We propose a 4 3 -approximation in linear time for the metric traveling salesman reoptimization problem under vertex insertion. This constitutes an improvement of the time complexity of the best known existing bound since in (G. Ausiello, B. Escoffier, J. Monnot and V. Th. Paschos: Reoptimization of minimum and maximum traveling salesman’s tours. J. Discrete Algorithms 7(4): 453-463, 2009) a 4/...

We present an implementation of a linear-time approximation scheme for the traveling salesman problem on planar graphs with edge weights. We observe that the theoretical algorithm involves constants that are too large for practical use. Our implementation, which is not subject to the theoretical algorithm’s guarantee, can quickly find good tours in very large planar graphs. 1998 ACM Subject Cla...

It is known that in case the distance matrix in the Travelling Salesman Problem (TSP) fulllls certain combinatorial conditions (e.g. the Demidenko conditions , the Kalmanson conditions or the Supnick conditions) then the TSP is solvable in polynomial time. This paper deals with the problem of recognizing Euclidean instances of the TSP for which there is a renumbering of the cities such that the...

In this research, we discuss the intermittent traveling salesman problem (ITSP), which extends the traditional traveling salesman problem (TSP) by imposing temperature restrictions on each node. These additional constraints limit the maximum allowable visit time per node, and result in multiple visits for each node which cannot be serviced in a single visit. We discuss three different temperatu...

For realizing large-scale distribution network simulation applicable to supply-chain management, it is required to solve hundreds of time constraint large-scale (100 cities) Traveling Salesman Problem (TSP) within interactive response time, with practicable optimality. Thus, a "selfish-gene with limited allowance" type GA is proposed. Here, each gene of an individual satisfies only its constrai...

This paper presents the differences between two NP problems. It focuses in the Euclidian 2 Dimension Travelling Salesman Problems and General Assign Problems. The main results are the triangle reduction to verify the solution in polynomial time for the former and for the later the solution to the Noted Conjecture of the NP-Class, NP is not P.

The article studies the generalisation of the maximum flow of minimum cost problem for the case of maximum discrete dynamic flow of minimum travelling cost and travelling time. The approach is based on iteratively generating efficient extreme points in the objective space by solving a series of single objective maximum flow problems with different objective functions. On each of the iterations,...

We develop a polynomial time approximation algorithm for the maximum traveling salesman problem. It guarantees a solution value of at least r times the optimal one for any given r < 5 7 .

This paper discusses an implementation of a dynamic programming approach to the traveling salesman problem that runs in time linear in the number of cities. Optimality can be guaranteed when precedence constraints of a certain type are present, and many problems involving time windows fall into this class. Perhaps the most interesting feature of the procedure is that an auxiliary structure is b...

The Generalized Traveling Salesman Problem is a variation of the well known Traveling Salesman Problem in which the set of nodes is divided into clusters; the objective is to find a minimum-cost tour passing through one node from each cluster. We present an effective heuristic for this problem. The method combines a genetic algorithm (GA) with a local tour improvement heuristic. Solutions are e...