Cross-selling is a strategy to recommend products to customers based on their past purchases or the purchases of other customers with the same profile. The best known algorithm for the analysis of a client shopping basket is known in the literature as market basket analysis. This dissertation discusses the discovery of sequential patterns in large databases and aims at implementing an efficient algorithm that transforms the shopping cart problem into a maximum clique problem. First, input data is transformed into a graph and maximum cliques are detected to discover the most frequent relationship between the items on the transaction. The dissertation also includes experiments that evaluate the efficiency of the algorithm for large data volumes.