VertexCoverByRounding

Difference (from prior major revision) (no other diffs)

Removed: 7,11d6

prove: The cost of S is at most twice the minimum cost of any vertex cover.

The ratio

: (cost of optimal solution to original problem)/(cost of optimal solution to relaxed problem)

Changed: 13,18c8

is called the integrality gap of the integer linear program. (In case
of a maximization problem, the integrality gap is the reciprocal. The
integrality gap of the problem is the worst-case integrality gap for
any instance of the problem.

prove: The integrality gap of the above integer linear program for min-cost vertex cover is 2.

prove: The cost of S is at most twice the minimum cost of any vertex cover.

Added: 19a10

prove: The IntegralityGap of the above integer linear program for min-cost vertex cover is 2.

2-approximation algorithm for min-cost vertex cover by rounding:

Let x be a min-cost fractional vertex cover.
Return the set S of vertices v having x(v) ≥ 1/2.

prove: The set S of vertices is a vertex cover.

prove: The cost of S is at most twice the minimum cost of any vertex cover.

prove: The IntegralityGap of the above integer linear program for min-cost vertex cover is 2.