Approximation algorithms for the maximum Hamiltonian path problem with specified endpoint(s)

This paper deals with the problem of constructing Hamiltonian paths of optimal weight, called HPPs,t if the two endpoints are specified, HPPs if only one endpoint is specified. We show that HPPs,t is Image -differential approximable and HPPs is Image -differential approximable. Moreover, we observe that these problems cannot be differential approximable better than Image . Based upon these results, we obtain new bounds for standard ratio: a Image -standard approximation for MImage HPPs,t and a Image for MImage HPPs, which can be improved to Image for MImage HPPs,t[a,2a] (all the edge weights are within an interval [a,2a]), to Image for MImage HPPs[a,2a] and to Image for MImage HPPs,t[a,2a], to Image for MImage HPPs[a,2a].ou