L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. 9th Annual ACM Symposium on Theory of Computing, pages 49--60, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....( 1] have surpassed the logarithmic bound on the search procedure. These two papers are based on a global rebalancing scheme combined with the bucketing techniques presented in [13] For the pointer machine model of computation, steps have been made towards this direction by researchers (see [3, 4, 8, 9, 10, 12, 17]) but the problem remained tantalizingly open. The best solution is given by Brodal ( 3] who proposed a finger search tree with constant insertion, but with O(log # n) deletion time. This time bound of the delete operation is a direct result of our di#culty to handle e#ciently deletions in a ....

L.J. Guibas, E.M. McCreight, M.P. Plass and J.R. Roberts. A New Representation for Linear Lists. In Proc. 9th Annual ACM Symposium On Theory of Computing (STOC), pages 49-60. ACM, 1977.

....n) time bound of a classical search; but in applications like merging where there is a locality of reference in the sequence of search targets, finger searching yields a significantly tighter time bound. Finger search was introduced on a variant of Btrees by Guibas, McCreight, Plass, and Roberts [9] in 1977. Since then, finger search based on modification of balanced search trees has been studied by many researchers, e.g. Brown and Tarjan [7, 2 3 trees] Huddleston and Mehlhorn [11, a, b) trees] Tsakalidis [22, AVL trees] Tarjan and Van Wyk [21, heterogeneous finger search trees] and ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. 9th Annual ACM Symposium on Theory of Computing, pages 49--60, 1977.

....time bound of a classi cal search; but in applications like merging where there is a locality of reference in the sequence of search targets, finger searching yields a significantly tighter time bound. Finger search was introduced on a variant of B trees by Guibas, McCreight, Plass, and Roberts [9] in 1977. Since then, finger search based on modification of balanced search trees has been studied by many researchers, e.g. Brown and Tarjan [7, 2 3 trees] Huddleston and Mehlhorn [11, a, b) trees] Tsakalidis [22, AVL trees] Tarjan and Van Wyk [21, heterogeneous finger search trees] and ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. 9th Annual ACM Symposium on Theory of Computing, pages 49-60, 1977.

....( 1] have surpassed the logarithmic bound on the search procedure. These two papers are based on a global rebalancing scheme combined with the bucketing techniques presented in [13] For the pointer machine model of computation, steps have been made towards this direction by researchers (see [3, 4, 8, 9, 10, 12, 17]) but the problem remained tantalizingly open. The best solution is given by Brodal ( 3] who proposed a nger search tree with constant insertion, but with O(log n) deletion time. This time bound of the delete operation is a direct result of our diculty to handle eciently deletions in a ....

L.J. Guibas, E.M. McCreight, M.P. Plass and J.R. Roberts. A New Representation for Linear Lists. In Computing (STOC), pages 49-60. ACM, 1977.

....Program (UROP) at UT Austin for which funding was provided by Cisco Systems and Proctor Gamble. Srinath Sridhar is also a recipient of the Nortel Networks scholarship. The information theoretic lower bound on the number of comparisons required to sort X was shown to be n lg(I=n) O(n) in [GMPR77]. Hence an algorithm is time optimal if it runs in O(n lg(I=n) n) It is well known that trying to measure the actual constants involved in an algorithm is not useful. However the number of comparisons performed by an algorithm remains invariant across di erent machines and platforms. For ....

....(To be precise, the number of comparisons performed by our algorithm is optimal with respect to its leading term and near optimal with respect to the second term. This is explained in the following section. 2 Earlier Results Adaptive sorting using the nger trees data structure introduced in [GMPR77], was the rst inversions sensitive time optimal sorting algorithm. Mehlhorn [Me79] introduced an algorithm with the same time bounds as nger trees. Both of these algorithms are considered impractical. As summarized by Elmasry [El02] other algorithms that are time optimal and ....

L.Guibas, E.McCreight, M.Plass and J.Roberts. A new representation of linear lists. ACM Symp. Theory of Computing. 9 (1977), 49-60.

....worst case time bounds or persistence. 1 Introduction A finger search tree is a type of balanced search tree in which access in the vicinity of certain preferred positions, indicated by fingers, is especially efficient. Finger search trees were introduced by Guibas, McCreight, Plass and Roberts [16] and further developed by many other researchers [4, 17, 20, 34, 32, 33] A common type of finger search tree, called a heterogeneous finger search tree in [31] is an ordinary balanced search tree (like an a,b tree for example) in which each node along the left path points to its parent instead ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. of the 9th Annual ACM Symposium on Theory of computing, pages 49--60. ACM Press, 1977.

....occuring in the case of an already sorted list, and the largest value in the case of a list in descending order. Inv(X) indicates how many exchanges of adjacent elements are needed to sort X (in, e.g. bubblesort) This quantity has been used as a measure of presortedness by several authors [1] [6], 7] The drawback with this measure is that inputs of the type (n 1; n 2; 2n; 1; 2; 3; n) have a quadratic number of inversions, even though such sequences are intuitively almost in order 22 and are also easy to sort using merging. The next measure handles this case very well. ....

....idea of presortedness. On the other hand the largest value of exc may be obtained for a permutation which is almost in order according to the three previous measures. III. The Concept of an Optimal Algorithm Several authors have de ned the concept of optimal algorithms for nearly sorted lists ([6], 7] Mannila [3] has uni ed these concepts into a widley accepted formal model for the analysis of adaptive sorting algorithms. Let m be a measure of pre sortedness and S a sorting algorithm which requires T S (X) steps on input X. Let below(X; m) be the number of permutations Y of f1; 2; ....

Guibas, L.J., McCreight E.M., Plass M.F. and Roberts J.R., A new representation of linear lists, Proc. 9th Annu. ACM Symp. Theory Comput. (1977) 49-60.

....the subtree rooted at a node is controlled by property c) Lemma 1 shows that the size is at least exponential in the rank. The last two properties are essential to achieve Meld in worst case constant time. The regularity constraint c) is a variation of the regularity constraint that Guibas et al. [9] used in their construction of finger search trees. The idea is that between two ranks where three sons have equal rank there is a rank of which there only is one son. Figure 1 shows a heap ordered tree that satisfies the requirements a) to d) the elements contained in the tree are omitted) h ....

....is reestablished after the above described transformations. We let x denote a string in f1; 2; 3g and y i strings in f1; 2g The table shows all the possible cases. Recall that c) states that between every two n i = 3 there is at least one n i = 1. The different cases are also considered in [9]. x3y 3 1y 2 23y 1 1 x3y 3 1y 2 31y 1 2 x3y 1 12 x3y 1 21 After the linking only b) can be violated at v because a son of rank r has been created. This problem can be solved by increasing the rank of v by one. Because of the given representation Meld can be performed in worst case ....

Leo J. Guibas, Edward M. McCreight, Michael F. Plass, and Janet R. Roberts. A new representation for linear lists. In Proc. 9thAnn. ACM Symp. on Theory of Computing (STOC), pages 49--60, 1977. 11

....s. First, we add (zu 1 )b and (yu 2 )b to f(s) see Figure 7.a) and then we compute the shortest paths to the rest of vertices of t, starting from the third principal vertex of t. In order to achieve linear complexity, we need to represent the funnels as finger trees, introduced by Guibas et al. [13]. Let L be an ordered list with n elements, L 1 is the sublist with the k first elements of L and L 2 the sublist containing the rest of the elements of L. If F , F 1 and F 2 denote finger trees storing these lists, the following operations take O(log(minf k; n Gamma k g) time: Find the k th ....

Leonidas J. Guibas, E. McCreight, M. Plass, and J. Roberts. A new representation for linear lists. In Proc. 9th Annu. ACM Sympos. Theory Comput., pages 49--60, 1977.

....there is a Hamiltonian path ending at them. The tower graph Q s is a perfectly balanced binary tree on s leaves with all the nodes on the same level connected 1 (Figure 2 (a) Clearly, v(Q s ) 2s 1 and d(Q s ) 5. Figure 2 (b) shows a 1 The general, such graphs are called finger trees [5]. 2 (a) b) Figure 1. The Moon graphs of (a) even and (b) odd number of vertices. 7 0 1 2 3 4 0 1 (a) b) Figure 2. The tower graph Q16 drawn as (a) a finger tree, and (b) a planar layout. The Hamiltonian paths from a leaf node to the root are shown in thickened lines. In (a) we also ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. ACM Symp. on Theory of Computing, pages 49--60, 1977.

....trees we access data through pointers to a fixed number of leaves ( fingers ) rather than through the root. This makes the access time dependent on the distance to the fingers rather than on the number of items in the list. Finger trees were introduced by Guibas, McCreight, Plass, and Roberts [6], as a variant of B trees. Huddleston and Mehlhorn refined this work in [8] still using B trees. Tsakalidis has presented a finger tree data structure based on AVL trees [16] Kosaraju [9] presents a more general structure which also has similar properties. In the appendix of [15] Tarjan and Van ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts "A new representation for linear lists," Proc. Ninth Annual ACM Symposium on Theory of Computing, (1977), pp.49-60.

....been presented by Levcopoulos and Overmars [13] and Fleischer [6] but neither of them support finger searches. Finger search trees with worst case constant insertion and deletion time for the restricted case where there are only a constant number of fixed fingers have been given by Guibas et al. [7], Kosaraju [12] and Tsakalidis [17] Finger search trees which allow any element of the list to be a finger and which obtain worst case O(log n) insertion and deletion time have been given by Harel and Lueker [8, 9] In this paper we present the first finger search tree implementation for the ....

Leo J. Guibas, Edward M. McCreight, Michael F. Plass, and Janet R. Roberts. A new representation for linear lists. In Proc. 9th Ann. ACM Symp. on Theory of Computing (STOC), pages 49--60, 1977.

....design representations of perfect leaf trees, square matrices, and many other information structures that automatically satisfy the given size or structural constraints. Let us illustrate the main ideas by means of example. As a first example, we will devise a representation of Toeplitz matrices [6] where a Toeplitz matrix is an 8,9;8 matrix = A CB such that = D FEG= IH JLK H J for 6:MONQPSR T 8 . Clearly, to represent a Toeplitz matrix of size 8U5V6 it suffices to store W2XY8U5V6 elements. Now, instead of designing a representation from scratch we first solve a related, ....

....Mathematics of Program Construction, MPC 98, Marstrand, Sweden, volume 1422 of Lecture Notes in Computer Science, pages 52 67. Springer Verlag, June 1998. 15 [5] W. Braun and M. Rem. A logarithmic implementation of flexible arrays. Memorandum MR83 4, Eindhoven University of Technology, 1983. [6] Thomas H. Cormen, Charles E. Leiserson, and Ronald L. Rivest. Introduction to Algorithms. The MIT Press, Cambridge, Massachusetts, 1991. 7] Victor J. Dielissen and Anne Kaldewaij. A simple, efficient, and flexible implementation of flexible arrays. In Third International Conference on ....

[Article contains additional citation context not shown here]

Leo J. Guibas, Edward M. McCreight, Michael F. Plass, and Janet R. Roberts. A new representation for linear lists. In Conference Record of the Ninth Annual ACM Symposium on Theory of Computing, pages 49--60, Boulder, Colorado, May 1977.

.... presented before for complete binary trees: levels can have as many nodes as (N 1) 2 while root to leaf paths all have the same size, i.e. log(N 1) In an effort to standardize the efficiency measure for multiple templates access, we model the access similarly to the so called finger updates [AGR94, GMPR77, HM82, K81]. What is given as input to access a template is a pointer (or finger) to a leader node and, from that node, an M size instance of the template is retrieved. The leader for T template is V.Auletta, A.De Vivo, V.Scarano 4 22 Multiple Templates Access of Trees in Parallel Memory Systems Journal ....

L.J. Guibas, E.M. McCreight, M.F. Plass, J.R. Roberts, "A New Representation for Linear Lists". proc. of 9th ACM Symp. on Theory of Computing, 1977, 49-60.

....all (a ) labels t) linkAll (add a t) insert a (linkAll t) The reimplementation of top down is worth the effort: a standard amortization argument shows that bottom up takes only linear time. Remark. Red black trees under the left spine view correspond closely to finger search trees [6]. A finger search tree is a representation of an ordered list that allows for efficient insertion in the vicinity of certain points, termed fingers. Here we have a single static finger at the front end of the list. This data structure may be of further interest because it makes a nice ....

Leo J. Guibas, Edward M. McCreight, Michael F. Plass, and Janet R. Roberts. A new representation for linear lists. In Conference Record of the Ninth Annual ACM Symposium on Theory of Computing, pages 49--60, Boulder, Colorado, May 1977.

....by height which allows us to access the front and the rear end simultaneously. Consequently, insertion requires only Theta(log(minfd; n Gamma dg) steps. 2 3 trees under the left spine or the double spine view are by no means a new data structure. They correspond to finger search trees (Guibas et al. 1977) with a static finger at the front end and or at the rear end of the sequence. A finger search tree is a data structure which represents an ordered sequence in such a way that searches are fast in the vicinity of a finger, where a finger points to an arbitrary position within the sequence. In an ....

Guibas, Leo J., McCreight, Edward M., Plass, Michael F., & Roberts, Janet R. 1977 (May). A new representation for linear lists. Pages 49--60 of: Conference record of the ninth annual ACM symposium on theory of computing.

....Links connecting nodes in the same level correspond to polygon edges. Links connecting nodes between two adjacent levels correspond to in and out pointers. In a skip list, there is an O(log c) path between any two bottom level nodes whose indices di#er by c, just as in the case of a finger tree [GMPR77]. This is basically the reason why H Walk takes time logarithmic in the traversal distance between an initial and a closest pair of features by walking in the Dobkin Kirkpatrick hierarchy. In the next two subsections, we first prove the result for the simple case of computing the distance between ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. ACM Symp. on Theory of Computing, pages 49--60, 1977.

....Links connecting nodes in the same level correspond to polygon edges. Links connecting nodes between two adjacent levels correspond to in and out pointers. In a skip list, there is an O(log c) path between any two bottom level nodes whose indices di#er by c, just as in the case of a finger tree [9]. This is basically the reason why H Walk takes time logarithmic in the traversal distance between an initial and a closest pair of features by walking in the Dobkin Kirkpatrick hierarchy. In the next two subsections, we first prove the result for the simple case of computing the distance between ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. ACM Symp. on Theory of Computing, pages 49--60, 1977.

....Links connecting nodes in the same level correspond to polygon edges. Links connecting nodes between two adjacent levels correspond to in and out pointers. In a skip list, there is an O(log c) path between any two bottom level nodes whose indices differ by c, just as in the case of a finger tree [9]. This is basically the reason why H Walk takes time logarithmic in the traversal distance between an initial and a closest pair of features by walking in the Dobkin Kirkpatrick hierarchy. In the next two subsections, we first prove the result for the simple case of computing the distance between ....

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. ACM Symp. on Theory of Computing, pages 49--60, 1977.

No context found.

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proc. 9th Annual ACM Symposium on Theory of Computing, pages 49--60, 1977.

No context found.

L.J. Guibas, E.M. McCreight, M.P. Plass and J.R. Roberts. A New Representation for Linear Lists. In Proc. 9th Annual ACM Symposium On Theory of Computing (STOC), pages 49-60. ACM, 1977.

No context found.

L. J. Guibas, E. M. McCreight, M. F. Plass, and J. R. Roberts. A new representation for linear lists. In Proceedings of the 9th Annual ACM Symposium on the Theory of Computing (STOCS'77), pages 49--60, 1977.

No context found.

Leonidas J. Guibas, E. McCreight, M. Plass, and J. Roberts. A new representation for linear lists. In Proc. 9th Annu. ACM Sympos. Theory Comput. (1977) 49--60.

No context found.

L.J. Guibas, E.M. McCreight, M.F. Plass, J.R. Roberts, "A New Representation for Linear Lists". Proc. of 9th ACM Symp. on Theory of Computing, 1977, pp. 49-60.

No context found.

GMPR77 Guibas L. J., McCreight E. M., Plass M. F., Roberts J. R., A New Representation for Linear Lists, in ACM Symposium on Theory of Computing (pages 49-60), May 1977.

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