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Some Results for Elementary Operations

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Efficient Algorithms

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5760))

Abstract

We present a number of results for elementary operations concerning the areas of data structures, computational geometry, graph algorithms and string algorithms. Especially, we focus on elementary operations like the dictionary operations, list manipulation, priority queues, temporal precedence, finger search, nearest common ancestors, negative cycle, 3-sided queries, rectangle enclosure, dominance searching, intersection queries, hidden line elimination and string manipulation.

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References

  1. Adel’son-Velskii, G.M., Landis, E.M.: An Algorithm for the Organization of Information. Dokl. Akad. Nauk SSSR 146, 263–266 (1962) (in Russian); English translation in Soviet. Math. 3, 1259–1262 (1962)

    Google Scholar 

  2. Andersson, A., Mattson, C.: Dynamic Interpolation Search in o(loglogn) Time. In: Lingas, A., Carlsson, S., Karlsson, R. (eds.) ICALP 1993. LNCS, vol. 700, pp. 15–27. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  3. Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making Data Structures Persistent. J. Comput. System Sci. 28, 86–124 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kaporis, A., Makris, C., Mavritsakis, G., Sioutas, S., Tsakalidis, A., Tsichlas, K., Zaroliagis, C.: ISB-tree: A new indexing scheme with efficient expected behaviour. In: Deng, X., Du, D.-Z. (eds.) ISAAC 2005. LNCS, vol. 3827, pp. 318–327. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Kaporis, A., Makris, C., Sioutas, S., Tsakalidis, A., Tsichlas, K., Zaroliagis, C.: Improved Bounds for Finger Search on a RAM. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 325–336. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  6. Kaporis, A., Makris, C., Sioutas, S., Tsakalidis, A., Tsichlas, K., Zaroliagis, C.: Dynamic Interpolation Search Revisited. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 382–394. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Mehlhorn, K., Tsakalidis, A.K.: An Amortized Analysis of Insertions into AVL-Trees. SIAM J. Comput. 15(1), 22–33 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mehlhorn, K., Tsakalidis, A.: Dynamic Interpolation Search. Journal of the ACM 40(3), 621–634 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  9. Tsakalidis, A.K.: Rebalancing Operations for Deletions in AVL-Trees. RAIRO Inform. Theor. 19(4), 323–329 (1985)

    MathSciNet  MATH  Google Scholar 

  10. Vitter, J.: External Memory Algorithms and Data Structures: dealing with massive data. ACM Computing Surveys 33(2), 209–271 (2001)

    Article  Google Scholar 

  11. Willard, D.E.: Searching unindexed and nonuniformly generated files in log log N time. SIAM J. Comput. 14(4), 1013–1029 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  12. Bender, M.A., Cole, R., Demaine, E.D., Farach-Colton, M., Zito, J.: Two Simplified Algorithms for Maintaining Order in a List. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 219–223. Springer, Heidelberg (2002)

    Google Scholar 

  13. Blum, N., Mehlhorn, K.: On the average number of Rebalancing Operations in weight-balanced trees. Theor. Comput. Sci. 11, 303–320 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  14. Buchsbaum, A., Tarjan, R.E.: Confluently Persistent Deques via Data Structural Bootstrapping. In: Proc. of the fourth annual ACM-SIAM Symposium on Discrete Algorithms, pp. 155–164 (1993)

    Google Scholar 

  15. Dietz, P.F.: Fully Persistent Arrays (Extended Abstract). In: Proc. of the Workshop on Algorithma and Data Structures, pp. 67–74 (1989)

    Google Scholar 

  16. Dietz, P.F.: A Space Efficient Variant of Path Copying for Partially Persistent Sorted Sets. J. Comput. System Sci. 53, 148–152 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Dietz, P.F.: Maintaining Order in a Linked List. In: Proc. 14th ACM STOC, pp. 122–127 (1982)

    Google Scholar 

  18. Dietz, P.F., Sleator, D.D.: Two Algorithms for Maintaining Order in a List. In: Proc. 19th ACM STOC, pp. 365–372 (1987)

    Google Scholar 

  19. Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making Data structures Persistent. J. Comput. System Sci. 28, 82–124 (1989)

    MathSciNet  MATH  Google Scholar 

  20. Nievergelt, I., Reingold, E.M.: Binary Search Tress of Bounded Balance. SIAM J. Comput. 2, 33–43 (1973)

    Article  MATH  Google Scholar 

  21. Tsakalidis, A.K.: Maintaining Order in a generalized Linked List. Acta Informatica 21(1), 101–112 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  22. Hoyer, P.: A General Technique for Implementation of Efficient Priority Queues. In: Proc. of the 3rd Israel Symposium on Theory of Computing systems (ISTCS) (1995)

    Google Scholar 

  23. Makris, C., Tsakalidis, A., Tsichlas, K.: Reflected Min-Max Heaps. Inf. Proc. Letters 86, 209–214 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  24. Williams, J.W.J.: Algorithm 232. Comm. ACM 7(6), 347–348 (1964)

    Google Scholar 

  25. Brodal, G.S., Makris, C., Sioutas, S., Tsakalidis, A., Tsichlas, K.: Optimal Solution for the Temporal Precedence Problem. Algorithmica 33(4), 494–510 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Pontelli, E., Ranjan, D.: A Simple Optimal Solution for the Temporal Precedence Problem on Pure Pointer Machines. Theory of Computing Systems 38, 115–130 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. Pontelli, E., Ranjan, D., Gupta, G.: On the Complexity of Parallel Implementation of Logic Programs. In: Ramesh, S., Sivakumar, G. (eds.) FST TCS 1997. LNCS, vol. 1346, pp. 123–137. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  28. Ranjan, D., Pontelli, E., Gupta, G., Longpre, L.: The Temporal Precedence problem. Algorithmica 28(3), 288–306 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  29. Brodal, G.S., Lagogiannis, G., Makris, C., Tsakalidis, A.K., Tsihlas, K.: Optimal Finger Search Trees in the Pointer Machime. J. of Comput. System Sci. 67, 381–418 (2003)

    Article  MATH  Google Scholar 

  30. Bentley, J.L., Sleator, D.D., Taran, R.E., Wei, V.K.: A locally adaptive Data Compression Scheme. Com. of ACM, 320–330 (1986)

    Google Scholar 

  31. Brown, M.R., Tarjan, R.E.: Design and Analysis of a Data Structure for representing Sorted Lists. SIAM J. Comput. 9, 594–614 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  32. Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making Data structures Persistent. J. Comput. System Sci. 28, 82–124 (1989)

    MathSciNet  MATH  Google Scholar 

  33. Driscoll, J.R., Sleator, D.D., Tarjan, R.E.: Full Persistent Lists with Catenation. J. ACM 41(5), 943–959 (1994)

    Article  MATH  Google Scholar 

  34. Duch, A., Martinez, C.: Improving the Performance of Multidimensional Search using Fingers. ACM Journal of Expermental Algorithmics 10, Art. no 2.4, 1–23 (2005)

    MathSciNet  MATH  Google Scholar 

  35. Elmasry, A.: Adaptive Sorting with AVL Trees. IFIP TCS, 307–316 (2004)

    Google Scholar 

  36. Estivill-Castro, V., Wood, D.: A survey of Adaptive Sorting Algorithms. ACM Computing Surveys 24, 441–475 (1992)

    Article  Google Scholar 

  37. Guibas, L.J., McCreight, E.M., Plass, M.F., Roberts, J.R.: A new represenation for Linear Lists. In: Proc. 9th Ann. ACM Symp. on Theory of Computing, pp. 49–60 (1978)

    Google Scholar 

  38. Huddleston, S., Mehlhorn, K.: A new Data Structure foe representing Sorted Lists. Acta Inform. 17, 157–184 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  39. Kosaraju, S.R.: Localized Search in Sorted Lists. In: Proc. 13th Ann. ACM Symp. on Theory of Computing, pp. 62–69 (1981)

    Google Scholar 

  40. Mehlhorn, K., Näher, S., Uhrig, C.: Deleting Versions in Persistent Data Structures. Tech. Report, Univ. of Saarland, Saarbrücken (1989)

    Google Scholar 

  41. Sarnak, N., Tarjan, R.E.: Planar Point Location using Persistent Search Trees. Comm. ACM 29, 669–679 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  42. Tarjan, R.E.: Private communication (1982)

    Google Scholar 

  43. Tsakalidis, A.K.: AVL-trees for Lícalized Search. Inform. and Control 67(1-3), 173–194 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  44. Tsakalidis, A.K.: A Simple Implementation for Localized Search. In: Proc. WG 1985, Internat. Workshop on Graph-theoretical Concepts in Computer Science, pp. 363–374. Trauner-Verlag (1985); An optimal Implementation for localized seach. Tech. Rep. A84/06, Fachbereich Angewandte Mathematik and Informatik. Universität des Saarlandes, Saarbrücken, West Germany (1984)

    Google Scholar 

  45. Harel, D., Tarjan, R.E.: Fast Algorithms for finding Nearest Common Ancestors. SIAM J. Comp. 13, 338–355 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  46. van Leeuwen, J.: Finding Lowest Common Ancestors in less than Logarithmic Time. Unpublished report, Amherst, NY (1976)

    Google Scholar 

  47. van Leeuwen, J., Tsakalidis, A.K.: An optimal Pointer Machine Algorithm for Nearest Common Ancestors. Tech. Report, UU-CS-88-17, dept. of Computer Science, Univ. of Utrecht, Utrecht (1988)

    Google Scholar 

  48. Tsakalidis, A.K.: The Nearest Common Ancestor in a Dynamic Tree. Acta Informatica 25, 37–54 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  49. Spirakis, R., Tsakalidis, A.: A very fast practical algorithm for finding a negative cycle in a digraph. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 397–406. Springer, Heidelberg (1986)

    Chapter  Google Scholar 

  50. Tsakalidis, A.: Finding a Negative Cycle in a Directed Graph. Techn. Report A85/05, Angewandte Mathematik und Informatik, FB-10, Univ. des Saarlandes, Saarbrücken (1985)

    Google Scholar 

  51. Alstrup, S., Brodal, G.S., Rauhe, T.: New Data Structures for Orthogonal Range Searching. In: FOCS 2000, pp. 198–207 (2000)

    Google Scholar 

  52. Fries, O., Mehlhorn, K., Näher, S., Tsakalidis, A.K.: A loglogn Data structure for Three-Sided Range Queries. Inf. Process. Lett. 25(4), 269–273 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  53. Willard, D.E.: Examining Computational Geometry, Van Emde Boas Trees and Hashing from the perspective of the Fussion Tree. SIAM J. Comp. 29(3), 1030–1049 (2000)

    Article  MATH  Google Scholar 

  54. Bistiolas, V., Sofotassios, D., Tsakalidis, A.: Computing Rectangle Enclosures. Comput. Geometry: Thery & Appl. 2(6), 301–308 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  55. Bozanis, R., Kitsios, N., Makris, C., Tsakalidis, A.: The Space-Optimal Version of a known Rectangle Enclosure Reporting Algorithm. Inf. Process. Letters 61, 37–41 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  56. Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: New Results on Intersection Query Problems. Computer J. 40(1), 22–29 (1997)

    Article  Google Scholar 

  57. Gupta, P., Janardan, R., Smid, M., Dasgupta, B.: The Rectangle Enclosure and Point-Dominance Problems. Intern. J. Comput. Geom. Applic. 7(5), 437–457 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  58. Lagogiannis, G., Makris, C., Tsakalidis, A.: A new Algorithm for Rectangle Enclosure Reporting. Inf. Process. Letters 72, 177–182 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  59. Lee, D.T., Preperata, F.P.: An improved Algorithm for the Rectangle Enclosure Problem. J. Algorithms 3, 218–224 (1982)

    Article  MathSciNet  Google Scholar 

  60. Makris, C., Tsakalidis, A.: Algorithms for three-dimensional Dominance Searching in linear space. Inf. Process. Letters 66, 277–283 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  61. Afshani, P.: On dominance reporting in 3D. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 41–51. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  62. Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: New upper Bounds gor Generalized Intersection Searching Problems. In: Fülöp, Z., Gecseg, F. (eds.) ICALP 1995. LNCS, vol. 944, pp. 464–474. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  63. Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: Red-Blue Inrersection Reporting for Objects of Non-Constant Size. Computer J. 39(6), 5410546 (1996)

    Article  Google Scholar 

  64. Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: New Results on Intersection Query Problems. Computer J. 40(1), 22–29 (1997)

    Article  Google Scholar 

  65. Grove, E.F., Murali, T.M., Vitter, J.S.: The object complexity model for hidden elimnination. Internat. J. Comput. Geom. Appl. 9, 207–217 (1999)

    Article  MATH  Google Scholar 

  66. Kitsios, N., Makris, C., Sioutas, S., Tsakalidis, A., Tsaknakis, J., Vasiliadis, B.: An Optimal Algotithm for reporting Visible Rectangles. Inf. Process. Letters, 283–288 (2002)

    Google Scholar 

  67. Kitsios, N., Tsakalidis, A.: Space-Optimal Hidden Line Elimination for Rectangles. Inf. Process. Letters 60, 195–200 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  68. Kitsios, N., Tsakalidis, A.: Space Reduction and an Extension for a Hidden Line Elimination Algorithm. Comp. Geom: Theory & Applic., 397–404 (1996)

    Google Scholar 

  69. Bakalis, A., Iliopoulos, C.S., Makris, C., Sioutas, S., Theodoridis, E., Tsakalidis, A., Tsichlas, K.: Locating Maximal Multirepeats in Multiple Strings under various Constraints. Comput. J. 50(2), 178–185 (2006)

    Article  Google Scholar 

  70. Christodoulakis, M., Iliopoulos, C., Mouchard, L., Tsakalidis, A., Tsichlas, K.: Computations of repetitions and Regularities of Biological Weighted Sequences. J. Comput. Biology 13(6), 1214–1231 (2006)

    Article  Google Scholar 

  71. Crochemore, M., Iliopoulos, C., Makris, C., Rytter, W., Tsakalidis, A., Tsichlas, K.: Approximate String matching with Gaps. Nordic J. Comput. 9(1), 54–65 (2002)

    MathSciNet  MATH  Google Scholar 

  72. Iliopoulos, C., Makris, C., Panagis, Y., Perdikuri, K., Theodoridis, E., Tsakalidis, A.: The Weighted Suffix Tree: An efficient Data Structure for handling Molecular Weighted Sequences and its Applications. Fundamenta Informaticae 71, 259–277 (2006)

    MathSciNet  MATH  Google Scholar 

  73. Iliopoulos, C., Mohamed, M., Mouchard, L., Perdikuri, K., Smyth, W.F., Tsakalidis, A.: String Regularities with don’t Cares. Nordic J. Comput. 10(1), 40–51 (2003)

    MathSciNet  MATH  Google Scholar 

  74. Iliopoulos, C., Perdikuri, K., Theodoridis, E., Tsakalidis, A., Tsichlas, K.: Algorithms for extracting Motifs from Biological Weighted Sequences. J. Discrete Algorithms 5, 229–242 (2007)

    Article  MathSciNet  MATH  Google Scholar 

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Tsakalidis, A.K. (2009). Some Results for Elementary Operations. In: Albers, S., Alt, H., Näher, S. (eds) Efficient Algorithms. Lecture Notes in Computer Science, vol 5760. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03456-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-03456-5_8

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