This document discusses algorithms for finding minimum cuts in graphs. It begins with an overview and definitions of graphs and multi-graphs. It then discusses the min-cut problem and presents an initial algorithm for finding min-cuts that recursively partitions the graph. The document goes on to revisit common recurrence relations and use insights from analyzing recurrences to modify the initial algorithm, making it faster by improving its success probability at each step while maintaining the same running time. It concludes by analyzing the new faster algorithm's recurrence relation.