10.1 Integer Programming and LP relaxation
For 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
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