Embedding complete ternary tree in hypercubes using AVL trees

A complete ternary tree is a tree in which every non-leaf vertex has exactly three children. We prove that a complete ternary tree of height h, TTh, is embeddable in a hypercube of dimension . This result coincides with the result of [2]. However, in this paper, the embedding utilizes the knowledge of AVL trees. We prove that a subclass of AVL trees is a subgraph of hypercube. The problem of embedding AVL trees in hypercube is an independent emerging problem

On Counting and Embedding a Subclass of Height-Balanced Trees

A height-balanced tree is a rooted binary tree in which, for every vertex v, the difference in the heights of the subtrees rooted at the left and right child of v (called the balance factor of v) is at most one. In this paper, we consider height-balanced trees in which the balance factor of every vertex beyond a level is 0. We prove that there are 22t-1 such trees and embed them into a generalized join of hypercubes

Managing your Trees: Insights from a Metropolitan-Scale Low-Power Wireless Network

Low-power wireless, such as IEEE 802.15.4, is envisioned as one key technology for wireless control and communication. In the context of the Advanced Metering Infrastructure (AMI), it serves as an energy-efficient communication technology for both communications at building-scale networks and city-scale networks. Understanding real-world challenges and key properties of 802.15.4 based networks is an essential requirement for both the research community and practitioners: When deploying and operating low-power wireless networks at metropolitan-scale, a deep knowledge is essential to ensure network availability and performance at production-level quality. Similarly, researchers require realistic network models when developing new algorithms and protocols. In this paper, we present new and real-world insights from a deployed metropolitan-scale low-power wireless network: It includes 300,000 individual wireless connected meters and covers a city with roughly 600,000 inhabitants. Our findings, for example, help to estimate real-world parameters such as the typical size of routing trees, their balance, and their dynamics over time. Moreover, these insights facilitate the understanding and the realistic calibration of simulation models in key properties such as reliability and throughput

Event-driven simulation scheme for spiking neural networks using lookup tables to characterize neuronal dynamics

Nearly all neuronal information processing and interneuronal communication in the brain involves action potentials, or spikes, which drive the short-term synaptic dynamics of neurons, but also their long-term dynamics, via synaptic plasticity. In many brain structures, action potential activity is considered to be sparse. This sparseness of activity has been exploited to reduce the computational cost of large-scale network simulations, through the development of event-driven simulation schemes. However, existing event-driven simulations schemes use extremely simplified neuronal models. Here, we implement and evaluate critically an event-driven algorithm (ED-LUT) that uses precalculated look-up tables to characterize synaptic and neuronal dynamics. This approach enables the use of more complex (and realistic) neuronal models or data in representing the neurons, while retaining the advantage of high-speed simulation. We demonstrate the method's application for neurons containing exponential synaptic conductances, thereby implementing shunting inhibition, a phenomenon that is critical to cellular computation. We also introduce an improved two-stage event-queue algorithm, which allows the simulations to scale efficiently to highly connected networks with arbitrary propagation delays. Finally, the scheme readily accommodates implementation of synaptic plasticity mechanisms that depend on spike timing, enabling future simulations to explore issues of long-term learning and adaptation in large-scale networks.This work has been supported by the EU projects SpikeFORCE (IST-2001-35271), SENSOPAC (IST-028056) and the Spanish National Grant (DPI-2004-07032

Design and Application of a Research Tool for Height Balanced Trees

This study is concerned with the development and extension of a class of height balanceti binary search trees known as HB(k} trees. HE(k} trees are an important alternative data structure in file systems wtere rapid access and rapiri update are desired. However, a precise analysis of expected system performance using HB(k) trees is impossible since a precise analysis of the expected behavior of HB{k) trees remains unfornmlated. A generalized class of HB(k) trees, known as PHB(kl,k2) trees, may pravide tte tool necessary to analyze the expected behavior of HE(k) trees. The design of algorithms for maintaining these trees and the subsequent implementation of the algorithms as part of a research tool for height balanced trees are also discussed. Results from an initial use of the research tool are presented.Computing and Information Science