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Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
G. Gutin, A. Yeo and A. Zverovich, Traveling salesman should not be greedy: domination analysis of greedy-type heuristics for the TSP. Discrete Applied Mathematics 117 (2002), 81–86. J. Bang-Jensen, G. Gutin and A. Yeo, When the greedy algorithm fails. Discrete Optimization 1 (2004), 121–127.
Rosenkrantz, Stearns & Lewis (1977) used the farthest-first traversal to define the farthest-insertion heuristic for the travelling salesman problem.This heuristic finds approximate solutions to the travelling salesman problem by building up a tour on a subset of points, adding one point at a time to the tour in the ordering given by a farthest-first traversal.
The Held–Karp algorithm, also called the Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman [1] and by Held and Karp [2] to solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour that visits each city exactly once before returning to ...
This algorithm is no longer the best polynomial time approximation algorithm for the TSP on general metric spaces. Karlin, Klein, and Gharan introduced a randomized approximation algorithm with approximation ratio 1.5 − 10 −36. It follows similar principles to Christofides' algorithm, but uses a randomly chosen tree from a carefully chosen ...
2-opt. In optimization, 2-opt is a simple local search algorithm for solving the traveling salesman problem.The 2-opt algorithm was first proposed by Croes in 1958, [1] although the basic move had already been suggested by Flood. [2]
The multi-fragment (MF) algorithm is a heuristic or approximation algorithm for the travelling salesman problem (TSP) (and related problems). This algorithm is also sometimes called the "greedy algorithm" for the TSP.
In combinatorial optimization, the set TSP, also known as the generalized TSP, group TSP, One-of-a-Set TSP, Multiple Choice TSP or Covering Salesman Problem, is a generalization of the traveling salesman problem (TSP), whereby it is required to find a shortest tour in a graph which visits all specified subsets of the vertices of a graph.