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Cliques and independent sets. A clique is a graph where there is an edge between every pair of nodes. The main 
problem of interest here is finding a clique in a larger graph (that is, identifying a clique as a subgraph). An independent 
set in a graph is a set of nodes where no pair is connected by an edge. In other words, finding an independent set is 
equivalent to taking the complement of the edge set and finding a clique. Finding a k-clique (a clique of k nodes) or 
finding the largest clique in a graph (the max-clique problem) is NP-hard. (For more information, see Chapter 11.)
Closest pair. Given a set of points in the Euclidean plane, find the two points that are closest to each other. This can be 
solved in loglinear time using the divide-and-conquer strategy (see Chapter 6).