Lecture 3 : Nondeterminism , NP , and NP - completeness
نویسنده
چکیده
• INDEPENDENT -SET = {[G, k] : G is an undirected graph with an independent set of vertices I ⊆ V (G) of size ≥ k} where a subset I is independent iff it contains no edges of G. – Guess a set I of size k. Verify that it contains no edges of G. • CLIQUE = {[G, k] : G is an undirected graph with an independent set of vertices C ⊆ V (G) of size ≥ k} where a subset C is a clique iff every edge on the vertices of C are in G. – Guess a set C of size k. Verify that all edges in C are present in G. • COMPOSITE = {[n] : n is a composite integer}. – Guess a set integers a and b. Verify that 1 < a, b < n and ab = n. • USTCONN = {[G, s, t] : G is an undirected path from s to t}. – Guess the path. Verify that it connects s and t.
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