The Travelling Salesman Problem (Edexcel A-Level Further Mathematics): Quizzes

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The Travelling Salesman Problem
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What is the main objective of the Travelling Salesman Problem?

Find the shortest route visiting all vertices exactly once and returning to start

In Classical TSP, what type of graph is involved?

Complete graph

What does the triangle inequality state for weights in Classical TSP?

Weight of (AC)(A \to C) \leq Weight of (AB)+(A \to B) + Weight of (BC)(B \to C)

In Practical TSP, what weight is assigned to missing edges?

Infinity (\infty)

What does the Nearest Neighbour Algorithm generate?

An upper bound for the minimum route

In Nearest Neighbour Algorithm, which vertex is selected next?

Nearest unvisited vertex

What is a key disadvantage of the Nearest Neighbour Algorithm?

Heavily influenced by starting vertex

What type of cycle does Classical TSP aim to find?

Hamiltonian cycle with minimum total weight

What technique is used to improve the Nearest Neighbour solution?

Shortcuts replacing route segments

What is a common mistake when using Nearest Neighbour Algorithm?

Not trying different starting vertices

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