Tsakalidis, A. Maintaining order in a generalized linked list. ACTA Informatica, 21:101-184, 1984.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....The problem has also been studied in the context of average case analysis [13, 16, 17] Raman [23] gives a scheme for maintaining N elements in order using polynomial space ( N ) and O(log N ) time per update. The update bound can be improved to O(log N ) by tuning existing algorithms [3, 8, 11, 27], and this bound is optimal [9] However, such a blowup in space is disastrous for data locality, so this work does not apply to the traversal problem. 2 Cache Oblivious Traversal in O( log log N) We rst consider the cache oblivious traversal problem without restriction on the number of ....

A. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101-112, May 1984.

....leaves store smaller indexed 2 3 trees, improving their performance from O(log n) to O(log n) amortized time. Structural decomposition differs from ideas used to solve decomposable search problems [BS80] and from other ad hoc instances of data structure decomposition (e.g. Die91, DR91, DS87, Tsa84, Wil83, Wil84] in that these previous results use only one level of decomposition, whereas bootstrapping is recursive. The rest of this thesis applies data structural bootstrapping to build efficient catenable heap ordered deques and confluently persistent deques. Chapter 2 discusses catenable ....

A. K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101--12, 1984.

....graphs. For trees they consider the ancestor and parent adjacency relations. They show how to obtain labels of size 2 log n for the ancestor relation. We refer the reader to [11, 1, 7] for further details of appilcations of labeling schemes supporting ancestor queries. Related results: Tsakalidis [12] shows that if we assign the preorder and postorder number to each node in a tree, a node v is an ancestor to a node w i preorder(v) preorder(w) postorder(v) This leads to a simple labeling scheme with labels of size 2 log n for the ancestor relation. Similarly, simple 2 log n labeling ....

A. K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101{ 112, 1984.

....problem with this version stamping method is that it requires arbitrary accuracy real arithmetic, which cannot be done in constant time. Practical solutions that take constant time for insertion, deletion, successor and predecessor queries, and comparisons do exist, however (Dietz Sleator, 1987; Tsakalidis, 1984). We A New Method for Functional Arrays 7 a b d c g f h e i v 0 v 1 v 2 v 3 v 1.5 v 0.8 v 0.6 v 0.7 v 0.5 (a) A version tree and the totally ordered version stamps that are applied to it. In the diagram arrows represent updates, and further, the array versions were created ....

Tsakalidis, Athanasios K. (1984). Maintaining order in a generalized linked list. Acta informatica, 21(1), 101--112.

....2 3 trees so that their leaves store smaller indexed 2 3 trees, improving their performance from O(log n) to O(log 3 n) amortized time. Structural decomposition differs from ideas used to solve decomposable search problems [5] and from other ad hoc instances of data structure decomposition (e.g. [14, 15, 16, 40, 42, 43]) in that these previous results use only one level of decomposition, whereas bootstrapping is recursive. Non destructive (or, in the parlance of Section 1.1, confluently persistent) deques have many uses in high level programming languages such as LISP, ML, and Scheme [35] in which ....

A. K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101--12, 1984.

....leaves store smaller indexed 2 3 trees, improving their performance from O(log n) to O(log n) amortized time. Structural decomposition differs from ideas used to solve decomposable search problems [BS80] and from other ad hoc instances of data structure decomposition (e.g. Die91, DR91, DS87, Tsa84, Wil83, Wil84] in that these previous results use only one level of decomposition, whereas bootstrapping is recursive. 1.4 Summary The rest of this thesis applies data structural bootstrapping to build efficient catenable heap ordered deques and confluently persistent deques. Chapter 2 ....

A. K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101--12, 1984.

....previously received. The cost is the total number of labelings and relabelings performed. There are practical applications of on line list labeling to the design of efficient data structures and algorithms. List labeling has been an especially fruitful approach to the order maintenance problem [Di82, Ts84, DS87, DZ90]. This problem involves the insertion and deletion of items into a linear list, and response to online queries on the relative order of items currently in the list. A low cost on line list labeling algorithm provides an efficient solution (or sometimes a component of an even more efficient ....

.... fundamental to the spatially structured maintenance in bounded media of changing data, such as text and pictures on a computer screen [Zh93] When the number of labels is at least n 1 ffl for some ffl 0, it is possible to limit the worst case cost for on line labeling of n items to O(n log n) [Di82, Ts84, DS87]. The analyses are subtle; but the best of the algorithms are both simple and fast, and hence practically useful. In this paper we show that the upper bound is tight, and in fact that Omega (n log n) relabelings are required even for an algorithm that is complicated and slow. Key words and ....

A. K. Tsakalidis, Maintaining order in a generalized linked list, Acta Informatica 21, 1 (May, 1984), 101--112.

....W is the set of nodes which change depth in the dominator tree and F = f(x; y)j(x; y) 2 Ex 2 Wg. Interspersed with edge insertions queries as does x dominate y can be answered in constant time. Proof. In stead of using the results from [5] we do as follows. The pointer machine algorithm from [15] is used for maintaining a tree to answer domination queries. The algorithm has the same complexity as the RAM algorithm. The algorithm from [2] is used for maintaining a tree to answer nca queries. The algorithm has the same complexity as the RAM algorithm, except for nca queries, which have the ....

A.K. Tsakalidis. Maintaining order in a generalized linked list. Acta informatica, 21:101--112, 1984.

....indexed lists that obeys the consistency and monotonicity conditions, and supports queries in constant worst case time and updates in O(1=ffl 2 ) amortized time. Thus, if ffl is regarded as a small constant then all operations run in O(1) time. 1. 2 Application: List labeling In a labeled list [4, 6, 14], each element has an integer label, such that if the list is traversed from head to tail, the labels increase monotonically. The updates are the same as for indexed lists. The query operation x) simply returns the label of list element x. A solution to the list labeling problem allows us to ....

....explicit labels and does not apply to this relaxed, natural model. However, most prior work has assumed the relaxed model. In some applications, though, explicit labels are required; e.g. when the labels are used as addresses into some other data structure. In the relaxed model, Tsakalidis [14] showed that O(1) amortized time per update suffices. This was later improved by Dietz and Sleator [7] who gave a simpler data structure which achieves the same bound, as well as a quite sophisticated solution which attains constant time in the worst case. When studying the list labeling problem ....

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A.K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21:101--112, 1984.

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Tsakalidis, A. Maintaining order in a generalized linked list. ACTA Informatica, 21:101-184, 1984.

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Tsakalidis, A. Maintaining order in a generalized linked list. ACTA Informatica, 21:101--184, 1984.

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A. K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101--112, May 1984.

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A.K. Tsakalidis. Maintaining order in a generalized linked list. Acta Informatica, 21(1):101-112, May 1984.

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