This paper addresses the optimization of movable antenna (MA) positions in a multiple-input single-output (MISO) communication system to maximize received signal power. Unlike previous works that focus on continuous search for optimal MA positions, this study proposes a discrete sampling approach, transforming the continuous optimization problem into a discrete point selection problem based on channel information. The point selection problem is then reformulated as a fixed-hop shortest path problem in graph theory, which is solved optimally using a polynomial-time algorithm. Additionally, a linear-time sequential update algorithm is introduced to achieve a high-quality suboptimal solution. Numerical results show that the proposed algorithms significantly outperform conventional fixed-position antennas with and without antenna selection, demonstrating the effectiveness of the proposed methods in enhancing communication performance.This paper addresses the optimization of movable antenna (MA) positions in a multiple-input single-output (MISO) communication system to maximize received signal power. Unlike previous works that focus on continuous search for optimal MA positions, this study proposes a discrete sampling approach, transforming the continuous optimization problem into a discrete point selection problem based on channel information. The point selection problem is then reformulated as a fixed-hop shortest path problem in graph theory, which is solved optimally using a polynomial-time algorithm. Additionally, a linear-time sequential update algorithm is introduced to achieve a high-quality suboptimal solution. Numerical results show that the proposed algorithms significantly outperform conventional fixed-position antennas with and without antenna selection, demonstrating the effectiveness of the proposed methods in enhancing communication performance.