K. S. Larsen and R. Fagerberg, Efficient rebalancing of B-trees with relaxed balance, Internat. J. Found. Comput. Sci. 7 (1996), 169# 186.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....are also allowed is presented by Nurmi et al. 28] This solution is analyzed in [16] and it is shown that for each update operation in a tree with maximum size n, O(log n) new rebalancing operations are needed. Relaxed balancing for B trees is introduced in [28] and further analyzed in [18]. Another concurrent B tree algorithm that uses the concept of relaxed balancing is the B link tree [15, 21, 30] Nurmi and Soisalon Soininen [26, 27] propose a relaxed version of red black trees which they call a chromatic tree. Chromatic trees are analyzed by Boyar and Larsen [6] and a more ....

K. Larsen and R. Fagerberg. B-trees with relaxed balance. In Proc. 9th International Parallel Processing Symposium, pages 196--202. IEEE Computer Society Press, 1995.

....is restored immediately after each update operation the actual rebalancing transformations can be delayed arbitrarily and interleaved freely with search and update operations. The literature contains a number of proposals for relaxed balancing in binary and multiway search trees [9] 10] [11], 12] 13] The previous solutions have different drawbacks, however, which we will avoid by the solution proposed in this paper. Except for the recent paper [18] all previous solutions are not based on the standard balancing transformations but require a large number of different new ....

....been carried out which has not changed the shape of the original tree. A possible sequence of those updates is a sequence of insertions of keys k 1 ; k r which is followed by a sequence of deletions of k 1 ; k r (or vice versa) Note, that the relaxed balancing scheme proposed in [11] generates even for such a sequence of updates a tree which is full of balance conflicts. On the other hand, if a sequence of updates happens to add a full layer of stratum trees from Z below the bottommost layer of the originally given Z stratified tree, our relaxed balancing scheme is not able ....

K.Larsen and R.Fagerberg, B-trees with relaxed balance. In: Proc. 9th International Parallel Processing Symposium, IEEE Computer Society Press, 1995, pp. 196--202.

....it has historical interest. It has also spawned a number of research efforts that, not surprisingly, are more elegant and more efficient than our original methodology. Soisalon Soininen and his coworkers have simplified and extended the ideas [21, 22, 25, 28] and Boyar, Fagerberg, and Larsen [9, 7, 8, 17, 18] have improved the efficiency under the amortized framework. More recently, Boug e, Gabarr o, and Messeguer [5, 6] have reexamined the issue of distributed rebalancing of search trees using the general approach espoused by Dijkstra et al. 10] They design a simple and abstract presentation of 22 ....

K. S. Larsen and R. Fagerberg. B-trees with relaxed balance. In Proceedings of the Ninth International Parallel Processing Symposium, pp. 196-- 202, 1995.

....are also allowed is presented by Nurmi et al. 13] 2 This solution is analyzed in [7] and it is shown that for each update operation in a tree with maximum size n, O(log n) new rebalancing operations are needed. Relaxed balancing for B trees is introduced in [13] and further analyzed in [8]. Nurmi and Soisalon Soininen [11, 12] propose a relaxed version of red black trees which they call a chromatic tree. The proposal of [12] is analyzed in [3] by Boyar and Larsen, and a more efficient set of rebalancing transformations is defined. It is shown that the number of rebalancing ....

K. Larsen and R. Fagerberg. B-trees with relaxed balance. In Proc. 9th International Parallel Processing Symposium, pages 196--202. IEEE Computer Society Press, 1995.

....9. Number of failures (two upper lines) and successes (two down lines) needed to rebalance a linked list of 0 n 100 nodes into a Red Black tree. Solid lines depict the HyperRed Black case. Dotted lines depict the Chromatic case. easily coded in the form of local rules. Other works in B trees are [26, 22, 25]. Skip Lists and Skip trees. Concurrentalgorithms on skip lists are not always very clear [39] In [31] X. Messeguer has introduced the skip trees a data structure which resembles to B trees (but are actually isomorphic to skip lists) It is rather straightforward to derive concurrent algorithms ....

K. Larsen and R. Fagerberg. Eficient rebalancing of B-trees with relaxed balance. Int. Jour. of Foundations of Comp. Sci., 7(2):169--186, 1996.

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K. S. Larsen and R. Fagerberg, Efficient rebalancing of B-trees with relaxed balance, Internat. J. Found. Comput. Sci. 7 (1996), 169# 186.

....also demonstrate that a binary tree scheme with the same complexities can be designed. This is an improvement over the existing results. 1 Introduction We focus on the type of multi way trees usually referred to as (a; b) trees [8, 15] and in particular, we adopt the relaxed (a; b) trees [11, 12]. In the context Supported in part by the Danish Natural Sciences Research Council (SNF) and in part by the IST Programme of the EU under contract number IST 1999 14186 (ALCOM FT) y Department of Mathematics and Computer Science, University of Southern Denmark, Main campus: Odense University, ....

Kim S. Larsen and Rolf Fagerberg. Ecient Rebalancing of B-Trees with Relaxed Balance. International Journal of Foundations of Computer Science, 7(2):169-186, 1996.

....also demonstrate that a binary tree scheme with the same complexities can be designed. This is an improvement over the existing results. 1 Introduction We focus on the type of multi way trees usually referred to as (a; b) trees [8, 15] and in particular, we adopt the relaxed (a; b) trees [11, 12]. In the context Supported in part by the Danish Natural Sciences Research Council (SNF) and in part by the IST Programme of the EU under contract number IST 1999 14186 (ALCOM FT) y Department of Mathematics and Computer Science, University of Southern Denmark, Main campus: Odense University, ....

Kim S. Larsen and Rolf Fagerberg. B-Trees with Relaxed Balance. In Proceedings of the 9th International Parallel Processing Symposium, pages 196-202. IEEE Computer Society Press, 1995.

....summary of the developments; more details can be found in [16] for example. Some of the ideas were initiated in [10, 14] AVL trees [1, 22] were investigated in [24, 27, 15] red black trees [3, 10, 30] in [25, 26, 7, 8, 5, 6, 16] and (a; b) trees [13, 21] B trees [4] 2 3 trees [12, 2] in [24, 17, 18]. In [19] a general result for balanced trees was developed, and in [31, 20, 11, 9, 23] some variations of the standard schemes were investigated. Locking in a parallel setting was discussed in [26, 6] In this paper, we investigate layered trees [29] A relaxed version of layered trees was ....

Kim S. Larsen and Rolf Fagerberg. Efficient Rebalancing of B-Trees with Relaxed Balance. International Journal of Foundations of Computer Science, 7(2):169--186, 1996.

....summary of the developments; more details can be found in [16] for example. Some of the ideas were initiated in [10, 14] AVL trees [1, 22] were investigated in [24, 27, 15] red black trees [3, 10, 30] in [25, 26, 7, 8, 5, 6, 16] and (a; b) trees [13, 21] B trees [4] 2 3 trees [12, 2] in [24, 17, 18]. In [19] a general result for balanced trees was developed, and in [31, 20, 11, 9, 23] some variations of the standard schemes were investigated. Locking in a parallel setting was discussed in [26, 6] In this paper, we investigate layered trees [29] A relaxed version of layered trees was ....

Kim S. Larsen and Rolf Fagerberg. B-Trees with Relaxed Balance. In Proceedings of the 9th International Parallel Processing Symposium, pages 196--202. IEEE Computer Society Press, 1995.

....strategies for main memory databases. Main memory search structures have gained new applications in large embedded systems, such as switching systems for mobile telephones. 1 Introduction Several proposals for solving the problem of relaxed balancing in search tree structures have been presented [3, 5, 6, 7, 8, 9, 10]. By relaxed balancing we mean that the balancing transformations usually connected with insert and delete Department of Mathematics and Computer Science, Odense University, Campusvej 55, DK 5230 Odense M, Denmark. Email: kslarsen imada.ou.dk. Some of the work was done while this author was ....

K.S.Larsen and R.Fagerberg, B-trees with relaxed balance. In: Proc. 9th International Parallel Processing Symposium, IEEE Computer Society Press, 1995, pp. 196--202.

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