R.F. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13(3):245{ 265, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of the rst edge on the path to the root, from which we immediately get a parent pointer. Unfortunately, the above axiomatic interface has been found too limited for many application of dynamic trees, and instead authors have worked directly with the Sleator and Tarjan s underlying representation [30, 5, 21, 24, 23, 14, 4, 1, 16, 9, 8, 7, 22]. In particular, this is the case for the previous solutions to the dynamic center [6] and median problems [3] and we believe part of the reason for their worse bounds and more complex solutions is diculties in working directly with Sleator and Tarjan s underlying representation. Of course, one ....

R.F. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13(3):245{ 265, 1995.

....O(n log 2 n) making it possible to compare much larger evolutionary trees. Our solution is based on two techniques: the smaller half trick, also used by methods for finding tandem repeats in strings, see e.g. 15] and a data structure related to the data structure for dynamic expression trees [7]. The rest of the paper is organized as follows. In Sect. 2, we introduce quartets and present our algorithm for computing the quartet distance between two unrooted evolutionary trees. In Sect. 3, we describe a hierarchical decomposition of unrooted trees which is an essential part of the data ....

....an unrooted tree T where all nodes have degree at most three, we in the following describe how to obtain a hierarchical decomposition of T with logarithmic height. Our decomposition is very similar to the decompositions used for solving the parallel and dynamic expression tree evaluation problems [3,7], but in our setting the underlying tree is considered to be unrooted. We base our hierarchical decomposition on the notion of components. We define a component C in T to be one of the following: i) ii) iii) iv) Figure 6. The four possible types of compositions of components 1. A set ....

R. F. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13(3):245-- 265, 1995.

....O(n log 2 n) making it possible to compare much larger evolutionary trees. Our solution is based on two techniques: the smaller half trick, also used by methods for nding tandem repeats in strings, e.g. 15] and a data structure related to the data structure for dynamic expression trees cf. [7]. The rest of the paper is organized as follows. In Sect. 2 we introduce quartets and present our algorithm for computing the quartet distance between two unrooted evolutionary trees. In Sect. 3 we describe a hierarchical decomposition of unrooted trees which is an essential part of the data ....

....an unrooted tree T where all nodes have degree at most three, we in the following describe how to obtain a hierarchical decomposition of T with logarithmic height. Our decomposition is very similar to the decompositions used for solving the parallel and dynamic expression tree evaluation problems [3, 7], but in our setting the underlying tree is considered to be unrooted. We base our hierarchical decomposition on the notion of components. We de ne a component C in T to be either 1. A single node of T , or 2. A connected subset of the nodes of T , such that at most two nodes in C are connected ....

R. F. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13(3):245-265, 1995.

.... other general tree transformation techniques exist: Frederickson s topology trees [10, 11] Sleator and Tarjan s dynamic trees [24] and Alstrup et al. s top trees [1, 2] One application of such a tree transformation is in Cohen and Tamassia s algorithm for dynamic expression tree evaluation [7]. For parallel algorithms on trees related techniques exist, e.g. the centroid decomposition technique of Megiddo [20] and the accelerated centroid decomposition technique of Cole and Vishkin [8] in [8, 20] centroid refers to the centroid paths in a tree) The rest of this paper is organized as ....

R. F. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13(3):245265, 1995.

....path compression) whose time complexity analysis is very difficult to analyze. See, e.g. 15] Examples of fundamental data structures used in three major application domains are mentioned below. Graphs and Networks adjacency matrix, adjacency lists, link cut tree [33] dynamic expression tree [5], topology tree [14] SPQR tree [8] sparsification tree [11] See also, e.g. 12, 22, 34] Text Processing string, suffix tree, Patricia tree. See, e.g. 16] Geometry and Graphics binary space partition tree, chain tree, trapezoid tree, range tree, segment tree, interval tree, ....

R. F. Cohen and R. Tamassia. Dynamic expression trees. Algorithmica, 13:245--265, 1995.

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