Potential-based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize … Read more
In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the dual simplex method with the most negative pivoting rule for LP. The bound is comparable with the bound given by Kitahara and Mizuno (2010) for the primal simplex method. We apply the result to the … Read more
We give an upper bound for the number of different basic feasible solutions generated by Dantzig’s simplex method (the simplex method with the most negative pivoting rule) for LP with bounded variables by extending the result of Kitahara and Mizuno (2010). We refine the analysis by them and improve an upper bound for a standard … Read more
We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at … Read more