Binary heap

Summary

A binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort. A binary heap is defined as a binary tree with two additional constraints: *Shape property: a binary heap is a complete binary tree; that is, all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right. *Heap property: the key stored in each node is either greater than or equal to (≥) or less than or equal to (≤) the keys in the node's children, according to some total order. Heaps where the parent key is greater than or equal to (≥) the child keys are called max-heaps; those where it is less than or equal to (≤) are called min-heaps. Efficient (logarithmic time) algorithms are known for the two operations needed to implement

Official source

https://en.wikipedia.org/wiki/Binary_heap

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (4)

Unsupervised Robust Nonparametric Learning Of Hidden Community Properties

Akhilesh Deepak Gotmare, Martin Jaggi, Mikhail Langovoy

We consider learning of fundamental properties of communities in large noisy networks, in the prototypical situation where the nodes or users are split into two classes according to a binary property, e.g., according to their opinions or preferences on a topic. For learning these properties, we propose a nonparametric, unsupervised, and scalable graph scan procedure that is, in addition, robust against a class of powerful adversaries. In our setup, one of the communities can fall under the influence of a knowledgeable adversarial leader, who knows the full network structure, has unlimited computational resources and can completely foresee our planned actions on the network. We prove strong consistency of our results in this setup with minimal assumptions. In particular, the learning procedure estimates the baseline activity of normal users asymptotically correctly with probability 1; the only assumption being the existence of a single implicit community of asymptotically negligible logarithmic size. We provide experiments on real and synthetic data to illustrate the performance of our method, including examples with adversaries.

2019

Heterogeneous Gossip

Davide Frey, Rachid Guerraoui, Anne-Marie Kermarrec, Maxime Monod

Gossip-based information dissemination protocols are considered easy to deploy, scalable and resilient to network dynamics. Load-balancing is inherent in these protocols as the dissemination work is evenly spread among all nodes. Yet, large-scale distributed systems are usually heterogeneous with respect to network capabilities such as bandwidth. In practice, a blind load-balancing strategy might significantly hamper the performance of the gossip dissemination. This paper presents HEAP, HEterogeneity-Aware gossip Protocol, where nodes dynamically adapt their contribution to the gossip dissemination according to their bandwidth capabilities. Using a continuous, itself gossip-based, approximation of relative bandwidth capabilities, HEAP dynamically leverages the most capable nodes by increasing their fanout, while decreasing by the same proportion that of less capable nodes. HEAP preserves the simple and proactive (churn adaptation) nature of gossip, while significantly improving its effectiveness. We extensively evaluate HEAP in the context of a video streaming application on a testbed of 270 PlanetLab nodes. Our results show that HEAP significantly improves the quality of the streaming over standard homogeneous gossip protocols, especially when the stream rate is close to the average available bandwidth.

2009

Gossiping Capabilities

Davide Frey, Rachid Guerraoui, Anne-Marie Kermarrec, Maxime Monod

Gossip-based protocols are now acknowledged as a sound basis to implement collaborative high-bandwidth content dissemination: content location is disseminated through gossip, the actual contents being subsequently pulled. In this paper, we present HEAP, HEterogeneity-Aware Gossip Protocol, where nodes dynamically adjust their contribution to gossip dissemination according to their capabilities. Using a continuous, itself gossip-based, approximation of relative capabilities, HEAP dynamically leverages the most capable nodes by (a) increasing their fanouts (while decreasing by the same proportion those of less capable nodes) and (b) employing them early in the dissemination chain. These, on the other hand, have an incentive to take on additional load as being first in the chain improves their perceived quality. A lightweight accountability mechanism is used to track selfish nodes that might declare a high capability in order to augment their perceived quality without contributing accordingly. We evaluate HEAP in the context of a video streaming application on a 236 PlanetLab nodes testbed. Our results shows that HEAP improves the quality of the streaming by 25% over a standard gossip protocol without impacting the average load or availability of the system.

2008

Related people

No results

Related units

No results

Related concepts (10)

Heap (data structure)

In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is a parent node of C, then the key (the value) of P

Sorting algorithm

In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order and lexicographical order, and either ascendin

Binary tree

In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the and the . A recursive definition usin

Related courses (2)

CS-250: Algorithms

The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, sorting and searching, and graph algorithms.

MATH-458: Programming concepts in scientific computing

The aim of this course is to provide the background in scientific computing. The class includes a brief introduction to basic programming in c++, it then focus on object oriented programming and c++ specific programming techniques.

Related lectures (11)

Related lectures