  Fluid antennas (FAs) and movable antennas (MAs) have emerged as promising
technologies in wireless communications, which offer the flexibility to improve
channel conditions by adjusting transmit/receive antenna positions within a
spatial region. In this letter, we focus on an MA-enhanced multiple-input
single-output (MISO) communication system, aiming to optimize the positions of
multiple transmit MAs to maximize the received signal power. Unlike the prior
works on continuously searching for the optimal MA positions, we propose to
sample the transmit region into discrete points, such that the continuous
antenna position optimization problem is transformed to a discrete sampling
point selection problem based on the point-wise channel information. However,
such a point selection problem is combinatory and challenging to be optimally
solved. To tackle this challenge, we ingeniously recast it as an equivalent
fixed-hop shortest path problem in graph theory and propose a customized
algorithm to solve it optimally in polynomial time. To further reduce the
complexity, a linear-time sequential update algorithm is also proposed to
obtain a high-quality suboptimal solution. Numerical results demonstrate that
the proposed algorithms can yield considerable performance gains over the
conventional fixed-position antennas with/without antenna selection.
