Lecture 7 1 Linear Programming Relaxations
The vertex cover approximation algorithm based on linear programming is very ele-gant and simple, but it requires the solution of a linear program. Our previous vertex cover approximation algorithm, instead, had a very fast linear-time implementation.
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10.1 Integer Programming and LP relaxation
pages.cs.wisc.eduFor vertex cover, the obvious rounding works: for each x v 1=2, set x v = 1 and include vin the vertex cover. For each xv <1=2, set x v = 0 and don’t include vin the vertex cover. It is easy to see that this is a feasible solution and forms a vertex cover. Consider any edge (u;v) 2E. Then, by construction, x