Part V - Graph Algorithms

Part V - Graph Algorithms offers a thorough exploration of fundamental and advanced graph algorithms essential for solving complex problems in graph theory. It begins with a foundational overview of elementary graph theory, covering core concepts such as graph properties, invariants, and theorems, and practical graph construction techniques in Rust. The section then delves into graph traversal algorithms, including depth-first search (DFS) and breadth-first search (BFS), along with advanced traversal techniques and their Rust implementations. It continues with an examination of single-source shortest path algorithms, such as Dijkstra’s and Bellman-Ford, comparing their applications and practical aspects in Rust. The focus expands to all-pairs shortest path problems, discussing Floyd-Warshall and Johnson’s algorithms, and their practical use cases and optimizations. The section also covers minimum spanning trees, detailing Kruskal’s, Prim’s, and Borůvka’s algorithms, along with their practical implementations. Network flow algorithms are explored next, including Ford-Fulkerson, Edmonds-Karp, and Dinic’s algorithms, as well as minimum-cost flow algorithms and advanced optimization topics. Finally, the section addresses matchings in bipartite graphs, featuring the Hungarian and Hopcroft-Karp algorithms, maximum cardinality matching, and their practical applications and optimizations.