)
  • 투고 : 2013.05.12
  • 심사 : 2013.12.13
  • 발행 : 2013.12.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

본 논문은 선형 병목할당 문제의 최적해를 간단히 찾는 알고리즘을 제안하였다. 일반적으로 병목할당 문제의 최적해는 한계 또는 증대경로 알고리즘으로 구한다. 제안된 알고리즘은 2단계를 수행하는 역-삭제 알고리즘이다. 첫 번째로, 행 또는 열의 개수가 1개가 될 때까지 최대 비용을 삭제하여 초기해를 구한다. 두 번째로 한계치 보다 큰 값이 초기해로 선택되었으면 해를 개선하는 과정을 수행하였다. 제안된 알고리즘을 28개의 병목 균형 할당 문제와 7개의 병목 불균형 할당 문제에 적용한 결과 최적해를 쉽게 찾는데 성공하였다.

This paper proposes an algorithm that easily finds an optimal solution for linear bottleneck assignment problems. It is either threshold or augmenting path algorithm that is generally used to solve the bottleneck assignment problem. This paper proposes a reverse-delete algorithm that follows 2 steps. Firstly, the algorithm deletes the maximum cost in a given matrix until it renders a single row or column. Next, the algorithm improves any solution that contains a cost exceeding the threshold value $c^*_{ij}$. Upon its application to 28 balanced assignment problems and 7 unbalanced problems, the algorithm is found to be both successful and simple.

키워드

참고문헌

  1. B. Rainer, M. Dell'Amico, and S. Martello, "Assignment Problems," SIAM, 2009.
  2. H. W. Kuhn, "The Hungarian Method for the Assignment Problem," Naval Research Logistics Quarterly, Vol. 2, pp. 83-97, 1955. https://doi.org/10.1002/nav.3800020109
  3. L. Ntaimo, "Introduction to Mathematical Programming: Operations Research: Transportation and Assignment Problems", Vol. 1, 4th edition, W. L. Winston and M. Venkataramanan, 2005.
  4. K. Kinahan and J. Pryor, "Algorithm Animations for Practical Optimization: A Gentle Introduction," http://optlab-server.sce.carleton.ca/POAnimations2007/Default.html, 2007.
  5. F. D. Croce, V. T. Paschos, and A. Tsoukias, "An Improved General Procedure for Lexigraphic Bottleneck Problems," Operations Research Letters, Vol. 24, No. 4, pp. 187-194, May 1999. https://doi.org/10.1016/S0167-6377(99)00013-9
  6. H. W. Corley and H. Golnabi, "Technical Note: A Generalized Bottleneck Assignment Problem," Journal of Optimization Theory and Applications, Vol. 36, No. 1, pp. 135-138, Jan 1982. https://doi.org/10.1007/BF00934343
  7. R. Burkard, M. Dell'Amico, and S. Martello, "Linear Assignment Problems, Section 6.6 Lexicographic Bottleneck Assignment Problem," pp. 198-202, SIAM, 2008.
  8. E. S. Page, "A Note on Assignment Problems," The Computer Journal, Vol. 6, No. 3, pp. 241-243, 1963. https://doi.org/10.1093/comjnl/6.3.241
  9. R. S. Garfinkel, "An Improved Algorithm for the Bottleneck Assignment Problem," Operations Research, Vol. 19, No. 7, pp. 1747-1751, Jul 1971. https://doi.org/10.1287/opre.19.7.1747
  10. R. E. Burkard, "Optimierung und Kontrolle: Selected Topics on Assignment Problems," Karl-Franzens-Universitat Graz & Technische Universitat Graz, 1999.
  11. U. Derigs, "Alternate Strategies for Solving Bottleneck Assignment Problems-Analysis and Computational Results," Computing, Vol. 33, No. 2, pp. 95-106, Feb 1984. https://doi.org/10.1007/BF02240182
  12. O. Gross, "The Bottleneck Assignment Problem," Report No. P-1620, The Rand Corporation, Santa Monica, California, 1959.
  13. R. Fulkerson, I. Glickberg, and O. Gross, "A Production Line Assignment Problem," Technical Report RM-1102, The Rand Corporation, Santa Monica, California, 1953.
  14. H. N. Gabow and R. E. Tarjan, "Algorithms for two Bottleneck Optimization Problems," Journal of Algorithms, Vol. 9, No. 3, pp. 411-417, Sep 1988. https://doi.org/10.1016/0196-6774(88)90031-4
  15. U. Pfershy, "The Random Linear Bottleneck Assignment Problem," RAIRO Operations Research, Vol. 30, No. 2, pp. 127-142, Feb 1996. https://doi.org/10.1051/ro/1996300201271
  16. Sang-Un Lee, "The Simplified Solution for Assignment Problem," Journal of the Institute of Internet, Broadcasting and Communication, Vol. 12, No. 5, pp. 141-151, 2012. https://doi.org/10.7236/JIWIT.2012.12.5.141
  17. Sang-Un Lee, "The Assignment Problem Algorithm Based on the First Selection Method of the Minimum Cost," Journal of the Institute of Internet, Broadcasting and Communication, Vol. 13, No. 5, pp. 163-171, 2013. https://doi.org/10.7236/JIIBC.2013.13.5.163
  18. D. N. Kumar, "Optimization Methods," IISc, Bangalore, 2008.
  19. Rai Foundation Colleges, "Information Research," Bachelor of Business Administration, Business Administration, 2008.
  20. S. Noble, "Lectures 15: The Assignment Problem," Department of Mathematical Sciences, Brunel University, 2000.
  21. A. Dimitrios, P. Konstantinos, S. Nikolaos, and S. Angelo, "Applications of a New Network-enabled Solver for the Assignment Problem in Computer-aided Education," Journal of Computer Science, Vol. 1, No. 1, pp. 19-23, Jan 2005. https://doi.org/10.3844/jcssp.2005.19.23
  22. R. M. Berka, "A Tutorial on Network Optimization," http://home.eunet.cz/berka/o/English/networks/node8.html, 1997.
  23. M. S. Radhakrishnan, "AAOC C222: Optimization," Birla Institute of Technology & Science, 2006.
  24. R. Burkard, M. D. Amico, and S. Martello, "Assignment Problems," SIAM Monographs on Discrete Mathematics and Applications, 2006.
  25. S. C. Niu, "Introduction to Operations Research," School of Management, The University of Texas at Dallas, 2004.
  26. W. Snyder, "The Linear Assignment Problem," Department of Electrical and Computer Engineering, North Carolina State University, 2005.
  27. M. E. Salassi, "AGEC 7123: Operations Research Methods in Agricultural Economics: Standard LP Form of the Generalized Assignment Problem," Department of Agricultural Economics and Agribusiness, Louisiana State University, 2005.
  28. K. Wayne, "Algorithm Design," http://www.cs.princeton.edu/-wayne/kleinberg-tardos/07assignment.pdf, 2005.
  29. J. Havlicek, "Introduction to Management Science and Operation Research," http://orms.czu.cz/text/transproblem.html, 2007.
  30. R. Sedgewick and K. Wayne, " Computer Science 226: Data Structures and Algorithms, Princeton University, 2002.
  31. J. E. Beasley, "Operations Research and Management Science: OR-Notes," Department of Mathematical Sciences, Brunel University, West London, 2004.
  32. D. Doty, "Munkres' Assignment Algorithm: Modified for Rectangular Matrices," KCVU, Murray State University, Dept. of Computer Science and Information Systems, 2008.
  33. M. A. Trick, "Network Optimizations for Consultants," http://mat.gsia.cmu.edu/mstc/ networks/ networks.html, 1996.
  34. Optimalon Software, "Transportation Problem (Minimal Cost)," http://www.optimalon.com/ examples/transport.htm, 2008.