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...

We consider the supercritical oriented percolation model. Let K be all the percolation points. For each u ∈ K, we write γu as its right-most path. Let G = ∪uγu. In this paper, we show that G is a single tree with only one topological end. We also present a relationship between K and G and construct a bijection between K and Z using the preorder traversal algorithm. Through applications of this ...

The traditional program refinement strategy cannot be refined to an executable program, and there are issues such as low verification reliability automation. To solve the above problems, this paper proposes a nonlinear construction method based on partition recursion Morgan's rules. First, we use recursive definition technique characterize initial specification. specification is then transforme...

Many of the problems with native XML databases relate to query performance and subsequently, it can be difficult to convince traditional database users of the benefits of using semior unstructured databases. Presently, there still lacks an index structure providing efficient support for structural queries and the traditional data-centric and content queries. This paper presents an extended inde...

Digital trees or tries are a general purpose flexible data structure that implements dictionaries built on words. The present paper is focussed on the average-case analysis of an important parameter of this tree-structure, i.e., the stack-size. The stack-size of a tree is the memory needed by a storage-optimal preorder traversal. The analysis is carried out under a general model in which words ...

This paper discusses the implementation of the binary coding scheme and its comparison with the post-order, preorder and in-order traversal techniques to test for ancestor-descendant relationships in k-ary trees (a tree in which any leaf node has up to k children). The approach used is assigning a unique binary code to each node in a tree. The value of the binary code for a node is the concaten...

We present a new method of regional identification, partition, and integral (RIPI) phase unwrapping for processing images, especially those with low quality, obtained from moiré interferometry experiments. By introducing the principle of preorder traversal of a general tree in data structures and then by applying the idea of a regional integral, the proposed method makes regional partition and ...

Cloud storage auditing is the process of verifying the integrity of the data stored in public cloud. The existing auditing protocols are based on the assumption that the client’s secret key for auditing is secure. In practical the secret key is not absolutely secure due to weak security settings at the client. If secret key for auditing is exposed, most of the current auditing protocols become ...

This work is mainly motivated by the description of a new approach for calculating the structural similarity of XML documents. Practically, the majority of existing work on XML documents clustering considers the tree structures of these documents as mere vectors and, therefore, does not take into account their hierarchical contexts. Furthermore, in order to calculate the structural similarity o...