This is an answer. Please summarize it A) Travelling salesman problem:The travelling salesman problem (TSP) is a computational issue in which the goal is to find the quickestdistance between a set of points and places. The points in the problem statement represent cities that asalesperson could visit. The objective of the distributor is to keep all travel costs and distance travelled to aminimum.TSP is always more concerned with finding the cheapest alternative than with finding the most efficient path.The large number of variables in TSP makes finding the quickest distance challenging, which makes estimated,quick, and cheap solutions all the more appealing.Application of TSP:In computer science, TSP is often used to determine the most effective path for data to travel betweennodes.• Identifying network or hardware optimization methods is one of the applications.Algorithm to solve TSP:The algorithm Minimum Spanning Tree is used to solve the TSP.There are approximate algorithms for solving TBS the problem. Only if the problem instance satisfies Triangle-Inequality do the approximate algorithms work. According to Triangle-Inequality for any given triangle, thesum of two sides of a triangle is always greater than the third side.We can build an approximation algorithm for TSP problem that returns a route that is never more than twicethe cost of an acceptable tour when the cost function satisfies the triangle inequality. The concept is to use aMinimum Spanning Tree (MST). The MST-based algorithm is shown below.Algorithm:1) Assume 1 is the beginning and ending point for the salesman.2) Using Prim's Algorithm, construct MST from 1 as the root.3) Add 1 to the list of vertices visited in the constructed MST's preorder walk. Let's take a look at the following scenario. The provided graph is the first diagram. The second diagram depictsMST with 1 as the root. MST has a preorder traversal of 1-2-4-3. The performance of this algorithm is 1-2-4-3-1,which is obtained by adding 1 at the end.The cost of the above algorithm's performance is never more than twice the cost of the best possible output.Let's look at how the above algorithm ensures this. To better understand this, let's describe the word"absolute walk." A complete walk lists all vertices when they are visited for the first time in preorder, as well aswhen they are returned after a subtree is visited for the first time in preorder. The above tree's complete walkwill be 1-2-1-4-1-3-1.The following are some important facts to prove the approximations.The best possible Traveling Salesman tour will never be less pricey than MST. (According to thedefinition, MST is a minimum cost tree that links all edges.)• A complete walk would cost at least twice more than MST (Every edge of MST is visited at-most twice)• The above algorithm produces a result that is less expensive than a complete walk. We print preorderwalk as output in the algorithm above. Two or more edges of a complete walk are replaced with a singleedge in preorder walk. 2-1 and 1-4, for example, are replaced by 1 edge 2-4. This is always valid if thegraph follows triangle inequality.from the above instruction, that we can conclude that the cost of output produced by the approximatealgorithm is never more than twice the cost of best possible solution. The output of this algorithm is 1-2-4-3-1.B) Time complexity of the algorithm:Time complexity of minimum spanning tree is o(v).

Question

This is an answer. Please summarize it A) Travelling salesman problem:The travelling salesman problem (TSP) is a computational issue in which the goal is to find the quickestdistance between a set of points and places. The points in the problem statement represent cities that asalesperson could visit. The objective of the distributor is to keep all travel costs and distance travelled to aminimum.TSP is always more concerned with finding the cheapest alternative than with finding the most efficient path.The large number of variables in TSP makes finding the quickest distance challenging, which makes estimated,quick, and cheap solutions all the more appealing.Application of TSP:In computer science, TSP is often used to determine the most effective path for data to travel betweennodes.• Identifying network or hardware optimization methods is one of the applications.Algorithm to solve TSP:The algorithm Minimum Spanning Tree is used to solve the TSP.There are approximate algorithms for solving TBS the problem. Only if the problem instance satisfies Triangle-Inequality do the approximate algorithms work. According to Triangle-Inequality for any given triangle, thesum of two sides of a triangle is always greater than the third side.We can build an approximation algorithm for TSP problem that returns a route that is never more than twicethe cost of an acceptable tour when the cost function satisfies the triangle inequality. The concept is to use aMinimum Spanning Tree (MST). The MST-based algorithm is shown below.Algorithm:1) Assume 1 is the beginning and ending point for the salesman.2) Using Prim's Algorithm, construct MST from 1 as the root.3) Add 1 to the list of vertices visited in the constructed MST's preorder walk. Let's take a look at the following scenario. The provided graph is the first diagram. The second diagram depictsMST with 1 as the root. MST has a preorder traversal of 1-2-4-3. The performance of this algorithm is 1-2-4-3-1,which is obtained by adding 1 at the end.The cost of the above algorithm's performance is never more than twice the cost of the best possible output.Let's look at how the above algorithm ensures this. To better understand this, let's describe the word&#34;absolute walk.&#34; A complete walk lists all vertices when they are visited for the first time in preorder, as well aswhen they are returned after a subtree is visited for the first time in preorder. The above tree's complete walkwill be 1-2-1-4-1-3-1.The following are some important facts to prove the approximations.The best possible Traveling Salesman tour will never be less pricey than MST. (According to thedefinition, MST is a minimum cost tree that links all edges.)• A complete walk would cost at least twice more than MST (Every edge of MST is visited at-most twice)• The above algorithm produces a result that is less expensive than a complete walk. We print preorderwalk as output in the algorithm above. Two or more edges of a complete walk are replaced with a singleedge in preorder walk. 2-1 and 1-4, for example, are replaced by 1 edge 2-4. This is always valid if thegraph follows triangle inequality.from the above instruction, that we can conclude that the cost of output produced by the approximatealgorithm is never more than twice the cost of best possible solution. The output of this algorithm is 1-2-4-3-1.B) Time complexity of the algorithm:Time complexity of minimum spanning tree is o(v).

Accepted Answer

Answered: Image /qna-images/answer/ef6c5989-e0bb-4045-8719-9c22ef32a314.jpg