We present a general numerical solution method for control problems with PDE-defined state variables over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs (and if necessary a linearization scheme) to derive constraints for a mixed-integer linear program (MILP) … Read more
We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks that are passive, i.e., do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow … Read more
In 2013, Orlin proved that the max flow problem could be solved in $O(nm)$ time. His algorithm ran in $O(nm + m^{1.94})$ time, which was the fastest for graphs with fewer than $n^{1.06}$ arcs. If the graph was not sufficiently sparse, the fastest running time was an algorithm due to King, Rao, and Tarjan. We … Read more
Given an undirected graph, we study the capacitated vertex separator problem which asks to find a subset of vertices of minimum cardinality, the removal of which induces a graph having a bounded number of pairwise disconnected shores (subsets of vertices) of limited cardinality. The problem is of great importance in the analysis and protection of … Read more
The family of Critical Node Detection Problems asks for finding a subset of vertices, deletion of which minimizes or maximizes a predefined connectivity measure on the remaining network. We study a problem of this family called the k-vertex cut problem. The problems asks for determining the minimum weight subset of nodes whose removal disconnects a … Read more
Data quality in population surveys suffers from missing responses. We use combinatorial optimization to create a complete and coherent data set. The methods are based on the widespread nearest neighbor hot deck imputation method that replaces the missing values with observed values from a close unit, the so-called donor. As a repeated use of donors … Read more
We consider a two-player interdiction problem staged over a graph where the leader’s objective is to minimize the cost of removing edges from the graph so that the follower’s objective, i.e., the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level $r$. Standard approaches for graph interdiction … Read more
Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more
This paper researches combinatorial algorithms for the multi-commodity flow problem. We relax the capacity constraints and introduce a \emph{penalty function} \(h\) for each arc. If the flow exceeds the capacity on arc \(a\), arc \(a\) would have a penalty cost. Based on the \emph{penalty function} \(h\), a new conception , \emph{equilibrium pseudo-flow}, is introduced. Then … Read more
We consider a time-dependent shortest path problem with possible waiting at each node and a global bound $W$ on the total waiting time. The goal is to minimize only the time travelled along the edges of the path, not including the waiting time. We prove that the problem can be solved in polynomial time when … Read more