The maximum traveling salesman problem (Max TSP) is one of the intensively researched combinatorial optimization problems. It consists of finding a  Hamiltonian cycle in a given complete weighted graph with the maximum total weight of the edges . This problem is APX-hard in the general and metric cases but admits efficient approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm. In this paper, we suggest the first polynomial-time approximation scheme for Max TSP in arbitrary metric space of fixed doubling dimension. In fact, the suggested algorithm implements a scheme EPTAS: for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time. Also, we propose a polynomial-time algorithm which finds asymptotically optimal solutions of the metric Max TSP in fixed and sublogarithmic doubling dimensions.
The maximum traveling salesman problem (Max TSP) is one of the intensively researched combinatorial optimization problems. It consists of finding a maximum-weight Hamiltonian cycle in a given complete weighted graph . This problem is APX-hard in the general and metric cases but admits approximation schemes in the geometric setting, when the vertices of the input graph are some points in fixed-dimensional real space and the edge weights are induced by some vector norm. In this paper, we suggest the first polynomial-time approximation scheme for Max TSP in arbitrary metric space of fixed doubling dimension. In fact, the suggested algorithm implements a scheme EPTAS: for any fixed \varepsilon\in(0,1), it computes a (1-\varepsilon)-approximate solution of the considered problem in cubic time. Also, we propose a polynomial-time algorithm which finds asymptotically optimal solutions of the metric Max TSP in fixed and sublogarithmic doubling dimensions.
A
maximum-weight
D
with the maximum total weight of the edges
D
efficient