In the field of computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering.
For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks.
A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a topological ordering of any DAG in linear time.
A topological ordering of a directed acyclic graph: every edge goes from earlier in the ordering (upper left) to later in the ordering (lower right). A directed graph is acyclic if and only if it has a topological ordering.
The graph shown above has many valid topological sorts, including:
The canonical application of topological sorting is in scheduling a sequence of jobs or tasks based on their dependencies. The jobs are represented by vertices, and there is an edge from x to y if job x must be completed before job y can be started (for example, when washing clothes, the washing machine must finish before we put the clothes in the dryer). Then, a topological sort gives an order in which to perform the jobs.
Other application is dependency resolution. Each vertex is a package and each edge is a dependency of package a on package 'b'. Then topological sorting will provide a sequence of installing dependencies in a way that every next dependency has its dependent packages to be installed in prior.
If you accumulate data on which you base your decision-making as an organization, you should probably think about your data architecture and possible best practices.
If you accumulate data on which you base your decision-making as an organization, you most probably need to think about your data architecture and consider possible best practices. Gaining a competitive edge, remaining customer-centric to the greatest extent possible, and streamlining processes to get on-the-button outcomes can all be traced back to an organization’s capacity to build a future-ready data architecture.
In what follows, we offer a short overview of the overarching capabilities of data architecture. These include user-centricity, elasticity, robustness, and the capacity to ensure the seamless flow of data at all times. Added to these are automation enablement, plus security and data governance considerations. These points from our checklist for what we perceive to be an anticipatory analytics ecosystem.
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Hello! Today I’ll be going over graphs . These data structures are the most widely used on the web, given the countless forms that a graph can organize values or even the data structures that can be made from them. In fact, the worldwide web itself can be represented as a graph. Let’s jump right into it!
In a previous blog post we talked about how to apply the Breadth First Search algorithm to the graph data structure. Today, let’s figure out how Depth First Search (DFS) works.
DFS is one of the fundamental algorithms used to search nodes and edges in a graph. It’s a form of a traversal algorithm.
Just a reminder, this is how our graph looks:
And this is our adjacency matrix (read here about adjacency matrix representation):
Based on the name we can assume that BFS focuses on the depth of the graph. The search starts at some root node and it keeps searching as far as possible each branch before backtracking.
Our task is to write an algorithm that explores routes as deep as possible before going back and exploring other routes. Let’s see how we can do it.
A week ago we learned about graph data structure. Today we will talk about how we can work with graphs. We will try to find distances between two nodes in a graph. This is one of the main uses of graphs and it’s called graph traversal. There are two main graph algorithms Breadth First Search (BFS) and Depth First Search (DFS) and today we will talk about BFS.
This is how our graph looks like:
Breadth First Search
In our example we will work with an adjacency matrix. This is how matrix represents graph above:
We will start with an input node, then visit all its neighbors which is one edge away. And then visit all their neighbors. Point is to determine how close the node is to the root node.
Function which we will write in a moment will return an object with key value pairs where key will represent node and value how far this node is from the root.
First we will loop over the adjacency matrix (2D array), create as many key value pairs as many nodes we have on the graph. Initially we will assign distance to the infinity which represents lack of connection between the nodes.
The opportunities big data offers also come with very real challenges that many organizations are facing today. Often, it’s finding the most cost-effective, scalable way to store and process boundless volumes of data in multiple formats that come from a growing number of sources. Then organizations need the analytical capabilities and flexibility to turn this data into insights that can meet their specific business objectives.
This Refcard dives into how a data lake helps tackle these challenges at both ends — from its enhanced architecture that’s designed for efficient data ingestion, storage, and management to its advanced analytics functionality and performance flexibility. You’ll also explore key benefits and common use cases.
As technology continues to evolve with new data sources, such as IoT sensors and social media churning out large volumes of data, there has never been a better time to discuss the possibilities and challenges of managing such data for varying analytical insights. In this Refcard, we dig deep into how data lakes solve the problem of storing and processing enormous amounts of data. While doing so, we also explore the benefits of data lakes, their use cases, and how they differ from data warehouses (DWHs).
This is a preview of the Getting Started With Data Lakes Refcard. To read the entire Refcard, please download the PDF from the link above.
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