Algorithms and flowcharts are two different tools used for creating new programs, especially in computer programming. An algorithm is a step-by-step analysis of the process, while a flowchart explains the steps of a program in a graphical way.

To write a logical step-by-step method to solve the problem is called the algorithm; in other words, an algorithm is a procedure for solving problems.

In order to solve a mathematical or computer problem, this is the first step in the process. An algorithm includes calculations, reasoning, and data processing.

Algorithms can be presented by natural languages, pseudocode, and flowcharts, etc. A flowchart is the graphical or pictorial representation of an algorithm with the help of different symbols, shapes, and arrows to demonstrate a process or a program. With algorithms, we can easily understand a program. The main purpose of using a flowchart is to analyze different methods. Several standard symbols are applied in a flowchart:. The symbols above represent different parts of a flowchart.

The process in a flowchart can be expressed through boxes and arrows with different sizes and colors. In a flowchart, we can easily highlight certain elements and the relationships between each part. If you compare a flowchart to a movie, then an algorithm is the story of that movie. In other words, an algorithm is the core of a flowchart.

Actually, in the field of computer programming, there are many differences between algorithm and flowchart regarding various aspects, such as the accuracy, the way they display, and the way people feel about them. Below is a table illustrating the differences between them in detail.

It is not surprising that algorithms are widely used in computer programming. However, it can be applied to solving mathematical problems and even in everyday life.

Here comes a question: how many types of algorithms? According to Dr. As a result, he has listed 32 crucial algorithms in computer science. Despite the complexity of algorithms, we can generally divide algorithms into six fundamental types based on their function. It refers to a way to solve problems by repeatedly breaking down the problem into sub-problems of the same kind. The classic example of using a recursive algorithm to solve problems is the Tower of Hanoi.

Traditionally, the divide and conquer algorithm consists of two parts: 1. Developed by Richard Bellman in the s, the dynamic programming algorithm is generally used for optimization problems.

In this type of algorithm, past results are collected for future use. Like the divide and conquer algorithm, a dynamic programming algorithm simplifies a complex problem by breaking it down into some simple sub-problems.

### David Eppstein - Publications

This is another way of solving optimization problems â€” greedy algorithm. It refers to always finding the best solution in every step instead of considering the overall optimality.

That is to say, what he has done is just at a local optimum. Due to the limitations of the greedy algorithm, it has to be noted that the key to choosing a greedy algorithm is whether to consider any consequences in the future. The brute force algorithm is a simple and straightforward solution to the problem, generally based on the description of the problem and the definition of the concept involved.

You can also use "just do it! In short, a brute force algorithm is considered as one of the simplest algorithms, which iterates all possibilities and ends up with a satisfactory solution. Based on a depth-first recursive search, the backtracking algorithm focusing on finding the solution to the problem during the enumeration-like searching process.In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges.

We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. It is hard to underestimate the importance of the graph coloring problem in computer science and combinatorics. The problem is certainly among the most studied questions in those fields, and countless applications and variants have been tackled since it was first posed for the special case of maps in the mid-nineteenth century.

In this setting, an algorithmic graph problem is modelled in the dynamic environment as follows. There is an online sequence of insertion and deletion of edges or vertices, and our goal is to maintain the solution of the graph problem after each update.

A trivial way to maintain this solution is to run the best static algorithm for this problem after each update; however, this is clearly not optimal. A dynamic graph algorithm seeks to maintain some clever data structure for the underlying problem such that the time taken to update the solution is much smaller than that of the best static algorithm.

In this paper, we study the problem of maintaining a coloring in a dynamic graph undergoing insertions and deletions of both vertices and edges. We focus on the combinatorial aspect of the problemâ€”the trade-off between the number of colors used versus the number of recolorings per update. We present a strong general lower bound and two simple algorithms that provide complementary trade-offs.

A recoloring algorithm is an algorithm that maintains a proper coloring of a simple graph while that graph undergoes a sequence of updates. Each update adds or removes either an edge or a vertex with a set of incident edges. For example, an algorithm that computes the optimal coloring after every update is 1-competitive, but may recolor every vertex for every update.

At the other extreme, we can give each vertex a unique color, resulting in a linear competitive factor for an algorithm that re colors at most 1 vertex per update.

In Sect.

**13. Breadth-First Search (BFS)**

Using standard techniques, the algorithms can be made sensitive to the current instead of the maximum number of vertices in the graph. In addition, we present de-amortized versions of both algorithms in Sect. These de-amortized versions have the same competitive ratio and recolorings per update as the amortized versions. We provide lower bounds in Sect. To allow us to focus on the combinatorial aspects, we assume that we have access to an algorithm that, at any time, can color the current graph or an induced subgraph using few colors.

Still, this assumption is not as strong as it sounds. Dynamic graph coloring. The problem of maintaining a coloring of a graph that evolves over time has been tackled before, but to our knowledge, only from the points of view of heuristics and experimental results. In that problem, vertices lose their color, and the algorithm is asked to recolor them.

Online graph coloring. The online version of the problem is closely related to our setting, except that most variants of the online problem only allow the coloring of new vertices, which then cannot be recolored later.

They show their bound holds even when the model is relaxed to allow a constant fraction of the vertices to change color over the whole sequence. This, however, does not contradict our results. We allow our algorithms to recolor all vertices at some point, but we bound only the number of recolorings per update.

Dynamic graphs. Several techniques have been used for the maintenance of other structures in dynamic graphs, such as spanning trees, transitive closure, and shortest paths. Surveys by Demetrescu et al. Data structure dynamization. In this section, we describe the intuition behind the two complementary recoloring algorithms presented in this paper: the small and the large bucket algorithms.

## Dynamic Programming and Graph Algorithms in Computer Vision*

Both algorithms partition the vertices of the graph into a set of buckets. These colors are used to properly color the subgraph induced by the vertices the bucket contains.

This guarantees that the entire graph is always properly colored. This causes it to use more colors, but fewer recolorings per operation. Here n denotes the current number of vertices.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Incremental variants of these algorithms have a variety of important practical applications.

By "incremental" I mean those graph algorithms that can compute small changes to their outputs given small changes e. For example, a garbage collector accumulating the subgraph of heap allocated blocks reachable from the global roots. However, I do not recall seeing the subject of incremental graph algorithms discussed outside domain-specific literature e.

Richard Jones' new book on GC. Where can I find information on incremental graph algorithms or, for that matter, incremental algorithms in general? There's a survey article by Eppstein, Galil, and Italiano from They would describe what you're looking for as "fully dynamic algorithms"; "partially dynamic algorithms" are divided into "incremental algorithms", which allow only insertions, and "decremental algorithms", which allow only deletions.

### Fully Dynamic Graph Algorithms and Their Data Structures (thesis)

Beyond that, I suspect you're going to have to read the research literature â€” there are only a handful of researchers who work on dynamic graph algorithms. You should be able to find articles by examining the papers that cite the survey. Learn more. Incremental graph algorithms Ask Question. Asked 8 years, 11 months ago. Active 6 years, 7 months ago. Viewed 1k times.

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## The Connected Components Algorithm

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Latest commit. Git stats 3 commits. Failed to load latest commit information. View code. For both incremental and decremental case, a single data structure - Euler Tour Tree is maintained on a spanning forest of the graph.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Artificial Intelligence Stack Exchange is a question and answer site for people interested in conceptual questions about life and challenges in a world where "cognitive" functions can be mimicked in purely digital environment.

It only takes a minute to sign up. However, there seems to be a lack of resource to aid in understanding Dynamic Computational Graphs. The advantage of Dynamic Computational Graphs appears to include the ability to adapt to a varying quantities in input data. It seems like there may be automatic selection of the number of layers, the number of neurons in each layer, the activation function, and other NN parameters, depending on each input set instance during the training.

Is this an accurate characterization? What are the advantages of dynamic models over static models? Is that why DCGs are receiving much attention? In summary, what are DCGs and what are the pros and cons their use?

A Dynamic Computational Graph is a mutable system represented as a directed graph of data flow between operations. It can be visualized as shapes containing text connected by arrows, whereby the vertices shapes represent operations on the data flowing along the edges arrows. Note that such a graph defines dependencies in the data flow but not necessarily the temporal order of the application of operations, which can become ambiguous in the retention of state in vertices or cycles in the graph without an additional mechanism to specify temporal precedence.

A Dynamic Computational Graph framework is a system of libraries, interfaces, and components that provide a flexible, programmatic, run time interface that facilitates the construction and modification of systems by connecting a finite but perhaps extensible set of operations. PyTorch is the integration of the Torch framework with the Python language and data structuring.

Torch competes with Theano, TensorFlow, and other dynamic computational system construction frameworks. One of the components that can be used to construct a computational system is an element designed to be interconnected to create neural networks.

The availability of these supports the construction deep learning and back propagating neural networks. A wide variety of other systems involving the assembly of components that work with potentially multidimensional data in arbitrarily defined computational structures can also be constructed. The data can be scalar values, such as floating point numbers, integers, or strings, or orthogonal aggregations of these, such as vectors, matrices, cubes, or hyper-cubes.

The operations on the generalization of these data forms are discrete tensors and the structures created from the assembly of tensor operations into working systems are data flows. Dynamic Computational Graphs are not a particularly new concept, even though the term is relatively new. Nonetheless, the question correctly states that there are few well written resources available other than code examples from which one can learn the overall concept surrounding their emergence and use. One possible point of reference for beginning to understand DCGs is the Command design pattern which is one of the many design patterns popularized by the proponents of object oriented design.

The Command design pattern considers operations as computation units the details of which are hidden from the command objects that trigger them.GraphStream is hosted by the University of Le Havre. This algorithm computes connected components for a given graph. Connected components are the set of its connected subgraphs. Two nodes belong to the same connected component when there exists a path without considering the direction of the edges between them.

Therefore, the algorithm does not consider the direction of edges. The number of connected components of an undirected graph is equal to the number of connected components of the same directed graph. For the initial computation, let n be the number of nodes, then the complexity is 0 n.

This algorithm tries to handle the dynamics of the graph, trying not to recompute all from scratch at each change kind of re-optimization. In this way, each instance of the algorithm is registered as a graph sink. Each change in the graph topology may affect the algorithm.

To start using the algorithm, you first need an instance of org. Graphthen you only have to instantiate the algorithm class. Whether you specify a reference to the graph in the constructor or you set it with the init Graph method. The computation of the algorithm starts only when the graph is specified with the init Graph method or with the appropriated constructor. In case of a static graph, you may call the compute method. In case of a dynamic graph, the algorithm will compute itself automatically when an event node or edge added or removed occurs.

Finally you may ask the algorithm for the number of connected components at any moment with a call to the getConnectedComponentsCount method. It is possible to get rid of connected components belong a size threshold when counting the overall number of connected components.

It is also possible to define a ceiling size for the connected component. Above that size ceiling, connected components will not be counted. You can tag each node with an integer that identifies the component it pertains to using setCountAttribute String.

The argument of this method is an arbitrary name that will be used as attribute on each node of the graph. The value of this attribute will be an integer counting from zero that is different for each connected component. The getGiantComponent method gives you a list of nodes belonging to the biggest connected component of the graph.Graph Theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

Did you know, almost all the problems of planet Earth can be converted into problems of Roads and Cities, and solved? Graph Theory was invented many years ago, even before the invention of computer. Since then, people have come to realize that if we can convert any problem to this City-Road problem, we can solve it easily by Graph Theory. Graph Theory has many applications.

One of the most common application is to find the shortest distance between one city to another. We all know that to reach your PC, this web-page had to travel many routers from the server. Graph Theory helps it to find out the routers that needed to be crossed.

During war, which street needs to be bombarded to disconnect the capital city from others, that too can be found out using Graph Theory. Let's say, we have 6 cities. We mark them as 1, 2, 3, 4, 5, 6. Now we connect the cities that have roads between each other. This is a simple graph where some cities are shown with the roads that are connecting them.

Graph is simply a connection of these nodes and edges. A node can represent a lot of things. In some graphs, nodes represent cities, some represent airports, some represent a square in a chessboard. Edge represents the relation between each nodes. That relation can be the time to go from one airport to another, the moves of a knight from one square to all the other squares etc. In simple words, a Node represents any object and Edge represents the relation between two objects. If a node A shares an edge with node Bthen B is considered to be adjacent to A.

In other words, if two nodes are directly connected, they are called adjacent nodes. One node can have multiple adjacent nodes. In directed graphs, the edges have direction signs on one side, that means the edges are Unidirectional. On the other hand, the edges of undirected graphs have direction signs on both sides, that means they are Bidirectional.

Usually undirected graphs are represented with no signs on the either sides of the edges. Let's assume there is a party going on. The people in the party are represented by nodes and there is an edge between two people if they shake hands. Then this graph is undirected because any person A shake hands with person B if and only if B also shakes hands with A. In contrast, if the edges from a person A to another person B corresponds to A 's admiring Bthen this graph is directed, because admiration is not necessarily reciprocated.

The former type of graph is called an undirected graph and the edges are called undirected edges while the latter type of graph is called a directed graph and the edges are called directed edges.

A weighted graph is a graph in which a number the weight is assigned to each edge. Such weights might represent for example costs, lengths or capacities, depending on the problem at hand. An unweighted graph is simply the opposite. We assume that, the weight of all the edges are same presumably 1. A path represents a way of going from one node to another. It consists of sequence of edges.