Tree (data structure)

About: Tree (data structure) is a research topic. Over the lifetime, 44931 publications have been published within this topic receiving 749669 citations. The topic is also known as: tree structure & tree.

A two-stage RRT path planner for automated parking

Abstract: Path planning for automated parking remains challenged by the demand to balance general parking scenarios and computational efficiency. This paper proposes a two-stage rapid-exploring random tree (RRT) algorithm to improve the computational efficiency. At first the proposed algorithm performs space exploration and establishes prior knowledge, represented as waypoints, using cheap computation. Secondly a waypoint-guided RRT algorithm, with a sampling scheme biased by the waypoints, constructs a kinematic tree connecting the initial and goal configurations. Numerical study demonstrates that the two-stage algorithm achieves at least 2X faster than the baseline one-stage algorithm.

Prediction of annual tree growth and survival for thinned and unthinned evenaged maritime pine stands in Portugal from data with different time measurement intervals

Abstract: Abstract An annual individual tree survival and growth model was developed for pure even-aged stands of maritime pine in Portugal, using a large data set containing irregularly time-spaced measurements and considering thinning effects. The model is distance-independent and is based on a function for diameter growth, a function for height growth and a survival function. Two approaches are compared for modeling annual tree growth. The first approach directly estimates a future diameter or height using well-known growth functions formulated in difference form. The second approach estimates diameter or height using a function in differential form estimating the increment over a year period. In both approaches, the function parameters were related to tree and stand variables reflecting the competition status of the tree as well as of a thinning response factor. Variable growth and survival rates were assumed in the modeling approaches. An iterative method was used to continuously update tree and stand attributes using a cut-off to convert the survival probability for a living or a dead tree. The individual tree diameter growth model and the survival probability model were fitted simultaneously using seemingly unrelated regression (SUR). Parameters of the height function were obtained separately as the number of observations for height was much lower than the number of observations for diameter, which may affect the statistical inference and the estimation of contemporaneous cross-equation error correlation inherent to the system of equations. PRESS residuals were used to evaluate the predictive performance of the diameter and the height growth functions. Additional statistics based in the log likelihood function and also in the survival probability were computed to evaluate the survival function. The second modeling approach, which integrates components of growth expansion and decline, performed slightly better than the first approach. A variable accounting for the thinning response that was tested proved to be significant for predicting diameter growth, even if the model already included competition-related explanatory variables, namely the basal area of trees larger than the subject tree. However, this thinning response factor was not significant for predicting height growth.

A Distributed Algorithm to Construct Multicast Trees in WSNs: An Approximate Steiner Tree Approach

Abstract: Multicast tree is a key structure for data dissemination from one source to multiple receivers in wireless networks. Minimum length multicast tree can be modeled as the Steiner Tree Problem, and is proven to be NP-hard. In this paper, we explore how to efficiently generate minimum length multicast trees in wireless sensor networks (WSNs), where only limited knowledge of network topology is available at each node. We design and analyze a simple and distributed algorithm, which we call Toward Source Tree (TST), to build multicast trees in WSNs. We show three metrics of TST algorithm, i.e., running time, tree length and energy efficiency. We prove that its running time is O(√nlog n), the best among all existing solutions to our best knowledge. We prove that TST tree length is in the same order as Steiner tree, give a theoretical upper bound and use simulations to show the ratio between them is only 1.114 when nodes are uniformly distributed. We evaluate energy efficiency in terms of the number of forwarding nodes in multicast trees, and prove that it is order-optimal. We give an efficient way to construct multicast tree in support of transmission of voluminous data.

Robust estimation of latent tree graphical models: Inferring hidden states with inexact parameters

Abstract: Latent tree graphical models are widely used in computational biology, signal and image processing, and network tomography. Here we design a new efficient, estimation procedure for latent tree models, including Gaussian and discrete, reversible models, that significantly improves on previous sample requirement bounds. Our techniques are based on a new hidden state estimator which is robust to inaccuracies in estimated parameters. More precisely, we prove that latent tree models can be estimated with high probability in the so-called Kesten-Stigum regime with $O(log^2 n)$ samples where $n$ is the number of nodes.