We consider a reliable network design problem under uncertain edge failures. Our goal is to select a minimum-cost subset of edges in the network to connect multiple terminals together with high probability. This problem can be seen as a stochastic variant of the Steiner tree problem. We propose a scenario-based Steiner cut formulation, and a … Read more
Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature, by showing a one-to-one correspondence between IISs and … Read more
We introduce a practically important and theoretically challenging problem: finding the minimum cost path for PHEVs in a road network with refueling and charging stations. We show that this problem is NP-complete and present a mixed integer quadratically constrained formulation, a discrete approximation dynamic programming heuristic, and a shortest path heuristic as solution methodologies. Practical … Read more
We study an incremental network design problem, where in each time period of the planning horizon an arc can be added to the network and a maximum flow problem is solved, and where the objective is to maximize the cumulative flow over the entire planning horizon. After presenting two mixed integer programming (MIP) formulations for … Read more
In this paper we address the problem of identifying the most likely infection pattern responsible for the spread of a disease in a network. In particular, we focus on the scenario where limited information (i.e. infection reports) is available during an ongoing outbreak. For this problem we propose a maximum likelihood model and present an … Read more
The Internet is currently mostly exploited as a means to perform massive digital content distribution. Such a usage profile was not specifically taken into account while initially designing the architecture of the network: as a matter of fact, the Internet was instead conceived around the concept of host-to-host communications between two remote machines. To solve … Read more
Given a telecommunication network, modeled by a graph with capacities, we are interested in comparing the behavior and usefulness of two information propagation schemes, namely multicast and network coding, when the aforementioned network is subject to single arc failure. We consider the case with a single source node and a set of terminal nodes. The … Read more
Finding a global solution to the optimal power flow (OPF) problem is difficult due to its nonconvexity. A convex relaxation in the form of semidefinite programming (SDP) has attracted much attention lately as it yields a global solution in several practical cases. However, it does not in all cases, and such cases have been documented … Read more
We study the minimum concave cost flow problem over a two-dimensional grid network (CFG), where one dimension represents time ($1\le t\le T$) and the other dimension represents echelons ($1\le l\le L$). The concave function over each arc is given by a value oracle. We give a polynomial-time algorithm for finding the optimal solution when the … Read more
This paper develops various chance-constrained models for optimizing the probabilistic network design problem (PNDP), where we differentiate the quality of service (QoS) and measure the related network performance under uncertain demand. The upper level problem of PNDP designs continuous/discrete link capacities shared by multi-commodity flows, and the lower level problem differentiates the corresponding QoS for … Read more