Efficient Deployment of Base Stations in Wireless Communication Networks

In the design of wireless communication networks, we may have to interconnect n stations locating at given points in the plane such that the distance among each stations is as small as possible by introducing at most k extra stations subjective to a budget limit. In this paper, our goal is to determine the locations of the extra k stations interconnecting the existing n stations to minimize the longest distance among stations. This is so-called bottleneck Steiner tree problem, which also has applications in VLSI routing, WDM optical networks design and phylogenetic tree reconstruction. The problem has been proved to be NP-hard and cannot be approximated in the performance ratio 2 in polynomial time in both Euclidean and rectilinear plane and approximation algorithms in the best possible performance ratios presented for the problem in both planes. In this paper, we improve the time complexity of the approximation algorithms and conduct simulations to demonstrate the validness of our improvements.Published versio