S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-- 184, 1982.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....supporting deletions as well as for the general structure. Each block at level i 1 considering the insertion tree structure has maximum degree 3b i 1 , for which by equation 4 holds that b i 3(i 1) 1 . Thus, the degree of the blocks at level i is O(2 ) First we use level linking ([11]) on the node tree structure. As a result, the search procedure basically starts from a leaf pointed by a finger f and traverses the ancestors of f until we find the first ancestor v (or one adjacent to this node by using level pointers) that contains x in his range. Then we search the specific ....

S. Huddleston and K. Mehlhorn. A New Data Structure for Representing Sorted Lists. Acta Informatica, 17:157-184, 1982. 16

....merging. Hwang and Lin [13] described how to optimally merge two sorted lists of length n 1 and n 2 , where n 1 n 2 , with ) comparisons. Brown and Tarjan [7] described how to achieve the same number of comparisons for merging two AVL trees in time ) and Huddleston and Mehlhorn [12] showed a similar result for level linked (2,4) trees. In our algorithm we will use a slightly extended version of level linked (2,4) trees where each element has an associated weight. The rest of this section contains basic definitions and lemmas that we will use in the latter sections. In ....

....how to maintain a set of sorted lists of elements as a collection of level linked (2,4) trees where the elements are stored at the leaves in sorted order from left to right, and each element can have an associated real valued weight. For a detailed treatment of level linked (2,4) trees see [12] and [17, Section III.5] The operations we consider supported are: NewTree(e, w) Creates a new tree T containing the element e with associated weight w. Search(p, e) Searches for the element e starting the search at the leaf of a tree T that p points to. Returns a reference to the leaf in T ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

....a given search range using O(log B N B ) block operations. This data structure was implemented and its performance was evaluated on a simulated memory hierarchy. This paper presents the results of this simulation for various combinations of block and memory sizes. 1 Introduction The B tree [10, 17, 22, 27] is the classic externalmemory search tree, and it is widely used in both theory and practice. The B tree is designed to support insert, delete, search, and scan on a two level memory hierarchy consisting of main memory and disk. The basic structure is a balanced tree having a fan out proportional ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157{ 184, 1982.

....fast access and update operations. For a generic n element ordered data set that is accessed and updated uniformly, this goal is typically satisfied by dictionaries that achieve O(log n) time performance for searches and updates; for example, AVL trees [2] red black trees [12] and (a, b) trees [13]. Nevertheless, many dictionary applications involve sets of weighted data items that are searched and updated non uniformly according to those weights; that is, they are biased. For example, most operating systems textbooks (e.g. see Stallings [23] devote major coverage to methods for dealing ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--84, 1982.

....and deletions can be implemented in time proportional to the number of structural changes in the tree. This allows us to transfer any results previously proven on these two operations, such as an amortized O(1) time bound and the actual distribution of work at di#erent depths of the tree [11]. In the development of our finger search algorithm, we also obtain a simple in order walk algorithm with worstcase O(1) work per increment. We believe that this improvement over the previous amortized O(1) bound can be used in database applications when the overall performance is very sensitive ....

....x Figure 1: Parent, Peer, and Spine As stated, our design is based on degree balanced search trees. All the leaves in such a tree are at the same depth and its balance is maintained by varying the degree of internal nodes between fixed constants. 23 trees [2] B trees [3] and (a, b) trees [11] are all variants of degree balanced search trees. Red Black trees [10] can also be viewed as degree balanced easily via the isomorphism with 2 3 4 trees. We sometimes simplify our presentation by assuming a complete binary search tree (BST ) but we also show how to account for this to retain ....

[Article contains additional citation context not shown here]

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-- 184, 1982.

....and deletions can be implemented in time proportional to the number of structural changes in the tree. This allows us to transfer any results previously proven on these two operations, such as an amortized O(1) time bound and the actual distribution of work at different depths of the tree [11]. In the development of our finger search algorithm, we also obtain a simple in order walk algorithm with worst case O(1) work per increment. We believe that this improvement over the previous amortized O(1) bound can be used in database applications when the overall performance is very sensitive ....

....lail FIGURE 1: Parent, Peer, and Spine As stated, our design is based on degree balanced search trees. All the leaves in such a tree are at the same depth and its balance is maintained by varying the degree of internal nodes between fixed constants. 2 3 trees [2] B trees [3] and (a, b) trees [11] are all variants of degree balanced search trees. Red Black trees [10] can also be viewed as degree balanced easily via the isomorphism with 2 3 4 trees. We sometimes simplify our presentation by assuming a complete binary search tree (BST) but we also show how to account for this to retain full ....

[Article contains additional citation context not shown here]

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Info'matica, 17:157184, 1982.

....supporting deletions as well as for the general structure. Each block at level i 1 considering the insertion tree structure has maximum degree 3b i 1 , for which by equation 4 holds that b i 2 3(i 1) 1 . Thus, the degree of the blocks at level i is ) First we use level linking ([11]) on the node tree structure. As a result, the search procedure basically starts from a leaf pointed by a nger f and traverses the ancestors of f until we nd the rst ancestor v (or one adjacent to this node by using level pointers) that contains x in his range. Then we search the speci c ....

S. Huddleston and K. Mehlhorn. A New Data Structure for Representing Sorted Lists. Acta Informatica, 17:157-184, 1982.

....that admit fast access and update operations. For a generic n element ordered data set that is accessed and updated uniformly, this goal is typically satis ed by dictionaries that achieve O(log n) time search and update performance; e.g. AVL trees [2] red black trees [12] and (a; b) trees [13]. Nevertheless, many dictionary applications involve sets of weighted data items subject to non uniform access patterns that are biased according to the weights. For example, operating systems (e.g. see Stallings [22] deal with biasing in memory requests. Other recent examples of biased sets ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Inf., 17:157-84, 1982.

....merging. Hwang and Lin [13] described how to optimally merge two sorted lists of length n 1 and n 2 , where n 1 n 2 , with ) comparisons. Brown and Tarjan [7] described how to achieve the same number of comparisons for merging two AVL trees in time ) and Huddleston and Mehlhorn [12] showed a similar result for level linked (2,4) trees. In our algorithm we will use a slightly extended version of level linked (2,4) trees where each element has an associated weight. Due to lack of space proofs have been omitted. The omitted details can be found in [5] 1.1 Preliminaries Some ....

....how to maintain a set of sorted lists of elements as a collection of level linked (2,4) trees where the elements are stored at the leaves in sorted order from left to right, and each element can have an associated real valued weight. For a detailed treatment of level linked (2,4) trees see [12] and [16, Section III.5] The operations we consider supported are: NewTree(e, w) Creates a new tree T containing the element e with associated weight w. Search(p, e) Search for the element e starting the search at the leaf of a tree T that p points to. Returns a reference to the leaf in T ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

....The complexity measures in this model are the number of I Os used to solve a problem (answer a query) and the number of disk blocks used. Aggarwal and Vitter showed that O( N is the external memory equivalent of the well known O(N log 2 N) internal memory sorting bound. Similarly, the B tree [10, 12, 18] is the external equivalent of an internal memory balanced search tree. It uses linear space, O(N B) blocks, to store N elements; supports updates in O(log B N) I Os; and performs one dimensional range queries in optimal O(log B N T B) I Os, where T is the number of reported elements. Using a ....

....in the same version of the structure to be comparable. In Section 2.1, we first sketch the persistent B tree of [11] and then in Section 2.2 we describe the modifications needed to use the tree in a vertical ray shooting structure. 2. 1 Persistent B tree A B tree, or more generally an (a, b) tree [18], is a balanced search tree with all leaves on the same level, and with all internal nodes except possibly the root having #(B) children (typically between B 2 and B) Normally, elements are stored in the leaves, and the internal nodes contain routing elements used to guide searches (sometimes ....

[Article contains additional citation context not shown here]

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

....in the same version of the structure to be comparable. In Section 2.1, we rst sketch the persistent B tree of [11] and then in Section 2.2 we describe the modi cations needed to use the tree in a vertical ray shooting structure. 2. 1 Persistent B tree A B tree, or more generally an (a; b) tree [18], is a balanced search tree with all leaves on the same level, and with all internal nodes except possibly the root having (B) children (typically between B=2 and B) Normally, elements are stored in the leaves, and the internal nodes contain routing elements used to guide searches (sometimes ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-184, 1982.

....structures implemented using the TPIE kernel. They are all part of the extended TPIE library. In this section, we briefly survey these data structures. B tree. The B tree [12] is the classical external memory data structure for online searching. In TPIE we implemented the more general (a; b) tree [14], supporting insertion, deletion, point query, range query, and bulk loading. All these operations are encapsulated in a templated C class. The template parameters allow the user to choose the Bulk loading is a term used in the database literature to refer to constructing an index from a ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

....in the data structure to element i 2 X. Reweight(X; i; w i ) Change the weight of i to w i . Biased dictionaries can improve on the (m log n) time required to perform m accesses on n items in classical, unbiased dictionaries such as AVL trees[3] red black trees [38] and (a; b) trees [41]. Let w i be the number of times item i is accessed. De ne W = i=1 w i . A biased dictionary with O search time for the i th item can perform m searches on n items in O(m(1 p i log p i ) time, where p i = m , which is optimal [2] 3.1.2 A New Structure for the Biased Dictionary ....

S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-84, 1982.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-- 184, 1982.

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Huddleston, S., and Mehlhorn, K. A New Data Structure for Representing Sorted Lists. Acta Informatica, 17:157-184, 1982.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--84, 1982.

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S. Huddleston and K. Mehlhorn. A New Data Structure for Representing Sorted Lists. Acta Informatica, 17:157-184, 1982.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--84, 1982.

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S. Huddleston and K. Mehlhorn, A new data structure for representing sorted lists, Acta Inform. 17 (1982), 157#184.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Inform., 17:157-184, 1982.

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Huddleston, S. and Mehlhorn, K. (1982) A new data structure for representing sorted lists. Acta Inform. 17, 157-184.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157-184, 1982.

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Huddleston, S., and Mehlhorn, K. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

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S. Huddleston and K. Mehlhorn. A new data structure for representing sorted lists. Acta Informatica, 17:157--184, 1982.

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