(b) In class, we discussed numerous clique and star relaxations, like the quasi-clique (where a fraction...

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(b) In class, we discussed numerous clique and star relaxations, like the quasi-clique (where a fraction 7 [0, 1] of all edges in a structure needs to exist), the k-club (where all nodes in a structure need to be within a distance of k from one another), etc. In a clique, all nodes need to be adjacent to every other node; what if we relaxed this property? What if we allowed all nodes to be connected to every other node but k-1 of them? That is, what if for any structure S, we want each node to be adjacent to at least |S| - k nodes in the same structure? Formulate the problem of finding the maximum cardinality such structure as an integer program and solve it for the les misrables network. What is the structure of maximum cardinality you find? (b) In class, we discussed numerous clique and star relaxations, like the quasi-clique (where a fraction 7 [0, 1] of all edges in a structure needs to exist), the k-club (where all nodes in a structure need to be within a distance of k from one another), etc. In a clique, all nodes need to be adjacent to every other node; what if we relaxed this property? What if we allowed all nodes to be connected to every other node but k-1 of them? That is, what if for any structure S, we want each node to be adjacent to at least |S| - k nodes in the same structure? Formulate the problem of finding the maximum cardinality such structure as an integer program and solve it for the les misrables network. What is the structure of maximum cardinality you find?

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Integer Linear Programming Formulation for Maximum Cardinality Structure with k1 Nonconnections Here... View the full answer