Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 35.2, Problem 5E
Program Plan Intro
To show that the optimal tour never crosses itself in a travelling salesmen problem of a given vertices with Euclidean distance.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
If a Genetic Algorithm only finds local optimal solutions, what should be done to find a better one globally?
Consider a graph G in the following
Find a path from a to g in the graph G using each search strategy of depth-first search, breadth-first search, least-cost search, best-first search, and A* search. Is the returned solution path an optimal one?
Use proof by induction for the Shortest Path Distance algorithm of graph G where u and in S(u,v) cannot = infinity on graph G
Chapter 35 Solutions
Introduction to Algorithms
Ch. 35.1 - Prob. 1ECh. 35.1 - Prob. 2ECh. 35.1 - Prob. 3ECh. 35.1 - Prob. 4ECh. 35.1 - Prob. 5ECh. 35.2 - Prob. 1ECh. 35.2 - Prob. 2ECh. 35.2 - Prob. 3ECh. 35.2 - Prob. 4ECh. 35.2 - Prob. 5E
Ch. 35.3 - Prob. 1ECh. 35.3 - Prob. 2ECh. 35.3 - Prob. 3ECh. 35.3 - Prob. 4ECh. 35.3 - Prob. 5ECh. 35.4 - Prob. 1ECh. 35.4 - Prob. 2ECh. 35.4 - Prob. 3ECh. 35.4 - Prob. 4ECh. 35.5 - Prob. 1ECh. 35.5 - Prob. 2ECh. 35.5 - Prob. 3ECh. 35.5 - Prob. 4ECh. 35.5 - Prob. 5ECh. 35 - Prob. 1PCh. 35 - Prob. 2PCh. 35 - Prob. 3PCh. 35 - Prob. 4PCh. 35 - Prob. 5PCh. 35 - Prob. 6PCh. 35 - Prob. 7P
Knowledge Booster
Similar questions
- Find the path from S to G using A* algorithm. Is it optimal ?arrow_forwardWith a weighted digraph, determine the monotonic shortest path between s and each of the other nodes. The path is monotonic if the weight of each edge along a route is strictly growing or strictly decreasing. The path ought to be easy to follow.(No vertices are repeated). Hint: To identify the optimal path, first relax the edges in ascending order; then relax the edges in descending order.arrow_forwardA tourist representative problem has the following questions: “Given a list of cities and the distances between each pair countries. What is the shortest possible route that visits each country exactly once and returns to the origin country? What is the possible route if the Greedy Algorithm is used? The table below lists down the distances (kilometers) between countries having direct routes as well as the corresponding distances between them. Show your graph and solutions. Manila Hongkong Sydney London New York Los Angeles California Manila - 1116 6260 10760 11740 13700 Hongkong 1116 - 7400 9646 12960 11656 Sydney 6260 7400 - 17020 16020 12078 London 10760 9646 17020 - 5585 8760 New York 11740 12960 16020 5585 - 3944 Los Angeles California 13700 11656 12078 8760 3944 -arrow_forward
- Let G be this weighted undirected graph, containing 7 vertices and 11 edges. For each of the 10 edges that do not appear (AC, AE, AF, AG, BF, BG, CD, CF, CG, DG), assign a weight of 1000. It is easy to see that the optimal TSP tour has total cost 51. Generate an approximate TSP tour using the algorithm, and calculate the total cost of your solution. Explain why your solution is not a 2-approximation.arrow_forwardTravelling Salesman Problem Statement: Given n cities with known distances betweeneach pair, find the shortest tour that passes through all the cities exactly once before returning tothe starting city. On the following graph:Use Exhaustive Search to find the shortest path, starting from a, and returning back to a.Show all paths/tour that will be taken into consideration in this approach, compute costs for eachtour involved, and find the most optimal path/tour from your computed costs. (Hint: Optimal path:minimum cost)arrow_forwardSolve the six city TSP by finding the approximate tour. Describe your algorithm. Prove that the cost of the approximate tour is no more than twice the cost of optimal tourarrow_forward
- Demonstrate that the decision problem variant is NP-complete; Exists, given a graph G and a cost objective c, a spanning tree where the maximum payment of any vertex does not exceed c?arrow_forwardWrite a pseudo-code for the 2-opt heuristic algorithm. The input to the algorithm should be a feasible solution to a TSP instance along with the specification of the origin node and the distance matrix as well the tour length of the corresponding feasible solution.arrow_forwardConsider the navigation problem shown in Figure 1. The number next to each edge is the cost of the performing the action corresponding to that edge. You start from A and your goal is to get to F. List the order in which nodes are expanded, which nodes are added to the fringe and which states are added to the closed set when performing Graph Search using: breadth-first search. depth-first search. iterative deepening search. uniform cost searcharrow_forward
- Consider the following search problem, represented as a graph. A is the start state and G is the goal. The number beside each edge is the transition cost. Find the cost of the path to the goal using Depth First Search with full duplicate detection, which explorer Children in lexicographical order.arrow_forwardSuppose that you want to get from vertex s to vertex t in an unweighted graph G = (V, E), but you would like to stop by vertex u if it is possible to do so without increasing the length of your path by more than a factor of α. Describe an efficient algorithm that would determine an optimal s-t path given your preference for stopping at u along the way if doing so is not prohibitively costly. (It should either return the shortest path from s to t or the shortest path from s to t containing u, depending on the situation)arrow_forwardSuppose we have the following undirected graph, and we know that the two bolded edges (B-E and G-E) constitute the global minimum cut of the graph. 1. If we run the Karger’s algorithm for just one time to find the global minimum cut, what is the probability for the algorithm to find the minimum cut correctly? Please show your reasoning process. 2. How many times do we need to run the Karger’s algorithm if we want to guarantee that the probability of success is greater than or equal to 0.95, by “success” we mean that there is at least one time the Karger’s algorithm correctly found the minimum cut. Please show your reasoning process. [You do not have to work out the exact value of a logarithm]arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole