Parametric min-cuts analysis in a network

AbstractThe all pairs minimum cuts problem in a capacitated undirected network is well known. Gomory and Hu showed that the all pairs minimum cuts are revealed by a min-cut tree that can be obtained by solving exactly (n−1) maximum flow problems, where n is the number of nodes in the network.In this paper we consider first the problem of finding parametric min-cuts for a specified pair of nodes when the capacity of an arc i is given by min{bi,λ}, where λ is the parameter, ranging from 0 to ∞. Next we seek the parametric min-cuts for all pairs of nodes, and achieve this by constructing min-cut trees for at most 2m different values of λ, where m is the number of edges in the network

A deep cut ellipsoid algorithm for convex programming

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported

A branch-and-cut algorithm for the strong minimum energy topology in wireless sensor networks

This paper studies the strong minimum energy topology design problem in wireless sensor networks. The objective is to assign transmission power to each sensor node in a directed wireless sensor network such that the induced directed graph topology is strongly connected and the total energy consumption is minimized. A topology is defined to be strongly connected if there exists a communication path between each ordered pair of sensor nodes. This topology design problem with sensor nodes defined on a plane is an NP-Complete problem. We first establish a lower bound on the optimal power consumption. We then provide three formulations for a more general problem defined on a general directed graph. All these formulations involve an exponential number of constraints. Second formulation is stronger than the first one. Further, using the second formulation, we lift the connectivity constraints to generate stronger set of constraints that yield the third formulation. These lifted cuts turn out to be extremely helpful in developing an effective branch-and-cut algorithm. A series of experiments are carried out to investigate the performance of the proposed branch-and-cut algorithm. These computational results over 580 instances demonstrate the effectiveness of our approach.OR in energy Wireless sensor network Minimum energy topology Branch and bound Cutting