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the 3-dimensional matching problem is NP-complete
Автор: Jan Verschelde
Загружено: 2024-07-27
Просмотров: 2514
Описание:
Given a tripartite graph, the 3-dimensional matching problem asks if there exists a perfect matching, that is: is there a list of triples of vertices, where each vertex appears exactly once by the selection of the edges between the sets in the partitioned vertex set. The lecture introduces a polynomial-time algorithm to reduce any arbitrary instance of the 3-satisfiability problem to an equivalent instance of the 3-dimensional matching problem. As 3-SAT is NP-complete, this shows that the 3-dimensional matching problem is NP-complete as well.
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