Lower bounds to the graph partitioning problem through generalized linear programming and network flows
A co-biclique of a simple undirected graph G = (V,E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C is an independent.) It is showed that a minimum-cost dependent set of G can be determined in polynomial...
Fractional programming consists in optimizing a ratio of two functions subject to some constraints. Different versions of this model, linear or nonlinear, have applications in various fields like combinatorial optimization, stochastic programming, data bases, and economy. Three resolution methods are presented: direct solution, parametric approach and solution of an equivalent problem.