The document discusses AVL trees, which are self-balancing binary search trees. AVL trees ensure that insertions and deletions perform in O(log n) time by enforcing that the heights of any two subtrees of a node differ by at most one. They use rotations to rebalance the tree after insertions or deletions. Single and double rotations are used to move nodes and restore the balance property. Maintaining the balance factor during insertions, deletions, and rotations requires adjusting the heights of nodes as they are moved.
Stockage, manipulation et analyse de données matricielles avec PostGIS RasterACSG Section Montréal
La plus importantes nouveautés de la base de données spatiale open source PostgreSQL/PostGIS 2.0 est le support pour les données raster. PostGIS Raster comprend un outil d’importation similaire à shp2pgsql basé sur GDAL et une série d’opérateurs SQL pour la manipulation et l'analyse des données matricielles. Le nouveau type RASTER est géoréférencé, multi-résolutions et multi-bandes et il supporte une valeur nulle (nodata) et un type de valeur de pixel par bande. PostGIS raster s’inspire de la simplicité de l’expérience vecteur offerte par PostGIS pour rendre toutes les opérations raster aussi simples que possible. Comme pour une couverture vecteur, une couverture raster est divisée en un ensemble d’enregistrements (une ligne = une tuile) stockés dans une seule table (contrairement à Oracle Spatial qui utilise deux types et donc deux tables ou plus). Il est possible d’importer une couverture complète et de la retuiler en une seule commande avec l’outil d’importation et de multiples résolutions de la même couverture peuvent être importées dans des tables adjacentes. Les propriétés des objets raster et de chacune des bandes peuvent être consultées et modifiées ainsi que les valeurs des pixels. Des fonctions existent pour obtenir le minimum, le maximum, la somme, la moyenne, la déviation standard, l’histogramme d’une tuile ou d’une couverture complète. Les fonctions ST_Intersection() et ST_Intersects() fonctionnent pratiquement de manière transparente entre des données raster et vecteur et une série de fonctions pour l’algèbre matricielle (ST_MapAlgebra()) permet de faire de l’analyse de type raster. Il est possible de reclasser les bandes et de les convertir en n’importe quel format d’écriture GDAL. Des fonctions pour générer des rasters et des bandes existent également pour du développement PL/pgSQL. Un driver GDAL pour convertir les couvertures raster en fichiers images est en développement et des plugins pour QGIS et svSIG existent déjà pour les visualiser.
The document discusses distributed linear classification on Apache Spark. It describes using Spark to train logistic regression and linear support vector machine models on large datasets. Spark improves on MapReduce by conducting communications in-memory and supporting fault tolerance. The paper proposes using a trust region Newton method to optimize the objective functions for logistic regression and linear SVM. Conjugate gradient is used to approximate the Hessian matrix and solve the Newton system without explicitly storing the large Hessian.
This chapter discusses techniques for computing data cubes from multidimensional datasets. It begins with basic concepts like data cube structure and computation. It then covers specific computation methods like multi-way array aggregation, bottom-up computation (BUC), and star-cubing. It also discusses challenges of computing high-dimensional cubes and approaches for minimizing computation. The chapter provides an overview of key data cube computation methods and optimization techniques.
This document discusses new performance features in Oracle Database 12c Release 1 (12.1.0.2). It summarizes seven new features: 1) Zone Maps, 2) Attribute Clustering, 3) In-Memory Column Store, 4) In-Memory Aggregation, 5) Approximate Count Distinct, 6) Automatic Big Table Caching, and 7) Full Database Caching. The document provides details on how each feature works and its performance benefits. It focuses in more depth on Zone Maps, Attribute Clustering, and In-Memory Aggregation.
Accelerating Collapsed Variational Bayesian Inference for Latent Dirichlet Al...Tomonari Masada
1. The document discusses accelerating collapsed variational Bayesian inference for latent Dirichlet allocation (CVB) using Nvidia CUDA compatible GPU devices.
2. It describes parallelizing CVB for LDA by assigning different topics to different GPU threads. This achieves near-linear speedup compared to a single-threaded CPU implementation.
3. Experiments on text and image datasets demonstrate that the GPU implementation provides faster inference over the CPU version, though data transfer latency and memory limits remain challenges for large-scale problems.
Aes encryption engine for many core processor arrays for enhanced securityIAEME Publication
This document describes two implementations of an Advanced Encryption Standard (AES) cipher with online key expansion mapped to a fine-grained many-core system. The first implementation, called "One Task One Processor", maps each step of the AES algorithm to a separate processor. The second implementation unrolls the AES algorithm loop nine times to break data dependencies and process multiple data blocks in parallel using about 60 cores. Evaluation on an FPGA shows the unrolled implementation achieves a throughput of 85.15 Gbps compared to 1.98 Gbps for the single-task implementation. The document also proposes a masked S-box technique to protect AES implementations from differential power analysis attacks.
Stockage, manipulation et analyse de données matricielles avec PostGIS RasterACSG Section Montréal
La plus importantes nouveautés de la base de données spatiale open source PostgreSQL/PostGIS 2.0 est le support pour les données raster. PostGIS Raster comprend un outil d’importation similaire à shp2pgsql basé sur GDAL et une série d’opérateurs SQL pour la manipulation et l'analyse des données matricielles. Le nouveau type RASTER est géoréférencé, multi-résolutions et multi-bandes et il supporte une valeur nulle (nodata) et un type de valeur de pixel par bande. PostGIS raster s’inspire de la simplicité de l’expérience vecteur offerte par PostGIS pour rendre toutes les opérations raster aussi simples que possible. Comme pour une couverture vecteur, une couverture raster est divisée en un ensemble d’enregistrements (une ligne = une tuile) stockés dans une seule table (contrairement à Oracle Spatial qui utilise deux types et donc deux tables ou plus). Il est possible d’importer une couverture complète et de la retuiler en une seule commande avec l’outil d’importation et de multiples résolutions de la même couverture peuvent être importées dans des tables adjacentes. Les propriétés des objets raster et de chacune des bandes peuvent être consultées et modifiées ainsi que les valeurs des pixels. Des fonctions existent pour obtenir le minimum, le maximum, la somme, la moyenne, la déviation standard, l’histogramme d’une tuile ou d’une couverture complète. Les fonctions ST_Intersection() et ST_Intersects() fonctionnent pratiquement de manière transparente entre des données raster et vecteur et une série de fonctions pour l’algèbre matricielle (ST_MapAlgebra()) permet de faire de l’analyse de type raster. Il est possible de reclasser les bandes et de les convertir en n’importe quel format d’écriture GDAL. Des fonctions pour générer des rasters et des bandes existent également pour du développement PL/pgSQL. Un driver GDAL pour convertir les couvertures raster en fichiers images est en développement et des plugins pour QGIS et svSIG existent déjà pour les visualiser.
The document discusses distributed linear classification on Apache Spark. It describes using Spark to train logistic regression and linear support vector machine models on large datasets. Spark improves on MapReduce by conducting communications in-memory and supporting fault tolerance. The paper proposes using a trust region Newton method to optimize the objective functions for logistic regression and linear SVM. Conjugate gradient is used to approximate the Hessian matrix and solve the Newton system without explicitly storing the large Hessian.
This chapter discusses techniques for computing data cubes from multidimensional datasets. It begins with basic concepts like data cube structure and computation. It then covers specific computation methods like multi-way array aggregation, bottom-up computation (BUC), and star-cubing. It also discusses challenges of computing high-dimensional cubes and approaches for minimizing computation. The chapter provides an overview of key data cube computation methods and optimization techniques.
This document discusses new performance features in Oracle Database 12c Release 1 (12.1.0.2). It summarizes seven new features: 1) Zone Maps, 2) Attribute Clustering, 3) In-Memory Column Store, 4) In-Memory Aggregation, 5) Approximate Count Distinct, 6) Automatic Big Table Caching, and 7) Full Database Caching. The document provides details on how each feature works and its performance benefits. It focuses in more depth on Zone Maps, Attribute Clustering, and In-Memory Aggregation.
Accelerating Collapsed Variational Bayesian Inference for Latent Dirichlet Al...Tomonari Masada
1. The document discusses accelerating collapsed variational Bayesian inference for latent Dirichlet allocation (CVB) using Nvidia CUDA compatible GPU devices.
2. It describes parallelizing CVB for LDA by assigning different topics to different GPU threads. This achieves near-linear speedup compared to a single-threaded CPU implementation.
3. Experiments on text and image datasets demonstrate that the GPU implementation provides faster inference over the CPU version, though data transfer latency and memory limits remain challenges for large-scale problems.
Aes encryption engine for many core processor arrays for enhanced securityIAEME Publication
This document describes two implementations of an Advanced Encryption Standard (AES) cipher with online key expansion mapped to a fine-grained many-core system. The first implementation, called "One Task One Processor", maps each step of the AES algorithm to a separate processor. The second implementation unrolls the AES algorithm loop nine times to break data dependencies and process multiple data blocks in parallel using about 60 cores. Evaluation on an FPGA shows the unrolled implementation achieves a throughput of 85.15 Gbps compared to 1.98 Gbps for the single-task implementation. The document also proposes a masked S-box technique to protect AES implementations from differential power analysis attacks.
Session 1 - Silva, Singh, Richardson at MLconf NYCMLconf
The document discusses using the Aligned Box Criterion (ABC) method to determine the optimal number of clusters in a dataset. ABC estimates reference distributions to determine the smallest number of clusters k such that adding another cluster does not significantly improve the clustering fit. ABC avoids the quadratic complexity of other methods, scales well to large, high-dimensional datasets, and is more robust to noise. It delivers good performance for estimating the number of clusters in real-world applications.
This document summarizes quantization design techniques including Lloyd-Max quantizers and variable rate optimum quantizers. It discusses the problem setup for scalar quantization and outlines the local optimality conditions, alternating optimization approach, and dynamic programming approach for designing Lloyd-Max quantizers. It also covers the problem setup for variable rate optimum quantizer design subject to an entropy constraint, and describes analyzing this using a generalized Lloyd-Max algorithm.
1) Kernel Bayes' rule provides a nonparametric approach to Bayesian inference using positive definite kernels. It represents probabilities as elements in a reproducing kernel Hilbert space.
2) Using kernel mean embeddings, kernel Bayes' rule computes the posterior kernel mean directly from covariance operators without needing to compute integrals or approximations.
3) Given samples from the joint distribution and the prior kernel mean, kernel Bayes' rule computes the posterior kernel mean as a weighted sum of prior sample kernel embeddings, providing a nonparametric realization of Bayesian inference.
2014-06-20 Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
Sparse matrix computations in MapReduceDavid Gleich
The document announces an ICME MapReduce workshop from April 29 to May 1, 2013. The workshop goals are to learn the basics of MapReduce and Hadoop and be able to process large volumes of scientific data. The workshop overview includes presentations on sparse matrix computations in MapReduce, extending MapReduce for scientific computing, and evaluating MapReduce for science. The document also discusses how to program data computers using MapReduce and Hadoop and provides examples of matrix operations like matrix-vector multiplication in MapReduce.
Spatial functions in MySQL 5.6, MariaDB 5.5, PostGIS 2.0 and othersHenrik Ingo
This document summarizes a presentation on spatial functions in MySQL 5.6, MariaDB 5.5, PostGIS 2.0 and MongoDB. It begins with definitions of key spatial concepts like points, lines, polygons and projections. Benchmark results show that MySQL and MariaDB significantly outperform other databases for spatial queries on polygons, with responses times around 1 millisecond. PostGIS has more advanced spatial features but lower performance. MongoDB performance was lower still and did not scale well with additional clients. The document concludes with recommendations to improve the user experience and performance of spatial databases.
Louis Britto is an independent trainer and motivator with over 25 years of experience in various industries and 9 years of professional training experience. He specializes in soft skills, interpersonal skills, motivation, sales, service, and leadership training. He has trained over 40,000 students on employability skills and designed an exclusive module for training freshers. He received the Best Trainer award from Sun Insurance in 2007.
Don Nairo vive en una finca en Casanare y se dedica a la ganadería. Quiere aprender a usar WhatsApp en su celular para comunicarse con su familia en otras partes del país. Gracias a Milena Rojas y al programa Redvolución, Nairo aprendió a usar las funciones básicas de WhatsApp como enviar y recibir mensajes, fotos y videos. Ahora puede mantenerse en contacto con su familia y se siente feliz de haber reducido la brecha digital con la ayuda del programa.
The document provides a summary of various items and scenes found at the Flea Market located in Yafo, Israel. It describes a wide variety of second-hand merchandise for sale, from clothes and appliances to antiques and furniture. The market attracts both local visitors and tourists who come to experience the atmosphere. Some of the items mentioned include old radios, books, typewriters, records, clothing, and other bric-a-brac. The document also references interactions between merchants and customers at the market.
This document provides instructions for using Grunt to compress JavaScript files. It describes installing Node.js and Grunt CLI, creating a project structure and package.json file, installing Grunt plugins, configuring Gruntfile.js to first concatenate JS files and then minify them into a single compressed file, and running Grunt to perform these tasks. The Gruntfile configuration concatenates source files into a combined.js file in the defined order, then uglifies this file to minify it.
The document discusses the development of scientific theories and experiments regarding atoms, light, and quantum mechanics. It describes early experiments and observations that led to discoveries such as the planetary model of the atom, the particle nature of light, and wave-particle duality. Later, quantum mechanics was developed to explain the intrinsic unpredictability of atomic behaviors and experiments such as the double slit experiment.
The energy industry faces a severe talent shortage due to a "double squeeze" - many current workers are retiring while the education system is not producing enough skilled new entrants. This is exacerbated by rapid technological changes. As a result, companies may not have sufficient skilled workers to capitalize on investments and growth opportunities despite billions being invested in new technologies and capacity expansion. The talent shortage could significantly impact the industry's ability to meet rising global energy demand and maximize economic potential.
Bao cao giam sat moi truong dinh ky, bao cao giam sat, bao cao moi truong, cong ty moi truong, tu van moi truong, dich vu moi truong, cong ty tu van moi truong, xu ly nuoc thai, xu ly khi thai
The document provides advice for brand work and strategy in 3 sentences or less:
Focus on doing excellent work for the brand to establish its role beyond just sponsorship; don't get involved just to test ideas but instead aim to create an impact; and trust your intuition which knows things your conscious mind hasn't figured out yet, while also being open to trying new approaches.
The document discusses the trend of "omni-colleagues," where companies are re-integrating human employees into digital interfaces and customer experiences. It notes that while companies had been moving towards more automated and robotic customer service, replacing human interactions was not working. Specifically:
- Companies are emphasizing their employees as "colleagues" rather than "staff" to build camaraderie between employees and customers. Some services now rate and review individual employees.
- Companies are providing digital tools to employees but also training them in social skills to have more meaningful interactions with customers.
- Moving forward, companies will look to equip employees to take meaningful actions for users through digital tools, making employees "omni-
Madison Marie's first year was documented through photos of her first bath, celebrating her first Fourth of July, a day at the pool, and dressing up for Halloween. The photos chronicle some of Madison's milestones and adventures during her infant year through brief captions.
The Commissioner for Older People in Wales conducted a review of the experiences of older people in hospitals in Wales. The review found inconsistencies in care, with some patients feeling treated with dignity while others felt like numbers. The Commissioner made 12 recommendations to improve leadership, dementia care, continence needs, communication, discharges, volunteers, staffing, environments, and use of patient feedback. Health boards and the Welsh government responded and are monitoring progress on implementing changes to improve hospital care for older patients.
Session 1 - Silva, Singh, Richardson at MLconf NYCMLconf
The document discusses using the Aligned Box Criterion (ABC) method to determine the optimal number of clusters in a dataset. ABC estimates reference distributions to determine the smallest number of clusters k such that adding another cluster does not significantly improve the clustering fit. ABC avoids the quadratic complexity of other methods, scales well to large, high-dimensional datasets, and is more robust to noise. It delivers good performance for estimating the number of clusters in real-world applications.
This document summarizes quantization design techniques including Lloyd-Max quantizers and variable rate optimum quantizers. It discusses the problem setup for scalar quantization and outlines the local optimality conditions, alternating optimization approach, and dynamic programming approach for designing Lloyd-Max quantizers. It also covers the problem setup for variable rate optimum quantizer design subject to an entropy constraint, and describes analyzing this using a generalized Lloyd-Max algorithm.
1) Kernel Bayes' rule provides a nonparametric approach to Bayesian inference using positive definite kernels. It represents probabilities as elements in a reproducing kernel Hilbert space.
2) Using kernel mean embeddings, kernel Bayes' rule computes the posterior kernel mean directly from covariance operators without needing to compute integrals or approximations.
3) Given samples from the joint distribution and the prior kernel mean, kernel Bayes' rule computes the posterior kernel mean as a weighted sum of prior sample kernel embeddings, providing a nonparametric realization of Bayesian inference.
2014-06-20 Multinomial Logistic Regression with Apache SparkDB Tsai
Logistic Regression can not only be used for modeling binary outcomes but also multinomial outcome with some extension. In this talk, DB will talk about basic idea of binary logistic regression step by step, and then extend to multinomial one. He will show how easy it's with Spark to parallelize this iterative algorithm by utilizing the in-memory RDD cache to scale horizontally (the numbers of training data.) However, there is mathematical limitation on scaling vertically (the numbers of training features) while many recent applications from document classification and computational linguistics are of this type. He will talk about how to address this problem by L-BFGS optimizer instead of Newton optimizer.
Bio:
DB Tsai is a machine learning engineer working at Alpine Data Labs. He is recently working with Spark MLlib team to add support of L-BFGS optimizer and multinomial logistic regression in the upstream. He also led the Apache Spark development at Alpine Data Labs. Before joining Alpine Data labs, he was working on large-scale optimization of optical quantum circuits at Stanford as a PhD student.
Sparse matrix computations in MapReduceDavid Gleich
The document announces an ICME MapReduce workshop from April 29 to May 1, 2013. The workshop goals are to learn the basics of MapReduce and Hadoop and be able to process large volumes of scientific data. The workshop overview includes presentations on sparse matrix computations in MapReduce, extending MapReduce for scientific computing, and evaluating MapReduce for science. The document also discusses how to program data computers using MapReduce and Hadoop and provides examples of matrix operations like matrix-vector multiplication in MapReduce.
Spatial functions in MySQL 5.6, MariaDB 5.5, PostGIS 2.0 and othersHenrik Ingo
This document summarizes a presentation on spatial functions in MySQL 5.6, MariaDB 5.5, PostGIS 2.0 and MongoDB. It begins with definitions of key spatial concepts like points, lines, polygons and projections. Benchmark results show that MySQL and MariaDB significantly outperform other databases for spatial queries on polygons, with responses times around 1 millisecond. PostGIS has more advanced spatial features but lower performance. MongoDB performance was lower still and did not scale well with additional clients. The document concludes with recommendations to improve the user experience and performance of spatial databases.
Louis Britto is an independent trainer and motivator with over 25 years of experience in various industries and 9 years of professional training experience. He specializes in soft skills, interpersonal skills, motivation, sales, service, and leadership training. He has trained over 40,000 students on employability skills and designed an exclusive module for training freshers. He received the Best Trainer award from Sun Insurance in 2007.
Don Nairo vive en una finca en Casanare y se dedica a la ganadería. Quiere aprender a usar WhatsApp en su celular para comunicarse con su familia en otras partes del país. Gracias a Milena Rojas y al programa Redvolución, Nairo aprendió a usar las funciones básicas de WhatsApp como enviar y recibir mensajes, fotos y videos. Ahora puede mantenerse en contacto con su familia y se siente feliz de haber reducido la brecha digital con la ayuda del programa.
The document provides a summary of various items and scenes found at the Flea Market located in Yafo, Israel. It describes a wide variety of second-hand merchandise for sale, from clothes and appliances to antiques and furniture. The market attracts both local visitors and tourists who come to experience the atmosphere. Some of the items mentioned include old radios, books, typewriters, records, clothing, and other bric-a-brac. The document also references interactions between merchants and customers at the market.
This document provides instructions for using Grunt to compress JavaScript files. It describes installing Node.js and Grunt CLI, creating a project structure and package.json file, installing Grunt plugins, configuring Gruntfile.js to first concatenate JS files and then minify them into a single compressed file, and running Grunt to perform these tasks. The Gruntfile configuration concatenates source files into a combined.js file in the defined order, then uglifies this file to minify it.
The document discusses the development of scientific theories and experiments regarding atoms, light, and quantum mechanics. It describes early experiments and observations that led to discoveries such as the planetary model of the atom, the particle nature of light, and wave-particle duality. Later, quantum mechanics was developed to explain the intrinsic unpredictability of atomic behaviors and experiments such as the double slit experiment.
The energy industry faces a severe talent shortage due to a "double squeeze" - many current workers are retiring while the education system is not producing enough skilled new entrants. This is exacerbated by rapid technological changes. As a result, companies may not have sufficient skilled workers to capitalize on investments and growth opportunities despite billions being invested in new technologies and capacity expansion. The talent shortage could significantly impact the industry's ability to meet rising global energy demand and maximize economic potential.
Bao cao giam sat moi truong dinh ky, bao cao giam sat, bao cao moi truong, cong ty moi truong, tu van moi truong, dich vu moi truong, cong ty tu van moi truong, xu ly nuoc thai, xu ly khi thai
The document provides advice for brand work and strategy in 3 sentences or less:
Focus on doing excellent work for the brand to establish its role beyond just sponsorship; don't get involved just to test ideas but instead aim to create an impact; and trust your intuition which knows things your conscious mind hasn't figured out yet, while also being open to trying new approaches.
The document discusses the trend of "omni-colleagues," where companies are re-integrating human employees into digital interfaces and customer experiences. It notes that while companies had been moving towards more automated and robotic customer service, replacing human interactions was not working. Specifically:
- Companies are emphasizing their employees as "colleagues" rather than "staff" to build camaraderie between employees and customers. Some services now rate and review individual employees.
- Companies are providing digital tools to employees but also training them in social skills to have more meaningful interactions with customers.
- Moving forward, companies will look to equip employees to take meaningful actions for users through digital tools, making employees "omni-
Madison Marie's first year was documented through photos of her first bath, celebrating her first Fourth of July, a day at the pool, and dressing up for Halloween. The photos chronicle some of Madison's milestones and adventures during her infant year through brief captions.
The Commissioner for Older People in Wales conducted a review of the experiences of older people in hospitals in Wales. The review found inconsistencies in care, with some patients feeling treated with dignity while others felt like numbers. The Commissioner made 12 recommendations to improve leadership, dementia care, continence needs, communication, discharges, volunteers, staffing, environments, and use of patient feedback. Health boards and the Welsh government responded and are monitoring progress on implementing changes to improve hospital care for older patients.
AVL Trees
Adelson-Velskii and Landis
Binary Search Tree - Best Time
All BST operations are O(d), where d is tree depth
minimum d is for a binary tree with N nodes
What is the best case tree?
What is the worst case tree?
So, best case running time of BST operations is O(log N)
Binary Search Tree - Worst Time
Worst case running time is O(N)
What happens when you Insert elements in ascending order?
Insert: 2, 4, 6, 8, 10, 12 into an empty BST
Problem: Lack of “balance”:
compare depths of left and right subtree
Unbalanced degenerate tree
Balanced and unbalanced BST
Approaches to balancing trees
Don't balance
May end up with some nodes very deep
Strict balance
The tree must always be balanced perfectly
Pretty good balance
Only allow a little out of balance
Adjust on access
Self-adjusting
Balancing Binary Search Trees
Many algorithms exist for keeping binary search trees balanced
Adelson-Velskii and Landis (AVL) trees (height-balanced trees)
Splay trees and other self-adjusting trees
B-trees and other multiway search trees
Perfect Balance
Want a complete tree after every operation
tree is full except possibly in the lower right
This is expensive
For example, insert 2 in the tree on the left and then rebuild as a complete tree
AVL - Good but not Perfect Balance
AVL trees are height-balanced binary search trees
Balance factor of a node
height(left subtree) - height(right subtree)
An AVL tree has balance factor calculated at every node
For every node, heights of left and right subtree can differ by no more than 1
Store current heights in each node
Height of an AVL Tree
N(h) = minimum number of nodes in an AVL tree of height h.
Basis
N(0) = 1, N(1) = 2
Induction
N(h) = N(h-1) + N(h-2) + 1
Solution (recall Fibonacci analysis)
N(h) > h ( 1.62)
Height of an AVL Tree
N(h) > h ( 1.62)
Suppose we have n nodes in an AVL tree of height h.
n > N(h) (because N(h) was the minimum)
n > h hence log n > h (relatively well balanced tree!!)
h < 1.44 log2n (i.e., Find takes O(logn))
Node Heights
Node Heights after Insert 7
Insert and Rotation in AVL Trees
Insert operation may cause balance factor to become 2 or –2 for some node
only nodes on the path from insertion point to root node have possibly changed in height
So after the Insert, go back up to the root node by node, updating heights
If a new balance factor is 2 or –2, adjust tree by rotation around the node
Single Rotation in an AVL Tree
Implementation
Single Rotation
Double Rotation
Implement Double Rotation in two lines.
Insertion in AVL Trees
Insert at the leaf (as for all BST)
only nodes on the path from insertion point to root node have possibly changed in height
So after the Insert, go back up to the root node by node, updating heights
If a new balance factor is 2 or –2, adjust tree by rotation around the node
Insert in BST
Insert in AVL trees
Example of Insertions in an A
The document discusses AVL trees, which are self-balancing binary search trees. It explains that AVL trees ensure that the heights of the left and right subtrees of every node differ by at most one. This balancing property is maintained during insertions and deletions by performing single or double rotations if the balancing factor becomes too large. The document provides examples of insertions that require single or double rotations to rebalance the tree. It also notes some pros and cons of using AVL trees compared to other search tree structures.
AVL trees are self-balancing binary search trees. They ensure that the height of the left and right subtrees of every node differ by no more than one. This balancing property is achieved through rotations during insertions and deletions. There are four types of rotations - single left, single right, double left, and double right - that are used to balance the tree as needed and maintain the height difference of no more than one.
This document discusses AVL trees, which are self-balancing binary search trees. It begins by explaining that binary search trees have O(log N) best case time for operations but can degrade to O(N) in the worst case if the tree becomes unbalanced. The document then introduces AVL trees, which maintain balance by ensuring that the heights of any node's two child subtrees differ by at most one. This guarantees search, insertion, and deletion operations take O(log N) time. The document explains the node height calculation and covers insertion and deletion algorithms in AVL trees through examples, including single and double rotations to rebalance the tree.
AVL trees are self-balancing binary search trees. They ensure that the heights of the two subtrees of any node differ by at most one. This balance property is maintained during insertions and deletions via rotations. There are two types of rotations needed - a single rotation to balance nodes where the imbalance is on one side, and a double rotation to balance nodes where the imbalance is on both sides. All operations on AVL trees, including rotations, take O(log n) time, making them efficient for search, insertion, and deletion.
Binary search tree.
Balancedand unbalanced BST.
Approaches to balancing trees.
Balancing binary search trees.
Perfect balance.
Avl trees 1962.
Avl good but both perfect balance.
Height of an AVL tree
Nood
CS-102 BT_24_3_14 Binary Tree Lectures.pdfssuser034ce1
The document discusses operations on heaps and leftist trees. Key points include:
- Heaps can be used to implement priority queues, with operations like MAX-HEAPIFY, BUILD-MAX-HEAP, and HEAPSORT taking O(log n) time on average.
- Leftist trees are a type of self-balancing binary search tree that supports priority queue operations like insertion and deletion in O(log n) time.
- Leftist trees have properties like shortest root-to-leaf paths being O(log n) that allow them to efficiently support priority queue operations through melding of subtrees.
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slackshyamraj55
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Fueling AI with Great Data with Airbyte WebinarZilliz
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Ocean lotus Threat actors project by John Sitima 2024 (1).pptxSitimaJohn
Ocean Lotus cyber threat actors represent a sophisticated, persistent, and politically motivated group that poses a significant risk to organizations and individuals in the Southeast Asian region. Their continuous evolution and adaptability underscore the need for robust cybersecurity measures and international cooperation to identify and mitigate the threats posed by such advanced persistent threat groups.
Programming Foundation Models with DSPy - Meetup SlidesZilliz
Prompting language models is hard, while programming language models is easy. In this talk, I will discuss the state-of-the-art framework DSPy for programming foundation models with its powerful optimizers and runtime constraint system.
Salesforce Integration for Bonterra Impact Management (fka Social Solutions A...Jeffrey Haguewood
Sidekick Solutions uses Bonterra Impact Management (fka Social Solutions Apricot) and automation solutions to integrate data for business workflows.
We believe integration and automation are essential to user experience and the promise of efficient work through technology. Automation is the critical ingredient to realizing that full vision. We develop integration products and services for Bonterra Case Management software to support the deployment of automations for a variety of use cases.
This video focuses on integration of Salesforce with Bonterra Impact Management.
Interested in deploying an integration with Salesforce for Bonterra Impact Management? Contact us at sales@sidekicksolutionsllc.com to discuss next steps.
How to Interpret Trends in the Kalyan Rajdhani Mix Chart.pdfChart Kalyan
A Mix Chart displays historical data of numbers in a graphical or tabular form. The Kalyan Rajdhani Mix Chart specifically shows the results of a sequence of numbers over different periods.
This presentation provides valuable insights into effective cost-saving techniques on AWS. Learn how to optimize your AWS resources by rightsizing, increasing elasticity, picking the right storage class, and choosing the best pricing model. Additionally, discover essential governance mechanisms to ensure continuous cost efficiency. Whether you are new to AWS or an experienced user, this presentation provides clear and practical tips to help you reduce your cloud costs and get the most out of your budget.
Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
Main news related to the CCS TSI 2023 (2023/1695)Jakub Marek
An English 🇬🇧 translation of a presentation to the speech I gave about the main changes brought by CCS TSI 2023 at the biggest Czech conference on Communications and signalling systems on Railways, which was held in Clarion Hotel Olomouc from 7th to 9th November 2023 (konferenceszt.cz). Attended by around 500 participants and 200 on-line followers.
The original Czech 🇨🇿 version of the presentation can be found here: https://www.slideshare.net/slideshow/hlavni-novinky-souvisejici-s-ccs-tsi-2023-2023-1695/269688092 .
The videorecording (in Czech) from the presentation is available here: https://youtu.be/WzjJWm4IyPk?si=SImb06tuXGb30BEH .
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away