An efficient approximation algorithm for the extension facility location problem on torus internetwork topology

摘要

The uncapacitated facility location problem is an NP-hard problem. Nowadays there are few studies on this problem in practical applications on the torus internetwork topology. The objective of this paper is to extend the facility location problem on the two-dimensional torus internetwork topology. At first, the extension facility location problem with two additional constraints is formulated as integer linear programming. Then, two embedding schemes are proposed respectively by partitioning the solutions of the extension problem into stars, which exhibit a trade-off between dilation and expansion. Finally, an efficient approximation algorithm is developed to find the integer solutions of the extension facility location problem. Moreover, the relative analysis of approximation guarantee of the proposed algorithm is given.