Approximating the size of a maximum clique: semidefinite programming.
Analyze the approximating the size of a maximum clique: semidefinite programming..
Examples
Input:"test_input_1"
Output:"output_1"
Input:"test_input_2"
Output:"output_2"
Hints
Start by recalling the definition of a clique and its maximum clique problem. How does semidefinite programming (SDP) relate to approximating the size of a maximum clique?
Consider the Lovász theta function, a well-known SDP-based approach for approximating the independence number of a graph. How can this function be adapted or extended to approximate the clique number instead?
Explore the duality between the clique number and the independence number in graph theory. How can you leverage the dual SDP formulation of the Lovász theta function to derive an approximation for the maximum clique size?
Approximating the size of a maximum clique: semidefinite programming.
Analyze the approximating the size of a maximum clique: semidefinite programming..