  We study a fundamental problem called Minimum Length Link Scheduling (MLLS)
which is crucial to the efficient operations of wireless networks. Given a set
of communication links of arbitrary length spread and assume each link has one
unit of traffic demand in wireless networks, the problem MLLS seeks a schedule
for all links (to satisfy all demands) of minimum number of time-slots such
that the links assigned to the same time-slot do not conflict with each other
under the physical interference model. In this paper, we will explore this
problem under three important transmission power control settings: linear power
control, uniform power control and arbitrary power control. We design a suite
of new and novel scheduling algorithms and conduct explicit complexity analysis
to demonstrate their efficiency. Our algorithms can account for the presence of
background noises in wireless networks. We also investigate the fractional case
of the problem MLLS where each link has a fractional demand. We propose an
efficient greedy algorithm of the approximation ratio at most
$(K+1)^{2}\omega$.
