Back to Topic 3.16 — Route algorithms (HL only)
3.16.2Math AI HL8 flashcards

Route inspection & travelling salesman

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Card 1 of 83.16.2
3.16.2
Question

What does the Chinese postman (route inspection) problem find?

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All 8 Flashcards — Route inspection & travelling salesman

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Card 1concept

Question

What does the Chinese postman (route inspection) problem find?

Answer

The shortest CLOSED walk that uses every EDGE at least once and returns to the start.

Card 2concept

Question

When can the postman traverse every edge exactly once?

Answer

When every vertex has even degree (an Eulerian circuit exists); then the answer is just the sum of all edges.

Card 3concept

Question

Route-inspection method with odd vertices?

Answer

Pair the odd-degree vertices so the total of the shortest paths between the pairs is least; add that to the sum of all edges.

Card 4formula

Question

CPP length formula?

Answer

Sum of all edges + minimum pairing of the odd-degree vertices' shortest paths.

Card 5concept

Question

What does the travelling salesman problem (TSP) find?

Answer

The shortest CLOSED route visiting every VERTEX exactly once and returning to the start (a Hamiltonian cycle).

Card 6concept

Question

How do you get an upper bound for the TSP?

Answer

Nearest-neighbour algorithm: from the start, always go to the nearest unvisited vertex, then return to start. Its length is an upper bound.

Card 7concept

Question

How do you get a lower bound for the TSP (deleted-vertex method)?

Answer

Delete a vertex; find the MST of the rest; add the two cheapest edges from the deleted vertex back.

Card 8concept

Question

Edge problem or vertex problem?

Answer

Route inspection covers every EDGE; travelling salesman visits every VERTEX. Pick by what must be covered.

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