Computer Science · Design and Analysis of Algorithms
Statement I: Given a graph G = (V, E) in which each vertex v ∈ V has an associated positive weight w(v), we can use linear programming to find a lower bound on the weight of the minimum-weight vertex cover. Statement II: This lower bound can be found by maximizing the objective function ∑v ∈ V w(v)x(v) subject to x(u) + x(v) ≥ 1 for each (u, v) ∈ E, x(v) ≤ 1 for each v ∈ V, and x(v) ≥ 0 for each v ∈ V. In the light of the above statements, choose the correct answer:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Both Statement I and Statement II are correct
- 2Both Statement I and Statement II are incorrect
- 3Statement I is correct but Statement II is incorrect✓
- 4Statement I is incorrect and Statement II is correct
Correct answer
Statement I is correct but Statement II is incorrect
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