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Problems in Data Structures and Algorithms

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Graph Theory, Combinatorics and Algorithms

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References

  1. G. M. Adel’son-Vel’skii and E.M. Landis, An algorithm for the organization of information, Soviet Math Dokl. 3: 1259–1262 (1962).

    Google Scholar 

  2. M. Ajtai, J. Komlós, and E. Szemerédi, Sorting in c log n parallel steps, Combinatorica 3: 1–19 (1983).

    MathSciNet  MATH  Google Scholar 

  3. O. Borůvka, O jistém problému minimálním, Práce Mor. Přírověd. Spol. v Brně (Acta Societ. Scient. Natur. Moravicae) 3: 37–58 (1926).

    Google Scholar 

  4. B. Chazelle, The soft heap: an approximate priority queue with optimal error rate, J. Assoc. Comput. Mach. 47: 1012–1027 (2000).

    MathSciNet  MATH  Google Scholar 

  5. B. Chazelle, Aminimum spanning tree algorithm with inverse-Ackermann type complexity, J. Assoc. Comput. Mach. 47: 1028–1047 (2000).

    MathSciNet  MATH  Google Scholar 

  6. R. Cole, B. Mishra, J. Schmidt, and A. Siegel, On the dynamic finger conjecture for splay trees, part I: splay sorting logn-block sequences, SIAM J. Computing 30:1–43 (2000).

    MathSciNet  MATH  Google Scholar 

  7. R. Cole, On the dynamic finger conjecture for splay trees, part II: the proof, SIAM J. Computing 30: 44–85 (2000).

    MATH  MathSciNet  Google Scholar 

  8. D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, J. Symbolic Computation 9: 251–280 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  9. E. D. Demaine, D. Harmon, J. Iacono, and M. PĂatraşcu, Dynamic optimality—almost, Proc 45 th Annual IEEE Symp. on Foundations of Computer Science, (2004) pp. 484–490.

    Google Scholar 

  10. E. W. Dijkstra, A note on two problems in connexion with graphs, Num. Mathematik 1:269–271 (1959).

    MATH  MathSciNet  Google Scholar 

  11. M. J. Fischer, Efficiency of equivalence algorithms, Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, eds., Plenum Press, New York, NY, (1972) pp. 153–168.

    Google Scholar 

  12. M. L. Fredman and M. E. Saks, The cell probe complexity of dynamic data structures, Proc. 21 st Annual ACM Symp. on Theory of Computing, (1989) pp. 345–354.

    Google Scholar 

  13. M. R. Fredman and R. E. Tarjan, Fibonacci heaps and their uses in improved network optimization algorithms, J. Assoc. Comput. Mach. 34: 596–615 (1987).

    MathSciNet  Google Scholar 

  14. H. N. Gabow, Z. Galil, and T. H. Spencer, Efficient implementation of graph algorithms using contraction, Proc. 25 th Annual IEEE Symp. on Found. of Comp. Sci., (1984) pp. 347–357.

    Google Scholar 

  15. H. N. Gabow, Z. Galil, T. Spencer, and R. E. Tarjan, Efficient algorithms for finding minimum spanning trees in directed and undirected graphs, Combinatorica 6: 109–122 (1986).

    MathSciNet  MATH  Google Scholar 

  16. B. A. Galler and M. J. Fischer, An improved equivalence algorithm, Comm. Assoc. Comput. Mach. 7: 301–303 (1964).

    MATH  Google Scholar 

  17. A. M. Garsia and M. L. Wachs, A new algorithm for minimal binary encodings, SIAM J. Comput. 6: 622–642 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  18. R. L. Graham and P. Hell, On the history of the minimum spanning tree problem, Annuals of the History of Computing 7: 43–57 (1985).

    MathSciNet  MATH  Google Scholar 

  19. L. J. Guibas and R. Sedgewick, A dichromatic framework for balanced trees, Proc. 19 th Annual IEEE Symp. on Foundations of Computer Science, (1978) pp. 8–21.

    Google Scholar 

  20. J. Hopcroft and J. D. Ullman, Set-merging algorithms, SIAM J. Comput. 2: 294–303 (1973).

    MathSciNet  MATH  Google Scholar 

  21. T. C. Hu and A. C. Tucker, Optimal computer search trees and variable-length alphabetic codes, SIAM J. Appl. Math 21: 514–532 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  22. D. A. Huffman, A method for the construction of minimum-redundancy codes, Proc. IRE 40: 1098–1101 (1952).

    Google Scholar 

  23. V. Jarník, O jistém problému minimálním, Práce Mor. Přírověd. Spol. v Brně (Acta Societ. Scient. Natur. Moraricae) 6: 57–63 (1930).

    Google Scholar 

  24. H. Kaplan, N. Shafrir, and R. E. Tarjan, Union-find with deletions, Proc. 13 th Annual ACM-SIAM Symp. on Discrete Algorithms, (2002) pp. 19–28.

    Google Scholar 

  25. D. R. Karger, P. N. Klein, and R. E. Tarjan, A randomized linear-time algorithm to find minimum spanning trees, J. Assoc. Comput. Mach. 42: 321–328 (1995).

    MathSciNet  MATH  Google Scholar 

  26. M. Karpinski, L. L. Larmore, and V. Rytter, Correctness of constructing optimal alphabetic trees revisited, Theoretical Computer Science 180: 309–324 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  27. M. Klawe and B. Mumey, Upper and lower bounds on constructing alphabetic binary trees, Proc 4 th Annual ACM-SIAM Symp. on Discrete Algorithms, (1993) pp. 185–193.

    Google Scholar 

  28. P. N. Klein and R. E. Tarjan, A randomized linear-time algorithm for finding minimum spanning trees, Proc. 26 th Annual ACM Symp. on Theory of Computing, (1994) pp. 9–15.

    Google Scholar 

  29. D. E. Knuth, The Art of Computer Programming, Vol. 1: Fundamental Algorithms, Second Edition, Addison-Wesley, Reading, MA, (1973) p. 572.

    Google Scholar 

  30. D. E. Knuth, Optimum binary search trees, Acta Informatica 1: 14–25 (1971).

    MATH  Google Scholar 

  31. J.B. Kruskal, On the shortest spannng subtree of a graph and the travelling saleman problem, Proc. Amer. Math. Soc. 7: 48–50 (1956).

    MATH  MathSciNet  Google Scholar 

  32. S. Pettie and V. Ramachandran, An optimal minimum spanning tree algorithm, J. Assoc. Comput. Mach. 49: 16–34 (2002).

    MathSciNet  Google Scholar 

  33. R. C. Prim, The shortest connecting network and some generalizations, Bell Syst. Tech. J. 36: 1389–1401 (1957).

    Google Scholar 

  34. M. Sharir and P. K. Agarwal, Davenport-Schinzel Sequences and Their Geometric Applications, Cambridge University Press, Cambridge, England, (1995).

    MATH  Google Scholar 

  35. D. D. Sleator and R. E. Tarjan, Self-adjusting binary search trees, J. Assoc. Comput. Mach. 32: 652–686 (1985).

    MathSciNet  MATH  Google Scholar 

  36. D. D. Sleator, R. E. Tarjan, and W. P. Thurston, Rotation distance, triangulations, and hyperbolic geometry, J. Amer. Math Soc. 1: 647–682 (1988).

    MathSciNet  MATH  Google Scholar 

  37. R. E. Tarjan, Efficiency of a good but not linear set union algorithm, J. Assoc. Comput. Mach. 22: 215–225 (1975).

    MATH  MathSciNet  Google Scholar 

  38. R. E. Tarjan, A class of algorithms which require nonlinear time to maintain disjoint sets, J. Comput. Syst. Sci. 18: 110–127 (1979).

    MATH  MathSciNet  Google Scholar 

  39. R. E. Tarjan, Applications of path compression on balanced trees, J. Assoc. Comput. Mach. 26: 690–715 (1979).

    MATH  MathSciNet  Google Scholar 

  40. R. E. Tarjan, Updating a balanced search tree in O(1) rotations, Info. Process. Lett. 16:253–257 (1983).

    MATH  MathSciNet  Google Scholar 

  41. R. E. Tarjan, Sequential access in splay trees takes linear time, Combinatorica 5: 367–378 (1985).

    MATH  MathSciNet  Google Scholar 

  42. R. E. Tarjan and J. van Leeuwen, Worst-case analysis of set union algorithms, J. Assoc. Comput. Mach. 31: 246–281 (1984).

    Google Scholar 

  43. R. Wilbur, Lower bounds for accessing binary search trees with rotations, SIAM J. Computing 18: 56–67 (1989).

    Google Scholar 

  44. A. C. Yao, An O(|E|loglog|V|) algorithm for finding minimum spanning trees, Info. Process. Lett. 4: 21–23 (1975).

    MATH  Google Scholar 

  45. F. F. Yao, Efficient dynamic programming using quadrangle inequalities, Proc. 12 th Annual ACM Symp. on Theory of Computing, (1980) pp. 429–435.

    Google Scholar 

  46. http://cristal.inria.fr/ICFP2001/prog-contest/

    Google Scholar 

  47. http://www.link.cs.cmu.edu/splay/

    Google Scholar 

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Tarjan, R.E. (2005). Problems in Data Structures and Algorithms. In: Golumbic, M.C., Hartman, I.BA. (eds) Graph Theory, Combinatorics and Algorithms. Operations Research/Computer Science Interfaces Series, vol 34. Springer, Boston, MA. https://doi.org/10.1007/0-387-25036-0_2

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