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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 ...
In the worst case, the algorithm results in a tour that is much longer than the optimal tour. To be precise, for every constant r there is an instance of the traveling salesman problem such that the length of the tour computed by the nearest neighbour algorithm is greater than r times the length of the optimal tour. Moreover, for each number of ...
www.math.uwaterloo.ca /tsp /concorde.html The Concorde TSP Solver is a program for solving the travelling salesman problem . It was written by David Applegate , Robert E. Bixby , Vašek Chvátal , and William J. Cook , in ANSI C , and is freely available for academic use.
In combinatorial optimization, Lin–Kernighan is one of the best heuristics for solving the symmetric travelling salesman problem. [citation needed] It belongs to the class of local search algorithms, which take a tour (Hamiltonian cycle) as part of the input and attempt to improve it by searching in the neighbourhood of the given tour for one that is shorter, and upon finding one repeats the ...
For example, a greedy strategy for the travelling salesman problem (which is of high computational complexity) is the following heuristic: "At each step of the journey, visit the nearest unvisited city." This heuristic does not intend to find the best solution, but it terminates in a reasonable number of steps; finding an optimal solution to ...
The traveling salesman problem, in which a solution is a cycle containing all nodes of the graph and the target is to minimize the total length of the cycle The Boolean satisfiability problem , in which a candidate solution is a truth assignment, and the target is to maximize the number of clauses satisfied by the assignment; in this case, the ...
There exist inputs to the travelling salesman problem that cause the Christofides algorithm to find a solution whose approximation ratio is arbitrarily close to 3/2. One such class of inputs are formed by a path of n vertices, with the path edges having weight 1 , together with a set of edges connecting vertices two steps apart in the path with ...
A figure illustrating the vehicle routing problem. The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises the travelling salesman problem (TSP).