Explore a quantum algorithm that achieves quadratic speedup in finding marked vertices using quantum walks. Delve into the comparison between exhaustive search, structured search, and search by random walk methods. Examine constraints and applications of this approach, including Szegedy's 2004 work on detecting and finding marked elements. Analyze the original, absorbing, and interpolated walks, as well as quantum fast-forwarding techniques. Investigate the connection to classical walks and gain insights into the final results of this quantum speedup algorithm.