On-line k-truck problem and its competitive algorithms

In this paper, based on the Position Maintaining Strategy (PMS for short), on-line scheduling of k-truck problem, which is a generalization of the famous k-server problem, is originally presented by our team. We proposed several competitive algorithms applicable under different conditions for solving the on-line k-truck problem. First, a competitive algorithm with competitive ratio 2k + 1/theta is given for any theta greater than or equal to 1. Following that, if theta greater than or equal to (c + 1)/(c - 1) holds, then there must exist a (2k - 1)-competitive algorithm for k-truck problem, where c is the competitive ratio of the on-line algorithm about the relevant k-server problem. And then a greedy algorithm with competitive ratio 1 + lambda/theta, where lambda is a parameter related to the structure property of a given graph, is given. Finally, competitive algorithms with ratios 1 + 1/theta are given for two special families of graphs.