NP Completeness , Part 3 Richard Cole December 1 , 2008 1 Reduction Techniques
نویسنده
چکیده
1.1 Generalization Quite often, a problem one wants to show NP-Complete (NPC) is a generalization of a known NPC problem. For example, the Traveling Seller problem is a generalization of the Hamiltonian Circuit Problem. Showing that the generalized problem is NPhard is trivial: the identity reduction suffices. Or to put it another way, a polynomial time algorithm for the generalized problem is also a polynomial time algorithm for the more specialized problem.
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NP Completeness , Part 2
Example 1 Undirected Hamiltonian Path (UHP) and Undirected Hamiltonian Circuit (UHC) are the same problems as the corresponding problems for directed graphs, but the new problems are for undirected graphs. Claim 2 Given a polynomial time algorithm for Undirected Hamiltonian Path (UHP) there is a polynomial time algorithm for Directed Hamiltonian Path. 1. A DHP builds the triple (H, p, q), where...
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