Related papers: Minimum-Peak-Cost Flows Over Time
In this paper we show that every maximum minimum-cost flow over time problem has an optimal solution with a repeated structure if the given time horizon is large enough.
The robust minimum cost flow problem under consistent flow constraints (RobMCF$\equiv$) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF$\equiv$ problem, we consider demand and supply that are subject to uncertainty.…
We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to fast, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity…
We study the problem of determining the worst optimal value and characterizing the corresponding worst-case scenarios in minimum cost network flow problems with interval uncertainty in arc capacities. In this setting, each capacity can take…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
We introduce and study a class of optimization problems we coin replenishment problems with fixed turnover times: a very natural model that has received little attention in the literature. Nodes with capacity for storing a certain commodity…
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…
In this paper we provide new randomized algorithms with improved runtimes for solving linear programs with two-sided constraints. In the special case of the minimum cost flow problem on $n$-vertex $m$-edge graphs with integer…
Path marginal cost (PMC) is a crucial component in solving path-based system-optimal dynamic traffic assignment (SO-DTA), dynamic origin-destination demand estimation (DODE), and network resilience analysis. However, accurately evaluating…
We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with $m$ edges and polynomially bounded integral demands, costs, and capacities in $m^{1+o(1)}$ time. Our algorithm builds the flow through a…
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…
We study a variant of Min Cost Flow in which the flow needs to be connected. Specifically, in the Connected Flow problem one is given a directed graph $G$, along with a set of demand vertices $D \subseteq V(G)$ with demands $\mathsf{dem}: D…
We give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal…
We consider the Minimum Multi-Commodity Flow Subgraph (MMCFS) problem: given a directed graph $G$ with edge capacities $\mathit{cap}$ and a retention ratio $\alpha\in(0,1)$, find an edge-wise minimum subgraph $G' \subseteq G$ such that for…
Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network)…
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…
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…
In this paper we give an $\widetilde{O}((nm)^{2/3}\log C)$ time algorithm for computing min-cost flow (or min-cost circulation) in unit capacity planar multigraphs where edge costs are integers bounded by $C$. For planar multigraphs, this…
Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…