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
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)
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)
Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making Data Structures Persistent. J. Comput. System Sci. 28, 86–124 (1989)
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)
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)
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)
Mehlhorn, K., Tsakalidis, A.K.: An Amortized Analysis of Insertions into AVL-Trees. SIAM J. Comput. 15(1), 22–33 (1986)
Mehlhorn, K., Tsakalidis, A.: Dynamic Interpolation Search. Journal of the ACM 40(3), 621–634 (1993)
Tsakalidis, A.K.: Rebalancing Operations for Deletions in AVL-Trees. RAIRO Inform. Theor. 19(4), 323–329 (1985)
Vitter, J.: External Memory Algorithms and Data Structures: dealing with massive data. ACM Computing Surveys 33(2), 209–271 (2001)
Willard, D.E.: Searching unindexed and nonuniformly generated files in log log N time. SIAM J. Comput. 14(4), 1013–1029 (1985)
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)
Blum, N., Mehlhorn, K.: On the average number of Rebalancing Operations in weight-balanced trees. Theor. Comput. Sci. 11, 303–320 (1980)
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)
Dietz, P.F.: Fully Persistent Arrays (Extended Abstract). In: Proc. of the Workshop on Algorithma and Data Structures, pp. 67–74 (1989)
Dietz, P.F.: A Space Efficient Variant of Path Copying for Partially Persistent Sorted Sets. J. Comput. System Sci. 53, 148–152 (1996)
Dietz, P.F.: Maintaining Order in a Linked List. In: Proc. 14th ACM STOC, pp. 122–127 (1982)
Dietz, P.F., Sleator, D.D.: Two Algorithms for Maintaining Order in a List. In: Proc. 19th ACM STOC, pp. 365–372 (1987)
Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making Data structures Persistent. J. Comput. System Sci. 28, 82–124 (1989)
Nievergelt, I., Reingold, E.M.: Binary Search Tress of Bounded Balance. SIAM J. Comput. 2, 33–43 (1973)
Tsakalidis, A.K.: Maintaining Order in a generalized Linked List. Acta Informatica 21(1), 101–112 (1984)
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)
Makris, C., Tsakalidis, A., Tsichlas, K.: Reflected Min-Max Heaps. Inf. Proc. Letters 86, 209–214 (2003)
Williams, J.W.J.: Algorithm 232. Comm. ACM 7(6), 347–348 (1964)
Brodal, G.S., Makris, C., Sioutas, S., Tsakalidis, A., Tsichlas, K.: Optimal Solution for the Temporal Precedence Problem. Algorithmica 33(4), 494–510 (2002)
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)
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)
Ranjan, D., Pontelli, E., Gupta, G., Longpre, L.: The Temporal Precedence problem. Algorithmica 28(3), 288–306 (2000)
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)
Bentley, J.L., Sleator, D.D., Taran, R.E., Wei, V.K.: A locally adaptive Data Compression Scheme. Com. of ACM, 320–330 (1986)
Brown, M.R., Tarjan, R.E.: Design and Analysis of a Data Structure for representing Sorted Lists. SIAM J. Comput. 9, 594–614 (1980)
Driscoll, J.R., Sarnak, N., Sleator, D.D., Tarjan, R.E.: Making Data structures Persistent. J. Comput. System Sci. 28, 82–124 (1989)
Driscoll, J.R., Sleator, D.D., Tarjan, R.E.: Full Persistent Lists with Catenation. J. ACM 41(5), 943–959 (1994)
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)
Elmasry, A.: Adaptive Sorting with AVL Trees. IFIP TCS, 307–316 (2004)
Estivill-Castro, V., Wood, D.: A survey of Adaptive Sorting Algorithms. ACM Computing Surveys 24, 441–475 (1992)
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)
Huddleston, S., Mehlhorn, K.: A new Data Structure foe representing Sorted Lists. Acta Inform. 17, 157–184 (1982)
Kosaraju, S.R.: Localized Search in Sorted Lists. In: Proc. 13th Ann. ACM Symp. on Theory of Computing, pp. 62–69 (1981)
Mehlhorn, K., Näher, S., Uhrig, C.: Deleting Versions in Persistent Data Structures. Tech. Report, Univ. of Saarland, Saarbrücken (1989)
Sarnak, N., Tarjan, R.E.: Planar Point Location using Persistent Search Trees. Comm. ACM 29, 669–679 (1986)
Tarjan, R.E.: Private communication (1982)
Tsakalidis, A.K.: AVL-trees for LÃcalized Search. Inform. and Control 67(1-3), 173–194 (1985)
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)
Harel, D., Tarjan, R.E.: Fast Algorithms for finding Nearest Common Ancestors. SIAM J. Comp. 13, 338–355 (1984)
van Leeuwen, J.: Finding Lowest Common Ancestors in less than Logarithmic Time. Unpublished report, Amherst, NY (1976)
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)
Tsakalidis, A.K.: The Nearest Common Ancestor in a Dynamic Tree. Acta Informatica 25, 37–54 (1988)
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)
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)
Alstrup, S., Brodal, G.S., Rauhe, T.: New Data Structures for Orthogonal Range Searching. In: FOCS 2000, pp. 198–207 (2000)
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)
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)
Bistiolas, V., Sofotassios, D., Tsakalidis, A.: Computing Rectangle Enclosures. Comput. Geometry: Thery & Appl. 2(6), 301–308 (1993)
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)
Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: New Results on Intersection Query Problems. Computer J. 40(1), 22–29 (1997)
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)
Lagogiannis, G., Makris, C., Tsakalidis, A.: A new Algorithm for Rectangle Enclosure Reporting. Inf. Process. Letters 72, 177–182 (1999)
Lee, D.T., Preperata, F.P.: An improved Algorithm for the Rectangle Enclosure Problem. J. Algorithms 3, 218–224 (1982)
Makris, C., Tsakalidis, A.: Algorithms for three-dimensional Dominance Searching in linear space. Inf. Process. Letters 66, 277–283 (1998)
Afshani, P.: On dominance reporting in 3D. In: Halperin, D., Mehlhorn, K. (eds.) ESA 2008. LNCS, vol. 5193, pp. 41–51. Springer, Heidelberg (2008)
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)
Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: Red-Blue Inrersection Reporting for Objects of Non-Constant Size. Computer J. 39(6), 5410546 (1996)
Bozanis, P., Kitsios, N., Makris, C., Tsakalidis, A.: New Results on Intersection Query Problems. Computer J. 40(1), 22–29 (1997)
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)
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)
Kitsios, N., Tsakalidis, A.: Space-Optimal Hidden Line Elimination for Rectangles. Inf. Process. Letters 60, 195–200 (1996)
Kitsios, N., Tsakalidis, A.: Space Reduction and an Extension for a Hidden Line Elimination Algorithm. Comp. Geom: Theory & Applic., 397–404 (1996)
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)
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)
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)
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)
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)
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)
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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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