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4 votes
1 answer
250 views

$k$-Opt TSP Local Search is NOT exact when $k = \lceil |V|/2 \rceil$

I've been self-studying the book Algorithms by Papadimitriou, Dasgupta and Vazirani. I am having a hard time with a question about local search involving the traveling salesman problem (TSP). We'll sa …
Fimpellizzeri's user avatar
3 votes
1 answer
228 views

$k$-Opt TSP Local Search is exact when $k = |V| - 1$

I've been self-studying the book Algorithms by Papadimitriou, Dasgupta and Vazirani. I am having a hard time with a question about local search involving the traveling salesman problem (TSP). We'll sa …
Fimpellizzeri's user avatar
3 votes
Accepted

$k$-Opt TSP Local Search is exact when $k = |V| - 1$

Searching more on the topic, I've found this post on Math SE with a much stronger result that in particular implies the existence of $T_1$ as defined above. I will reproduce it here to keep things sel …
Fimpellizzeri's user avatar