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Amortized computational complexity. (English) Zbl 0599.68046
A powerful technique in the complexity analysis of data structures is amortization, or averaging over time. Amortized running time is a realistic but robust complexity measure for which we can obtain surprisingly tight upper and lower bounds on a variety of algorithms. By following the principle of designing algorithms whose amortized complexity is low, we obtain ”self-adjusting” data structures that are simple, flexible and efficient. This paper surveys recent work by several researchers on amortized complexity.

##### MSC:
 68Q25 Analysis of algorithms and problem complexity 68P10 Searching and sorting 68-02 Research exposition (monographs, survey articles) pertaining to computer science
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##### References:
 [1] Adelson-Velskii, G. M.; Landis, E. M., An algorithm for the organization of information, Soviet Math. Dokl., 3, 1259, (1962) [2] Aho, AlfredV.; Hopcroft, JohnE.; Ullman, JeffreyD., The design and analysis of computer algorithms, (1975) · Zbl 0326.68005 [3] Allen, Brian; Munro, Ian, Self-organizing binary search trees, J. Assoc. Comput. Mach., 25, 526, (1978) · Zbl 0388.68060 [4] Bayer, R., Symmetric binary B-trees: data structure and maintenance algorithms, Acta Informat., 1, 290, (197172) · Zbl 0233.68009 [5] Bayer, R.; McCreight, E., Organization of large ordered indexes, Acta Inform., 1, 173, (1972) · Zbl 0226.68008 [6] Worst-case analysis of self-organising sequential search heuristicsProc. 20th Allerton Conference on Communication, Control, and Computing, to appear [7] Bitner, JamesR., Heuristics that dynamically organize data structures, SIAM J. Comput., 8, 82, (1979) · Zbl 0395.68022 [8] Brown, MarkR.; Tarjan, RobertE., Design and analysis of a data structure for representing sorted lists, SIAM J. Comput., 9, 594, (1980) · Zbl 0446.68047 [9] Linear lists and priority queues as balanced binary treesTechnical ReportSTAN-CS-72-259Computer Science Dept., Stanford UniversityStanford, CA1972 [10] Gabow, HaroldN.; Tarjan, RobertEndre, A linear-time algorithm for a special case of disjoint set union, J. Comput. System Sci., 30, 209, (1985) · Zbl 0572.68058 [11] Galler, B. A.; Fischer, M. J., An improved equivalence algorithm, Comm. ACM, 7, 301, (1964) · Zbl 0129.10302 [12] A new representation for linear listsConference Record of the Ninth Annual ACM Symposium on Theory of Computing (Boulder, Colo., 1977)Assoc. Comput. Mach., New York19774960 [13] Guibas, LeoJ.; Sedgewick, Robert, A dichromatic framework for balanced trees, 19th Annual Symposium on Foundations of Computer Science (Ann Arbor, Mich., 1978), 8, (1978), IEEE, Long Beach, Calif. [14] Hopcroft, John; Tarjan, Robert, Efficient planarity testing, J. Assoc. Comput. Mach., 21, 549, (1974) · Zbl 0307.68025 [15] Robust balancing in B-treesProc. 5th GI-Conference on Theoretical Computer ScienceLecture Notes in Computer ScienceVol. 104Springer-VerlagNew York1981234244 [16] Huddleston, Scott; Mehlhorn, Kurt, A new data structure for representing sorted lists, Acta Inform., 17, 157, (1982) · Zbl 0481.68061 [17] Knuth, DonaldE., The art of computer programming. Volume 3, (1973) · Zbl 0302.68010 [18] Knuth, DonaldE.; Morris, Jr., JamesH.; Pratt, VaughanR., Fast pattern matching in strings, SIAM J. Comput., 6, 323, (1977) · Zbl 0372.68005 [19] Localized search in sorted listsProc. Thirteenth Annual ACM Symposium on Theory of Computing19786269 [20] Maier, D.; Salveter, S. C., Hysterical B-trees, Inform. Proc. Letters, 12, 199, (1981) [21] Nievergelt, J.; Reingold, E. M., Binary search trees of bounded balance, SIAM J. Comput., 2, 33, (1973) · Zbl 0262.68012 [22] Olivie, H., A new class of balanced search trees: half-balanced binary search trees, RAIRO Inform. Théor., 16, 51, (1982) · Zbl 0489.68056 [23] Rivest, Ronald, On self-organizing sequential search heuristics, Comm. ACM, 19, 63, (1976) · Zbl 0317.68025 [24] Rosenstiehl, Pierre; Tarjan, RobertE., Gauss codes, planar Hamiltonian graphs, and stack-sortable permutations, J. Algorithms, 5, 375, (1984) · Zbl 0588.68034 [25] Self-adjusting binary treesProc. Fifteenth Annual ACM Symposium on Theory of Computing1983235245 [26] Sleator, DanielD.; Tarjan, RobertE., Amortized efficiency of List update and paging rules, Comm. ACM, 28, 202, (1985) [27] Sleator, DanielDominic; Tarjan, RobertEndre, Self-adjusting heaps, SIAM J. Comput., 15, 52, (1986) · Zbl 0618.68017 [28] Sleator, DanielDominic; Tarjan, RobertEndre, Self-adjusting binary search trees, J. Assoc. Comput. Mach., 32, 652, (1985) · Zbl 0631.68060 [29] Tarjan, RobertEndre, Efficiency of a good but not linear set union algorithm, J. Assoc. Comput. Mach., 22, 215, (1975) · Zbl 0307.68029 [30] Tarjan, RobertEndre, A class of algorithms which require nonlinear time to maintain disjoint sets, J. Comput. System Sci., 18, 110, (1979) · Zbl 0413.68039 [31] Tarjan, RobertEndre, Updating a balanced search tree in $$O(1)$$ rotations, Inform. Process. Lett., 16, 253, (1983) · Zbl 0508.68041 [32] Tarjan, R. E., Data Structures and Network Algorithms, (1983) · Zbl 0584.68077 [33] Tarjan, RobertE.; van Leeuwen, Jan, Worst-case analysis of set union algorithms, J. Assoc. Comput. Mach., 31, 245, (1984) · Zbl 0632.68043 [34] Webster’s New World Dictionary of the American Language, (1964)
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