It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of...

The aim of this note is to generalize some recent results for binary trees by Panholzer and Prodinger [15] to a larger class of rooted trees. The number of descendants of a node j is the number of nodes in the subtree rooted at j, and the number of ascendants is the number of nodes between j and the root. Recently, Panholzer and Prodinger [15] studied the behavior of these parameters in binary ...

It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of...

We consider the following problem. For a binary tree T = (V; E) where V = f1; 2; :::; ng, given its inorder traversal and either its preorder or its postorder traversal, reconstruct the binary tree. We present a new parallel algorithm for this problem. Our algorithm requires O(n) space. The main idea of our algorithm is to reduce the reconstruction process to merging two sorted sequences. With ...

An efficient computational method is presented for state space analysis of singular systems via Haar wavelets. Singular systems are those in which dynamics are governed by a combination of algebraic and differential equations. The corresponding differential-algebraic matrix equation is converted to a generalized Sylvester matrix equation by using Haar wavelet basis. First, an explicit expressio...

An algorithm is presented for reconstructing a quadtree from its quadtree medial axis transform (QMAT). It is useful when performing operations for which the QMAT is well suited (e.g., thinning of an image). The algorithm is a postorder tree traversal which propagates the subsumption of each BLACK QMAT node in the eight possible directions. Analysis of the algorithm shows that its average execu...

In this paper we present several improvements of widely used parallel LU factorization methods on sparse matrices. First we introduce the LU elimination forest and then we characterize the L, U factors in terms of their corresponding LU elimination forest. This characterization can be used as a compact storage scheme of the matrix as well as of the task dependence graph. To improve the use of B...