Algorithm Design Questions Long
Maximum bipartite matching and maximum cardinality matching are both concepts in graph theory and refer to different types of matching problems.
1. Maximum Bipartite Matching:
A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that there are no edges between vertices within the same set. A bipartite matching in a bipartite graph is a set of edges such that no two edges share a common vertex. The maximum bipartite matching problem aims to find the largest possible matching in a bipartite graph.
Key characteristics of maximum bipartite matching:
- It is applicable only to bipartite graphs.
- The goal is to find the largest possible matching.
- The matching consists of edges that connect vertices from different sets.
- The matching is considered maximum when no additional edge can be added to it.
2. Maximum Cardinality Matching:
A cardinality matching in a graph is a set of edges such that no two edges share a common vertex. The maximum cardinality matching problem aims to find the largest possible matching in any type of graph, not necessarily bipartite.
Key characteristics of maximum cardinality matching:
- It is applicable to any type of graph, including bipartite and non-bipartite graphs.
- The goal is to find the largest possible matching.
- The matching consists of edges that connect any pair of vertices.
- The matching is considered maximum when no additional edge can be added to it.
In summary, the main difference between maximum bipartite matching and maximum cardinality matching lies in the type of graphs they are applicable to. Maximum bipartite matching is specific to bipartite graphs, while maximum cardinality matching can be applied to any type of graph.