9 Questions
What is the goal of the Traveling Salesman Problem (TSP)?
To find a tour of minimum cost visiting each city exactly once and finishing at the starting city
What type of graph can be used to model the cities in the TSP?
Complete graph of n vertices
What is the approximate algorithm that can be used for the TSP if the cost function satisfies the triangle inequality?
Approx-TSP using a minimum spanning tree (MST)
What happens if an edge is removed from the Hamiltonian cycle in the TSP?
The tour becomes a spanning tree
What complexity class is the Traveling Salesman Problem (TSP) categorized under?
NPC (Non-deterministic Polynomial time Complete)
What is a live node in the context of branch and bound?
A node that has been generated but its children are not yet generated
What does FIFO branch and bound search follow?
BFS-like method
What is an E node in the context of branch and bound?
A node that is being explored at the moment
What is a dead node in the context of branch and bound?
A node that is not being generated or explored any further
Study Notes
Traveling Salesman Problem (TSP)
- The goal of the TSP is to find the shortest possible tour that visits each city exactly once and returns to the starting city.
Graph Modeling
- The cities in the TSP can be modeled using a weighted complete graph.
Approximation Algorithm
- If the cost function satisfies the triangle inequality, an approximate algorithm that can be used for the TSP is the Christofides algorithm.
Hamiltonian Cycle
- If an edge is removed from the Hamiltonian cycle in the TSP, the result is no longer a Hamiltonian cycle.
Complexity Class
- The Traveling Salesman Problem (TSP) is categorized under the complexity class NP-hard.
Branch and Bound
Node Types
- A live node in the context of branch and bound is a node that has not been pruned and is still a candidate for further exploration.
- FIFO branch and bound search follows a first-in, first-out (FIFO) ordering of nodes.
- An E node in the context of branch and bound is an unfathomed node.
- A dead node in the context of branch and bound is a node that has been pruned and is not considered further.
Test your knowledge of the traveling salesman problem in this quiz. Explore the concepts of finding the minimum cost Hamiltonian cycle while visiting each city exactly once. Challenge yourself with questions on city connections and tour optimization in this classic optimization problem.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
