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Third,Ī full greedy randomized adaptive search procedure/variable neighborhood descent methodology enriched Second, an exact integer l inear programming (ILP) formulation for the MEWNC problem is proposed. Specifically, we prove that the MCC and MEWNC problems belong to the class of N P-complete problems. First, the computational complexity of both the MCC and MEWNC problems is established. The main contributions of this paperĪre threefold. The maximum edge-weight neighborhood clique (MEWNC) problem. The weighted version of the MCC problem is known as In this context, we are interested in finding the clique C ⊆ V such that the weighted sum associated withĮach edge shared between C and V − C is maximized. We can generalize this problem by considering the weights associated with eachĮdge. This problem is known in the literature as the maxĬut-clique (MCC) problem. Number of edges shared between C and V − C is maximized. (where the nodes are items and the edges represent correlation), we aim to find the clique C ⊆ V such that the For any given undirected graph G = (V, E )
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The focus willīe on the combinatorial problem and not on specific applications. Problem with valuable applications to MBA, especially in marketing and product placement. In this work, we address a combinatorial optimization As a consequence, the determination of a set of items with a highĬorrelation with others is a valuable tool for MBA. A clearīehavior is buying correlated items. In market basket analysis (MBA), the goal is to understand human behavior to maximize sales. Received 5 December 2018 received in revised form 23 March 2020 accepted 16 April 2020 Mathias Bourel, Eduardo Canale, Franco Robledo, Pablo Romero and Luis Stábile∗įacultad de Ingenierı́a, Instituto de Matemática y Estadı́stica, IMERL, Universidad de la República, Montevideo 11200,Į-mail: Complexity and heuristics for the weighted