A Vertex Cover of an undirected graph G is a subset of the nodes of G, such that every edge of G touches one of the selected nodes. The VERTEX-COVER problem is to decide if a graph G has a vertex cover of size k. VERTEX-COVER = { | G is an undirected graph with a k-node vertex cover } The VC3 problem is a special case of the VERTEX-COVER problem where the value of k is fixed at 3. VERTEX-COVER 3 = { | G is an undirected graph with a 3-node vertex cover } Use parts a-b below to show that Vertex-Cover 3 is in the class P. a. Give a high-level description of a decider for VC3. A high-level description describes an algorithm without giving details about how the machine manages its tape or head. b. Show that the decider in part a runs in deterministic polynomial time.
A Vertex Cover of an undirected graph G is a subset of the nodes of G,
such that every edge of G touches one of the selected nodes.
The VERTEX-COVER problem is to decide if a graph G has a vertex cover of size k.
VERTEX-COVER = { <G,k> | G is an undirected graph with a k-node vertex cover }
The VC3 problem is a special case of the VERTEX-COVER problem where the value of k is fixed at 3.
VERTEX-COVER 3 = { <G> | G is an undirected graph with a 3-node vertex cover }
Use parts a-b below to show that Vertex-Cover 3 is in the class P.
a. Give a high-level description of a decider for VC3.
A high-level description describes an algorithm
without giving details about how the machine manages its tape or head.
b. Show that the decider in part a runs in deterministic polynomial time.
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