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On Algorithms for Obtaining a Maximum Transversal

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Published:01 September 1981Publication History
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References

  1. 1 BERGE, C. The Theory of Graphs Methuen, London, 1962.Google ScholarGoogle Scholar
  2. 2 BUNCH, J.R., AND ROSE, D J., Eds In Proc Conf. Sparse Matrix Computations (Argonne National Laboratory, Sept 9-11, 1975), Academic Press, New York, 1976.Google ScholarGoogle Scholar
  3. 3 DUFF, I.S. Analysis of sparse systems. Ph.D. thesis, Oxford, England, 1972.Google ScholarGoogle Scholar
  4. 4 DUFF, I.S On permutations to block triangular form. J. Inst Math. Appl. 19 (1977), 339-342Google ScholarGoogle Scholar
  5. 5 DUFF, I S. A survey of sparse matrix research. Proc IEEE 65 (1977), 500-535.Google ScholarGoogle Scholar
  6. 6 DUFF, I S Algorithm 575 Permutations for a zero-free diagonal. ACM Trans. Math. Softw 7, 3 (Sept 1981), 387-390 Google ScholarGoogle Scholar
  7. 7 DUFF, I.S, AND REID, J K. An m~plementatlon of Tarjan's algorithm for the block triangulanzatlon of a matrix ACM Trans Math. Softw 4, 2 (June 1978), 137-147. Google ScholarGoogle Scholar
  8. 8 DULMAGE, A L, AND MENDELSOHN, N.S. A structure theory of b~partlte graphs of finite exterior dimension Trans Roy Soc. Can 53, Sec. 3 (1959), 1-13Google ScholarGoogle Scholar
  9. 9 DULMAGE, A L., AND MENDELSOHN, N.S. Two algorithms for bipartite graphs. J. SIAM 11 (1963), 183-194.Google ScholarGoogle Scholar
  10. 10 FORD, L.R, JR., AND FULKERSON, D.R. Flows in Networks. Princeton University Press, Princeton, N.J., 1962.Google ScholarGoogle Scholar
  11. 11 GUSTAVSON, F.G. Finding the block lower triangular form of a matrix. In Sparse Matrix Computations, J.R. Bunch and D J. Rose (Eds.), Academic Press, New York, 1976.Google ScholarGoogle Scholar
  12. 12 HALL, M. An algorithm for distinct representatives. Am. Math. Monthly 63 (1956), 716-717.Google ScholarGoogle Scholar
  13. 13 HALL, P. On representatives of subsets. J. London Math. Soc. 10, 37, pt. 1 (1935), 26-30Google ScholarGoogle Scholar
  14. 14 HARARY, F. Graph Theory. Addison-Wesley, Reading, Mass., 1969Google ScholarGoogle Scholar
  15. 15 HOPCROFT, J.E., AND KARP, R.M. An n5/2 algorithm for maximum matchings in bipartite graphs SIAM J. Comput. 2 (1973), 225-231.Google ScholarGoogle Scholar
  16. 16 SETTLER, P., AND WEIL, R. An algor,thm to provide structure for decomposition. In Proc Syrup on Sparse Matrices and their Apphcat~ons, R A. Willoughby (Ed.), IBM Rep. RA (11707), Yorktown Heights, N Y, 1969.Google ScholarGoogle Scholar
  17. 17 KONI6, D. Theor~e der endhchen und unendhchen Graphen Chelsea, New York, 1950.Google ScholarGoogle Scholar
  18. 18 KUHS, H W. The Hungarian method for solving the assignment problem. Naval Res. LogLst. Quart. 2 (1955), 83-97.Google ScholarGoogle Scholar
  19. 19 KUHN, H W Variants of the Hungarian method for assignment problems Naval Res Logzst Quart 3 (1957), 253-258.Google ScholarGoogle Scholar
  20. 20 STEWARD, D.V. On an approach to techniques for the analysis of the structure of large systems of equations. SIAM Rev. 4 (1962), 321-342Google ScholarGoogle Scholar
  21. 21 STEWARD, D.V Partitioning and tearing systems of equations. SIAM J Numer. Anal. 2 (1965), 345-365.Google ScholarGoogle Scholar
  22. 22 TARJAN, R. Depth-f'wst search and linear graph algorithms. SIAM J Comput 1 (1972), 146-160Google ScholarGoogle Scholar
  23. 23 WIBER6, T. Permutation of an unsymmetric matrix to block triangular form. Ph.D. dissertation, Dep of Informatzon Processing, Univ. Ume~, Ume~, Sweden, March 1977Google ScholarGoogle Scholar
  24. 24 WILLOUGHBY, R.A. Ed., Proc. Syrup. on Sparse Matrices and thew Applications, IBM Rep. RA 1 (11707), Yorktown Heights, N.Y., 1969.Google ScholarGoogle Scholar

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          cover image ACM Transactions on Mathematical Software
          ACM Transactions on Mathematical Software  Volume 7, Issue 3
          Sept. 1981
          147 pages
          ISSN:0098-3500
          EISSN:1557-7295
          DOI:10.1145/355958
          Issue’s Table of Contents

          Copyright © 1981 ACM

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          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 1 September 1981
          Published in toms Volume 7, Issue 3

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