Concepts116
Category
Bipartite Matching - Kuhn's Algorithm
Kuhn’s algorithm finds a maximum matching in a bipartite graph by repeatedly searching for augmenting paths using DFS.
König's Theorem
König's Theorem states that in any bipartite graph, the size of a maximum matching equals the size of a minimum vertex cover.
Flow - Modeling Techniques
Many classic problems can be modeled as a maximum flow problem by building the right network and capacities.
Minimum Cost Maximum Flow
Minimum Cost Maximum Flow (MCMF) finds the maximum possible flow from a source to a sink while minimizing the total cost paid per unit of flow along edges.
Min-Cut Max-Flow Theorem
The Max-Flow Min-Cut Theorem says the maximum amount you can push from source to sink equals the minimum total capacity you must cut to disconnect them.
Maximum Flow - Dinic's Algorithm
Dinic's algorithm computes maximum flow by repeatedly building a level graph with BFS and sending a blocking flow using DFS.
Maximum Flow - Ford-Fulkerson
Ford–Fulkerson finds the maximum possible flow from a source to a sink by repeatedly pushing flow along an augmenting path in the residual graph.
Biconnected Components
A biconnected component (block) is a maximal subgraph where removing any single vertex keeps it connected.
Virtual Tree (Auxiliary Tree)
A Virtual Tree (Auxiliary Tree) compresses a large tree into a much smaller tree that contains only the k important nodes and the LCAs needed to keep them connected.
LCA - Binary Lifting
Binary lifting precomputes 2^k ancestors for every node so we can jump upward in powers of two.
Strongly Connected Components
Strongly Connected Components (SCCs) partition a directed graph into maximal groups where every vertex can reach every other vertex in the group.
Bridge Tree
A bridge tree is built by contracting every 2-edge-connected component of an undirected graph into a single node, leaving only bridges as edges between nodes.