@techreport{TR-IC-97-14,
  number = {IC-97-14},
  author = {Macambira, Elder M. and de Souza, Cid C.},
  title = {The {Edge}-{Weighted} {Clique} {Problem}: {Valid} Inequalities, Facets and Polyhedral Computations},
  month = {October},
  year = {1997}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 25 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      Let $K_n=(V,E)$ be the complete undirected graph with weights
      $c_e$ associated to the edges in $E$. We consider the problem of
      finding the subclique $C = (U,F)$ of $K_n$ such that the sum of
      the weights of the edges in $F$ is maximized and $|U| \leq b$,
      for some $b \in [1,\ldots,n]$. This problem is called the
      Maximum Edge-Weighted Clique Problem (MEWCP) and is NP-hard.  In
      this paper we investigate the facial structure of the polytope
      associated to the MEWCP and introduce new classes of facets for
      this polytope.  Computational experiments with a branch-and-cut
      algorithm are reported confirming the strength of these
      inequalities.  All instances with up to 48 nodes could be solved
      without entering into the branching phase. Moreover, we show
      that some of these new inequalities also define facets of the
      Boolean Quadric Polytope and generalize previously known
      inequalities for this polytope.
  }
}