Concept

Arbre binaire de recherche

Résumé
En informatique, un arbre binaire de recherche ou ABR (en anglais, binary search tree ou BST) est une structure de données représentant un ensemble ou un tableau associatif dont les clés appartiennent à un ensemble totalement ordonné. Un arbre binaire de recherche permet des opérations rapides pour rechercher une clé, insérer ou supprimer une clé. Définition Définition générale Un arbre binaire de recherche est un arbre binaire dans lequel chaque nœud possède une clé, telle que chaque nœud du sous-arbre gauche ait une clé inférieure ou égale à celle du nœud considéré, et que chaque nœud du sous-arbre droit possède une clé supérieure ou égale à celle-ci — selon la mise en œuvre de l'ABR, on pourra interdire ou non des clés de valeur égale. Les nœuds que l'on ajoute deviennent des feuilles de l'arbre. Définitions spécifiques
  • Un arbre binaire de recherche est dit complet si tous les niveaux de l'arbre sont remplis, sauf éventuellement le dernier,
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Publications associées (31)

Network of Shortcuts: An Adaptive Data Structure for Tree-Based Search Methods

Andrea Bergamini

In this work we present a novel concept of augmenting a search tree in a packet-processing system with an dditional data structure, a Network of Shortcuts, in order to adapt the search to current input traffic patterns and significantly speed-up the frequently traversed search-tree paths. The method utilizes node statistics gathered from the tree and periodically adjusts the shortcut positions. After an overview of tree-search methods used in networking tasks such as lookup or classification, and a discussion of the impact of typical traffic characteristics, we argue that adding a small number of direct links, or shortcuts, to the few frequently traversed paths can significantly improve performance, at a very low cost. We present a shortcut-placement heuristic, compare our method to a standard caching mechanism and show how the use of different levels of aggregation in a search tree enables to achieve similar results with much fewer entries.
2005

Metric dimension of critical Galton–Watson trees and linear preferential attachment trees

Gergely Odor

The metric dimension of a graph G is the minimal size of a subset R of vertices of G that, upon reporting their graph distance from a distinguished (source) vertex v⋆, enable unique identification of the source vertex v⋆ among all possible vertices of G. In this paper we show a Law of Large Numbers (LLN) for the metric dimension of some classes of trees: critical Galton–Watson trees conditioned to have size n, and growing general linear preferential attachment trees. The former class includes uniform random trees, the latter class includes Yule-trees (also called random recursive trees), m-ary increasing trees, binary search trees, and positive linear preferential attachment trees. In all these cases, we are able to identify the limiting constant in the LLN explicitly. Our result relies on the insight that the metric dimension can be related to subtree properties, and hence we can make use of the powerful fringe-tree literature developed by Aldous and Janson et al.
2021

Distributed Time Series Analytics

Tian Guo

In recent years time series data has become ubiquitous thanks to affordable sensors and advances in embedded technology. Large amount of time-series data are continuously produced in a wide spectrum of applications, such as sensor networks, medical monitoring and so on. Availability of such large scale time series data highlights the importance of of scalable data management, efficient querying and analysis. Meanwhile, in the online setting time series carries invaluable information and knowledge about the real-time status of involved entities or monitored phenomena, which calls for online time series data mining for serving timely decision making or event detection. In this thesis we aim to address these important issues pertaining to scalable and distributed analytics techniques for massive time series data. Concretely, this thesis is centered around the following three topics: As the number of sensors that pervade our lives significantly increases (e.g., environmental sensors, mobile phone sensors, IoT applications, etc.), the efficient management of massive amount of time series from such sensors is becoming increasingly important. The infinite nature of sensor data poses a serious challenge for query processing even in a cloud infrastructure. Traditional raw sensor data management systems based on relational databases lack scalability to accommodate large scale sensor data efficiently. Thus, distributed key-value stores in the cloud are becoming a prime tool to manage sensor data. However, currently there are no techniques for indexing and/or query optimization of the model-view sensor time series data in the cloud. In Chapter 2, we propose an innovative index for modeled segments in key-value stores, namely KVI-index. KVI-index consists of two interval indices on the time and sensor value dimensions respectively, each of which has an in-memory search tree and a secondary list materialized in the key-value store. The dramatic increase in the availability of data streams fuels the development of many distributed real-time computation engines (e.g., Storm, Samza, Spark Streaming, S4 etc.). In Chapter 3, we focus on a fundamental time series mining task in such a new computation paradigm, namely continuously mining dynamic (lagged) correlations in time series via a distributed real-time computation engine. Correlations reveal the hidden and temporal interactions across time series and are widely used in scientific data analysis, data-driven event detection, finance markets and so on. We propose the P2H framework consisting of a parallelism-partitioning based data shuffling and a hypercube structure based computation pruning method, so as to enhance both the communication and computation efficiency for mining correlations in the distributed context. In numerous real-world applications large datasets collected from observations and measurements of physical entities are inevitably noisy and contain outliers. The outliers in such large and noisy datasets can dramatically degrade the performance of standard distributed machine learning approaches such as s regression trees. In Chapter 4 we present a novel distributed regression tree approach that utilizes robust regression statistics, statistics that are more robust to outliers, for handling large and noisy datasets. Then we present an adaptive gradient learning method for recurrent neural networks (RNN) to forecast streaming time series in the presence of both outliers and change points.
EPFL2017
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