Related papers: Balanced flows for transshipment problems
We describe a simple deterministic near-linear time approximation scheme for uncapacitated minimum cost flow in undirected graphs with real edge weights, a problem also known as transshipment. Specifically, our algorithm takes as input a…
We consider an undirected graph $G = (VG, EG)$ with a set $T \subseteq VG$ of terminals, and with nonnegative integer capacities $c(v)$ and costs $a(v)$ of nodes $v\in VG$. A path in $G$ is a \emph{$T$-path} if its ends are distinct…
We introduce the Unsplittable Transshipment Problem in directed graphs with multiple sources and sinks. An unsplittable transshipment routes given supplies and demands using at most one path for each source-sink pair. Although they are a…
In this paper we study flow problems on temporal networks, where edge capacities and travel times change over time. We consider a network with $n$ nodes and $m$ edges where the capacity and length of each edge is a piecewise constant…
Let $G = (VG, AG)$ be a directed graph with a set $S \subseteq VG$ of terminals and nonnegative integer arc capacities $c$. A feasible multiflow is a nonnegative real function $F(P)$ of "flows" on paths $P$ connecting distinct terminals…
Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…
Connectivity (or equivalently, unweighted maximum flow) is an important measure in graph theory and combinatorial optimization. Given a graph $G$ with vertices $s$ and $t$, the connectivity $\lambda(s,t)$ from $s$ to $t$ is defined to be…
We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…
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…
We consider the problem of finding a feasible single-commodity flow in a strongly connected network with fixed supplies and demands, provided that the sum of supplies equals the sum of demands and the minimum arc capacity is at least this…
Let $\mathcal{H}$ be the class of bounded measurable symmetric functions on $[0,1]^2$. For a function $h \in \mathcal{H}$ and a graph $G$ with vertex set $\{v_1,\ldots,v_n\}$ and edge set $E(G)$, define \[ t_G(h) \; = \; \int \cdots \int…
Under general assumptions on the velocity field, it is possible to construct a flow that is forward untangled. Once such a flow has been selected, the associated transport problem is well-posed.
Strong resilience properties of dynamical flow networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the inflow at a non-destination node gets split among its outgoing links is…
We present a method for solving the transshipment problem - also known as uncapacitated minimum cost flow - up to a multiplicative error of $1 + \varepsilon$ in undirected graphs with non-negative edge weights using a tailored gradient…
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…
Interactions between an internal flow and wall deformation occur in many biological systems. Such interactions can involve a complex and rich dynamical behavior and a number of peculiarities which depend on the flow parameter range. The aim…
The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear…
In contrast to traditional flow networks, in additive flow networks, to every edge e is assigned a gain factor g(e) which represents the loss or gain of the flow while using edge e. Hence, if a flow f(e) enters the edge e and f(e) is less…
We introduce the notion of balance for directed graphs: a weighted directed graph is $\alpha$-balanced if for every cut $S \subseteq V$, the total weight of edges going from $S$ to $V\setminus S$ is within factor $\alpha$ of the total…
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…