Abstract:In this paper, a new representation of a binary tree is introduced, called the Catalan Cipher Vector, which is a vector of elements with certain properties. It can be ranked using a special form of the Catalan Triangle designed for this purpose. It is shown that the vector coincides with the level-order traversal of the binary tree and how it can be used to generate a binary tree from it. Streamlined algorithms for directly obtaining the rank from a binary tree and vice versa, using the Catalan Cipher Vector during the processes, are given. The algorithms are analyzed for time and space complexity and shown to be linear for both.The Catalan Cipher Vector enables a straightforward determination of the position and linking for every node of the binary tree, since it contains information for both every node's ancestor and the direction of linking from the ancestor to that node. Thus, it is especially well suited for binary tree generation. Using another structure, called a canonical state-space tableau, the relationship between the Catalan Cipher Vector and the level-order traversal of the binary tree is explained.

This paper investigates the performance of reactive and proactive routing protocols in a wireless sensor network for targeted enviroment. AODV and DSR are chosen as representatives for the reactive routing protocols and DSDV for the proactive. A wireless sensor network application for farm cattle monitoring is created. The proposed solution meets a desired requirement for periodically observing the condition of each individual animal, processing the gathered data and reporting it to the farmer. However, an implementation of a WSN needs to meet particular technical challenges before it can be suitable to be applied in cattle management. For this, multiple scenarios are presented with various situations to evaluate the performance of routing protocols in the WSNs. Finally, the results concerning data transportation from the mounted sensory devices to the mobile nodes are discussed and analyzed.

This paper presents the time complexity analysis of the Binary Tree Roll algorithm. The time complexity is analyzed theoretically and the results are then confi rmed empirically. The theoretical analysis consists of fi nding recurrence relations for the time complexity, and solving them using various methods. The empirical analysis consists of exhaustively testing all trees with given numbers of nodes and counting the minimum and maximum steps necessary to complete the roll algorithm. The time complexity is shown, both theoretically and empirically, to be linear in the best case and quadratic in the worst case, whereas its average case is shown to be dominantly linear for trees with a relatively small number of nodes and dominantly quadratic otherwise.

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In the process of introduction of information as well as data capabilities the first approach is adding technology that can be used in many spheres for buildings and upgrading apparatus and utensils. However the focus of this study is on the deficiency of current elevators associated with efficiency and debugging of the errors or security systems where we concentrate on the introduction of new trends which advise that elevators should be implemented with intelligent devices. Smart elevators easily provide means to predict and prevent errors and bring the chances of an error to a minimum. Needless to say is that a range of negative effects are unavoidable when it comes to the introduction of new technology. This paper will illustrate both the advantages and the disadvantages of using intelligent devices in elevators and through an analysis of the various options using Multi- Criteria Analysis method perform ranking of the presented solutions.