Related papers: Minimum-Cost Flows Over Time
Analyzing big data in a highly dynamic environment becomes more and more critical because of the increasingly need for end-to-end processing of this data. Modern data flows are quite complex and there are not efficient, cost-based,…
There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques…
We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by $\tilde O(m^{3/2})$. This matches the best known bounds, which previously have only been achieved by numerical algorithms…
This paper studies a variant of the minimum-cost flow problem in a graph with convex cost function where the demands at the vertices are functions depending on a one-dimensional parameter $\lambda$. We devise two algorithmic approaches for…
This article focuses on a biobjective extension of the maximum flow network interdiction problem, where each arc in the network is associated with two capacity values. Two maximum flows from a source to a sink are to be computed…
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 present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
In this paper, we present an improved algorithm for the maximum flow problem on general networks with $n$ vertices and $m$ arcs. We show how to solve the problem in $O(mn)$ time, when $m = O(n^{2-\epsilon})$, for some $0 <\epsilon \leq 1$.…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
In this note, we first prove that the solution of mean curvature flow on a finite time interval $[0,T)$ can be extended over time $T$ if the space-time integration of the norm of the second fundamental form is finite. Secondly, we prove…
We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs,…
We study the maximum flow problem in directed H-minor-free graphs where H can be drawn in the plane with one crossing. If a structural decomposition of the graph as a clique-sum of planar graphs and graphs of constant complexity is given,…
In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The…
We present an $\tilde{O}\left(m^{\frac{10}{7}}U^{\frac{1}{7}}\right)$-time algorithm for the maximum $s$-$t$ flow problem and the minimum $s$-$t$ cut problem in directed graphs with $m$ arcs and largest integer capacity $U$. This matches…
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…
We suggest a global perspective on dynamic network flow problems that takes advantage of the similarities to port-Hamiltonian dynamics. Dynamic minimum cost flow problems are formulated as open-loop optimal control problems for general…
In this paper, we address the minimum-cost node-capacitated multiflow problem in an undirected network. For this problem, Babenko and Karzanov (2012) showed strongly polynomial-time solvability via the ellipsoid method. Our result is the…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
We consider some flow-time minimization problems in the unrelated machines setting. In this setting, there is a set of $m$ machines and a set of $n$ jobs, and each job $j$ has a machine dependent processing time of $p_{ij}$ on machine $i$.…