Related papers: The Complexity of Computing a Robust Flow
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…
We study the classic NP-Hard problem of finding the maximum $k$-set coverage in the data stream model: given a set system of $m$ sets that are subsets of a universe $\{1,\ldots,n \}$, find the $k$ sets that cover the most number of distinct…
This paper studies the fundamental problem of how to reroute $k$ unsplittable flows of a certain demand in a capacitated network from their current paths to their respective new paths, in a congestion-free manner and fast. This scheduling…
Motivated by the challenge of analyzing data sets with periodic boundary conditions to investigate transportation properties, we introduce a concept of circular max-flow for graphs mapped onto the circle. Unlike classical max-flow…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
The power flow (PF) problem is a fundamental problem in power system engineering. Many popular solvers face challenges, such as convergence issues. One can try to rewrite the PF problem into a fixed point equation, which can be solved…
We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…
Robust optimization(RO) is an important tool for handling optimization problem with uncertainty. The main objective of RO is to solve optimization problems due to uncertainty associated with constraints satisfying all realizations of…
We study the computational complexity of scheduling jobs on a single speed-scalable processor with the objective of capturing the trade-off between the (weighted) flow time and the energy consumption. This trade-off has been extensively…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…
We consider high dimensional variants of the maximum flow and minimum cut problems in the setting of simplicial complexes and provide both algorithmic and hardness results. By viewing flows and cuts topologically in terms of the simplicial…
In this paper we consider the problem of finding a maximum weight set subject to a $k$-extendible constraint in the data stream model. The only non-trivial algorithm known for this problem to date---to the best of our knowledge---is a…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination…
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…
Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to…
Computing cohesive subgraphs is a central problem in graph theory. While many formulations of cohesive subgraphs lead to NP-hard problems, finding a densest subgraph can be done in polynomial time. As such, the densest subgraph model has…
In multi-hop wireless networks, flow demands mean that some nodes have routing demands of transmitting their data to other nodes with a certain level of transmission rate. When a set of nodes have been deployed with flow demands, it is…
The maximum capacity path problem is to find a path from a source to a sink which has the maximum capacity among all paths. This paper addresses an extension of this problem which considers loss factors. It is called the generalized maximum…