  Beacon node placement, node-to-node measurement, and target node positioning
are the three key steps for a localization process. However, compared with the
other two steps, beacon node placement still lacks a comprehensive, systematic
study in research literatures. To fill this gap, we address the Beacon Node
Placment (BNP) problem that deploys beacon nodes for minimal localization error
in this paper. BNP is difficult in that the localization error is determined by
a complicated combination of factors, i.e., the localization error differing
greatly under a different environment, with a different algorithm applied, or
with a different type of beacon node used. In view of the hardness of BNP, we
propose an approximate function to reduce time cost in localization error
calculation, and also prove its time complexity and error bound. By
approximation, a sub-optimal distribution of beacon nodes could be found within
acceptable time cost for placement. In the experiment, we test our method and
compare it with other node placement methods under various settings and
environments. The experimental results show feasibility and effectiveness of
our method in practice.
