Two nodes of a wireless network may not be able to communicate with each other directly perhaps due to obstacles or insufficient signal strength. This necessitates the use of intermediate nodes to relay information. Often, one designates a (preferably small) subset of them to relay these messages (i.e., to serve as a virtual backbone for … Read more
We study the robust resource constrained shortest path problem (RCSPP) under uncertainty in cost and multiple resource consumption. Contrary to the deterministic RCSPP where the cost and the consumption of resources on an arc are known and fixed, the robust RCSPP models the case where both the cost and the resource consumption are random, and … Read more
Influence maximization problems aim to identify key players in (social) networks and are typically motivated from viral marketing. In this work, we introduce and study the Generalized Least Cost Influence Problem (GLCIP) that generalizes many previously considered problem variants and allows to overcome some of their limitations. A formulation that is based on the concept … Read more
We study network models where flows cannot be split or merged when passing through certain nodes, i.e., for such nodes, each incoming arc flow must be matched to an outgoing arc flow of identical value. This requirement, which we call “no-split no-merge” (NSNM), appears in railroad applications where train compositions can only be modified at … Read more
The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and … Read more
We study the existence and uniqueness of equilibria for perfectly competitive markets in capacitated transport networks. The model under consideration is rather general so that it captures basic aspects of related models in, e.g., gas or electricity networks. We formulate the market equilibrium model as a mixed complementarity problem and show the equivalence to a … Read more
We consider uniqueness and multiplicity of market equilibria in a short-run setup where traded quantities of electricity are transported through a capacitated network in which power flows have to satisfy the classical lossless DC approximation. The firms face fluctuating demand and decide on their production, which is constrained by given capacities. Today, uniqueness of such … Read more
Methods for distributed optimization have received significant attention in recent years owing to their wide applicability in various domains including machine learning, robotics and sensor networks. A distributed optimization method typically consists of two key components: communication and computation. More specifically, at every iteration (or every several iterations) of a distributed algorithm, each node in … Read more
In this paper, we propose new constraint generation algorithms for solving the two-stage robust minimum cost flow problem, a problem that arises from various applications such as transportation and logistics. In order to develop efficient algorithms under general polyhedral uncertainty set, we repeatedly exploit the network-flow structure to reformulate the two-stage robust minimum cost flow … Read more
In the analysis of networks, one often searches for tightly knit clusters. One property of a “good” cluster is a small diameter (say, bounded by $k$), which leads to the concept of a $k$-club. In this paper, we propose new path-like and cut-like integer programming formulations for detecting these low-diameter subgraphs. They simplify, generalize, and/or … Read more