Podcast
Questions and Answers
What is the goal of the Traveling Salesman Problem (TSP)?
What is the goal of the Traveling Salesman Problem (TSP)?
- To visit each city multiple times to maximize sales
- To find the shortest path between two specific cities
- To find the most efficient route between all cities
- To find a tour of minimum cost visiting each city exactly once and finishing at the starting city (correct)
What type of graph can be used to model the cities in the TSP?
What type of graph can be used to model the cities in the TSP?
- Binary tree
- Directed graph with weighted edges
- Cyclic graph
- Complete graph of n vertices (correct)
What is the approximate algorithm that can be used for the TSP if the cost function satisfies the triangle inequality?
What is the approximate algorithm that can be used for the TSP if the cost function satisfies the triangle inequality?
- Bellman-Ford algorithm
- Depth-first search algorithm
- Greedy algorithm
- Approx-TSP using a minimum spanning tree (MST) (correct)
What happens if an edge is removed from the Hamiltonian cycle in the TSP?
What happens if an edge is removed from the Hamiltonian cycle in the TSP?
What complexity class is the Traveling Salesman Problem (TSP) categorized under?
What complexity class is the Traveling Salesman Problem (TSP) categorized under?
What is a live node in the context of branch and bound?
What is a live node in the context of branch and bound?
What does FIFO branch and bound search follow?
What does FIFO branch and bound search follow?
What is an E node in the context of branch and bound?
What is an E node in the context of branch and bound?
What is a dead node in the context of branch and bound?
What is a dead node in the context of branch and bound?
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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.
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