Computer Viruses

There are no optimal solutions without P=NP.

P=Polynomial time, NP=Nondeterministic Polynomial time

Maximization problems are expressed as α<1. 1/2 approximation algorithm for a maximization problem is P because the solution is half of optimal value. NP hard is the increasing numbers of optimal value. Specific solutions are optimal than promised by the performance guarantee.

E={e1, . . . , en}

This is elements.

S1,S2,・・・Sm are subjects of E.

Sj⊆E, wj≧0

wj is weight for for each subset Sj.

The goal is to find a minimum-weight collection of subsets that covers all of E, which is P=NP.

I⊆{1, . . . , m}

If wj= 1 for each subset j, the problem is called the unweighted set cover problem, which is P≠NP.

Then you detect computer viruses.

G=(V,E)

This is the undirected graph.

wi≧0

wi is weight for each vertex i∈V.

The goal is to find a minimum-weight subset of vertices C⊆V.
(i, j)∈E, and i∈C or j∈C

If wi= 1 for each vertex i, the problem is an unweighted vertex cover problem.

Computer viruses are everywhere.