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Results tagged with graphs
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user 145191
Questions about graphs, discrete structures of nodes which are connected by edges, including trees and graphs with weighted edges.
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 …
- 235
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 …
- 235
3
votes
Accepted
$k$-Opt TSP Local Search is exact when $k = |V| - 1$
This follows from a result of Thomason, published in Section 2 of
Thomason, A.G., Hamiltonian Cycles and Uniquely Edge Colourable Graphs, Ann. Discrete Math. 3, 259-268 (1978). … In particular, $4$-regular graphs have at least $4$ distinct Hamiltonian pairs.
NOTE: In our particular case, $G$ is the union of two edge-disjoint Hamiltonian cycles. …
- 235
1
vote
1
answer
1k
views
How to determine if a tree $T = (V, E)$ has a perfect matching in $O(|V| + |E|)$ time
This is a problem I've come across while studying on my own; it's from Algorithms by Papadimitriou, Dasgupta and Vazirani.
Specifically, the problem statement is:
Give a linear-time algorithm that ta …
- 235