Related papers: Adaptive Network Flow with $k$-Arc Destruction
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…
In this paper, we study robust transshipment under consistent flow constraints. We consider demand uncertainty represented by a finite set of scenarios and characterize a subset of arcs as so-called fixed arcs. In each scenario, we require…
By Menger's theorem the maximum number of arc-disjoint paths from a vertex s to a vertex t in a directed graph equals the minumum number of arcs needed to disconnect s and t, i.e., the minimum size of an s-t-cut. The max-flow problem in a…
We study the robust maximum flow problem and the robust maximum flow over time problem where a given number of arcs $\Gamma$ may fail or may be delayed. Two prominent models have been introduced for these problems: either one assigns flow…
Finding a Steiner strongly $k$-arc-connected orientation is particularly relevant in network design and reliability, as it guarantees robust communication between a designated set of critical nodes. Kir\'aly and Lau (FOCS 2006) introduced a…
In network flow problems, there is a well-known one-to-one relationship between extreme points of the feasibility region and trees in the associated undirected graph. The same is true for the dual differential problem. In this paper, we…
For a digraph $D$ and some $X \subseteq V(D)$, the inversion of $X$ is the operation of flipping all arcs both of whose endvertices are in $X$. We initiate the study of establishing arc-connectivity properties by applying inversions of…
We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…
Maximum Flow Network Interdiction Problem (MFNIP) is known to be strongly NP-hard problem. We solve a simple form of MFNIP in polynomial time. We review the reduction of MFNIP from the clique problem. We propose a polynomial time solution…
The complexity of the maximum common connected subgraph problem in partial $k$-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial $2$-trees. On the other…
We examine the dynamic network flow problem under the assumption that the flow consists of discrete units. The dynamic network flow problem is commonly addressed in the context of developing evacuation plans, where the flow is typically…
We study dynamic network flows with uncertain input data under a robust optimization perspective. In the dynamic maximum flow problem, the goal is to maximize the flow reaching the sink within a given time horizon $T$, while flow requires a…
Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where…
Many engineered systems, such as energy and transportation infrastructures, are networks governed by non-linear physical laws. A primary challenge for operators of these networks is to achieve optimal utilization while maintaining safety…
In the unsplittable flow problem on a path, we are given a capacitated path $P$ and $n$ tasks, each task having a demand, a profit, and start and end vertices. The goal is to compute a maximum profit set of tasks, such that for each edge…
This papers considers the problem of maximizing the load that can be served by a power network. We use the commonly accepted Linear DC power network model and consider wo configuration options: switching lines and using FACTS devices. We…
We consider the routing flow shop problem with two machines on an asymmetric network. For this problem we discuss properties of an optimal schedule and present a polynomial time algorithm assuming the number of nodes of the network to be…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…
Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for…