Related papers: Designing Optimal Flow Networks
Engineering networks fall into the category of large-scale networks with heterogeneous nodes such as sources and sinks. The survivability analysis of such networks requires the analysis of the connectivity of the network components for…
In a seminal paper, Chen, Roughgarden and Valiant studied cost sharing protocols for network design with the objective to implement a low-cost Steiner forest as a Nash equilibrium of an induced cost-sharing game. One of the most intriguing…
We consider minimum-cardinality Manhattan connected sets with arbitrary demands: Given a collection of points $P$ in the plane, together with a subset of pairs of points in $P$ (which we call demands), find a minimum-cardinality superset of…
Network flows often exhibit a hierarchical tree-like structure that can be attributed to the minimisation of dissipation. The common feature of such systems is a single source and multiple sinks (or vice versa). In contrast, here we study…
Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at most 1 and the number of additional points is minimized. We…
In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the…
Numerous networks, such as transportation, distribution and delivery networks optimize their designs in order to increase efficiency and lower costs, improving the stability of its intended functions, etc. Networks that distribute goods,…
When the underlying physical network layer in optimal network flow problems is a large graph, the associated optimization problem has a large set of decision variables. In this paper, we discuss how the cycle basis from graph theory can be…
When planning transportation whose operation requires non-consumable resources, the peak demand for allocated resources is often of higher interest than the duration of resource usage. For instance, it is more cost-effective to deliver…
While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum…
Over the past decades, engineering systems have developed as networks of systems that deliver multiple services across multiple domains. This work aims to develop an optimization program for a dynamic, hetero-functional graph theory-based…
In a network where the cost of flow across an edge is nonlinear in the volume of flow, and where sources and destinations are uniform, one can consider the relationship between total volume $v$ of flow through the network and the minimum…
In the Group Steiner Tree problem (GST), we are given a (vertex or edge)-weighted graph $G=(V,E)$ on $n$ vertices, a root vertex $r$ and a collection of groups $\{S_i\}_{i\in[h]}: S_i\subseteq V(G)$. The goal is to find a min-cost subgraph…
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…
The $k$-Steiner-2NCS problem is as follows: Given a constant $k$, and an undirected connected graph $G = (V,E)$, non-negative costs $c$ on $E$, and a partition $(T, V-T)$ of $V$ into a set of terminals, $T$, and a set of non-terminals (or,…
Existing techniques for the cost optimization of water distribution networks either employ meta-heuristics, or try to develop problem-specific optimization techniques. Instead, we exploit recent advances in generic NLP solvers and explore a…
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…
Given a flow network with variable suppliers and fixed consumers, the minimax flow problem consists in minimizing the maximum flow between nodes, subject to flow conservation and capacity constraints. We solve this problem over acyclic…
Let $G$ be an edge-weighted directed graph with $n$ vertices embedded on an orientable surface of genus $g$. We describe a simple deterministic lexicographic perturbation scheme that guarantees uniqueness of minimum-cost flows and shortest…
We analyze a new general representation for the Minimum Weight Steiner Tree (MST) problem which translates the topological connectivity constraint into a set of local conditions which can be analyzed by the so called cavity equations…