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Topology Management

Algorithm:

The topological management is a system of law of a graph acyclic, ie has no cycles, which consists in organizing linearly or in list or ascending descending , a set of vertices in disorder, for which you must first start a "vertex father bone, a vertex without predecessors and after visiting their neighbors, after you have visited their cough overlooked, will now examine another vertex , and similarly identify all its neighbors, and so recursively until it has visited all vertices . Briefly not visit a vertex until all its predecessors have been visited.

After already visited all vertices the directed graph, are arranged in a list d either ascending or descending , as required, and settle on the basis time cost of vertices .

Example: This is a common example applied to everyday life as simple as dressing.

• Above each vertex shows the cost of time.
• Distance / Completion

• The algorithm us back a linked list with nodes in the graph, in descending order time finalization.

• Once ordered and topologically can see precedence of the tasks:

1. Get the shirt before the belt and jersey.
2. Get the pants before shoes and belt .
3. Put on socks before shoes.

Pseudocode:

1. For each vertex "or" that the graph belongs to:
2. The state "or" not visited, that algorithm is started .
3. The parent should be null, because it has no predecessors.
4. The time starts from 0, obviously that starts the algorithm.
5. Then, if the state = not visited then: It starts the topological management.
6. Visited The state will change to that and was visited and analyzed their s predecessors.
7. So we add a 1 at the time because it is so slow at the apex .
8. Then for each vertex adjacent do:
9. If Status = Not visited then:
10. 's father will now be the vertex , as is next in order.
11. When the state of vertex = Completed:
12. times are added together and this would be the total cost for the system.
13. result is inserted in the list sorting algorithm topological .

Asymptotic Analysis :

The analysis asymptotic algorithm of of topological management is costly to pursue vertex without predecessors, several times.

The solution would pre-calculate how many predecessors of each vertex , store data in a vector update whenever adding a new vertex to solution.

Time Cost:

• Initialization:

First loop: O (n) --- means that will depend on the number of vertices that has the graph.

Second loop: Examination of all edges.

O (a + n) --- For adjacency lists.

O (n ^ 2) --- For adjacency matrix.

• Main Loop:

O (a + n) --- For adjacency lists.

O (n ^ 2) --- For adjacency matrix.

Data Structures:

• linked list: For this algorithm topological management, linked lists are used as the management already completed is a simple linear list of edges connecting the same way it had before.
• Isomorphism: Something has to do with ismorfismo , but are not related and is acyclic graph algorithm allows align vertices, while keeping the links between each of the vertices , ie accommodates only priority, but retains its structure .
• Trees: can also be said that this related to trees as these contain nodes also called vertices, and the trees come in different forms of organization.
• depth Search (DFS ): The topological management needs search algorithm DFS because you need to apply to go exploring nodes, and finally reach a linear order .
  

Applications:

• can be applicable to the reprecentacion phase of a project, where vertices represent tasks and edges relations time to them.
• Evaluation phase a semantic compiler.
• In everyday life it could implement simple things such as organizing utility bills to pay, because these days come in different , and differ in price and maturity, and to apply this algorithm, could sort in order of priority due to paying cash them in order, but we spend and spend no money to pay.
• We also would serve to find any cycle in a graph and identify it.
• also to find a problem or defect in a topological order algorithm.
  

Self

Personally this project and the other four I have been very helpful since the majority of topics covered were new to me, and I realized that are of great usefully applied to everyday life in relation to the management of topological, since I left as teaching to cases in which I can apply this algorithm. learned that a particular task is a (s) by seniority and other (s) as a result of this task, and that ultimately after are linked to one another. In conclusion from now on things that have to do that you can implement this algorithm, I facilitate the task, and therefore time and effort.

any doubt or question you have to leave your comment and I will answer the earliest possible time.

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Extra Points "Dijkstra Algorithm"



Dijkstra Algorithm:

In this algorithm, algorithm is also called the "shortest path" as it is to find and take 1 of the " n " possible ways to reach the goal, the path chosen should be the lowest cost, and is a of time, effort, distance, etc, if it s possible these features together in one camnino, then the algorithm would be more optimal yet.

is common to represent this algorithm with a graph, as shown in the example:

• vertices are listed to identify each point .
• edges are listed according to their weight or cost.
• starts from a base vertex, or vertex output.
• After setting a goal.
• Then the algorithm begins to recognize all possible paths to choose, for starters.
• Take the path of least cost or shortest.
• So on until the final point or goal.
• The sum of the total cost of the algorithm, it is therefore

  , the most optimal, since chosen the path that suited him.

That helps me??

If we realize this algorithm is more common than their name appears, since we use very often, if we reflect on either side that we think carefully what is the best way get to that place, either on how to get faster, how to get more cheaply or how to reach with the least effort and if possible one that meets all these requirements.

But focusing on my career, this algorithm is way too utlil, because today we could say that time is money, that is, the time is worth much, then I is very useful dominate this algorithm to apply to my career development as there are companies that pay very well that the job done on time and that is quality, and this algorithm is a very good reference to build on this aspect.

Video

Explanation:

The video above shows a robot, which is a deterministic machine that first recognizes the place where you are, then, by a computer linked to the robot, you assign points or goals to reach, and the robot travels the path that best suits you in this case the most optimal.

Difference Between Stripper

Extra Points "Quick Sort"

Definition:

system Quick Sort Quick sort is an algorithm that not only helps us to organize a list of unorganized data, but also to optimize the time is engaged in undertaking this work, since it allows direct " n" elements in a running time O (n log n) , which is very efficient.

Algorithm:

this function management system in a disorganized data list to choose a pivot , which can be chosen at random, but I think more convenient, to choose one that is in the middle, then send all items with value less than the next pivot and all left over the right side:

< pivote =" Izquierda element

item> pivot = Right

After

starts sort of left all the elements under the pivot in a recursive manner until they are sorted and so the right side, to the point where both sides are and order and consequently the entire list.

Example: (Dar click the word example to see it)

• is an unordered list which is represented by bars of different sizes.
• The algorithm first chooses a pivot.
• After the rest of the items evaluates them, so those who are less than the pivot the left side and sent the biggest of the right side.
• ago each side the same thing to them recursivamnte in order.
• And in the end as each side of the pivot is ordered then we would be a list in order.

To serve me??

Well to me personally, this algorithm is very useful because it allows me to organize data so that I can enlist sort a list of priorities to do, which saves me time and effort, but I think my career is an algorithm that I will be very useful, since there are multiple applications for this, as do programs that I organize certain data, which depends on the data sorted to obtain a result and if this results in what I can get a better time for me would be very useful use, an example would be, that when entering certain data (in disorder) have to take the median (Statistics) , then here would come to apply this algorithm very well.

Application to my daily life:

I am working on some music tapes, Audio Scream, and although not creean this algorithm "Quick Sort" is applicable here, and the team apparatus with which we differ from each other in weight and size, and moved by a truck, we have sufficient equipment to deal with 3 events at once:

Team:

• Gennie 2 Elevators.
• 2 JBL Netherlands.
• 8 Cerwin-Vega Bass.
• Peripheral 3.
• tip type 2 structures (and accessories).
• 4 white lights (Cabezas Mobiles).
• 10 Lights Black Power Spot (Cabezas Mobiles).
• 2 Load Centers.
• Technobeam 10 Lights.
• Speakers Mackie 12.
• Dj Turntables 3 (2 and 1 Denon Mixer c / u).
• 3 smoke machines.
• 2 Laptops.
• 3 Interfaces.
• Wiring (Extensions, Canon cables, AC power , etc).

* The list of equipment is ordered to form to its weight and size *

So sometimes it is necessary to lower the truck only low or no more than a structure or anything but cable, etc. . so if you put everything into the truck disorganized, besides that would not fit well, the time to draw something specific, we would first seek more time where it is and then move everything to get him out before, with the Quick Sort algorithm we avoid all these mishaps, so that before team up to the truck, we could accommodate as the weight and size, a heavier and deeper and larger among the more light and small forward. This way we know that if we get a bass Cerwin-Vega would know that the bottom or if we get a rac of lights, this will be in the middle, so we would know to move or lower to reach the target.

Video

Explanation:
The video shows the comparison of the method vs. Quick Sort. Bubble Sort (Bubble Land) both are sorting algorithms, but clearly shows that the Quick Sort is more efficient, ie it is faster and more functional, as the Quick Sort algorithm does the same task in fewer steps so sooner. In conclucion the Quick Sort algorithm is optimized in ordenaminento.

School Event Invitation Writing

5 Hamilton Road Project Presentation




Camino happens exactly once by each of the vertices of the graph. (You can not use all edges
).

In the mathematical field of graph theory, a Hamiltonian path in a graph is a path, a succession of adjacent edges, which visits all vertices of the graph once. If also the last vertex visited is adjacent to the first, the path is a Hamiltonian cycle.

The problem of finding a cycle (or path) Hamiltonian in an arbitrary graph is known to be NP-complete.

Roads and Hamiltonian cycles were named after William Rowan Hamilton, who invented the game of Hamilton, will release a toy that involves finding a Hamiltonian cycle on the edges of a graph of a dodecahedron. Hamilton solved this problem by using quaternions, but this solution does not generalize to all graphs.

A Hamiltonian path is a path that visits each vertex exactly once. A graph containing a Hamiltonian path is called a Hamiltonian cycle or Hamiltonian circuit if it is a cycle that visits each vertex exactly once (except the apex of which party and which arrives). A graph containing a Hamiltonian cycle is called a Hamiltonian graph.

can also say that Hamiltonian graphs are when they meet:

-Hamiltonian-circuit must be related, must be closed.

These concepts can be extended to directed graphs. Examples




The complete graph with more than 2 vertices is Hamiltonian.
All graphs are Hamiltonian cycles.
All Platonic solids, considered graphs are Hamiltonian.


Any Hamiltonian cycle can be converted into a Hamiltonian path by removing any of its vertices, but a Hamiltonian path in the cycle can be extended only if the end vertices are adjacent.


Bondy-Chvatal theorem

The best characterization of Hamiltonian graphs was given in 1972 by the Bondy-Chvatal theorem which generalizes the results previously found by GA Dirac. It basically says that a graph is Hamiltonian if there are enough edges. First we must define what is the lock of a graph.

Given a graph G with n vertices, the lock (cl (G)) is uniquely constructed from G by adding every edge uv if nonadjacent pair of vertices u and v holds that degree (v) + degree (u) ≥ n



A graph is Hamiltonian if and only if the lock graph is Hamiltonian.
Bondy-Chvatal (1972)


Like all complete graphs are Hamiltonian, all graphs which are Hamiltonian lock is complete. This result is based on the theorems of Dirac and Ore.


A graph with n vertices (n> 3) is Hamiltonian if every vertex has degree greater than or equal to n / 2.
Dirac (1952)


A graph with n vertices (n> 3) is Hamiltonian if the sum of the degrees of 2 non-adjacent vertices is greater than or equal to n.
Ore (1960)




However, there is a previous result of all these theorems.


A graph with n vertices (n ≥ 2) is Hamiltonian if the sum of the degrees of 2 vertices is greater than or equal to n-1. L. Redei
(1934)



As you can see, this theorem requested more than the previous hypothesis as the property of grade must be met for every vertex in the graph.


also spoken Hamiltonian path if not imposed return to the starting point, like a museum with a single door. For example, a horse can go all the squares of a chess board without passing twice for the same: it is a Hamiltonian path. Example of a Hamiltonian cycle in the graph of the dodecahedron.

Today, there are no known general methods for finding a Hamiltonian cycle in polynomial time, being force search gross of all possible paths or other methods too expensive. There are, however, methods to eliminate the existence of Hamiltonian cycles and paths in graphs small.

The problem of determining the existence of Hamiltonian cycles, enter all the NP-complete.

In computational complexity theory, the complexity class NP-complete is the subset of decision problems in NP such that any problem in NP can be reduced in each of the NP-complete problems. You could say that the NP-complete problems are NP hard problems and very likely not part of the complexity class P.