Related papers: A Note on the Quickest Minimum Cost Transshipment …
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
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…
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…
This work considers the problem of transmitting multiple compressible sources over a network at minimum cost. The aim is to find the optimal rates at which the sources should be compressed and the network flows using which they should be…
In the paper "The complexity of mean flow time scheduling problems with release times", by Baptiste, Brucker, Chrobak, D\"urr, Kravchenko and Sourd, the authors claimed to prove strong NP-hardness of the scheduling problem $P|pmtn,r_j|\sum…
We consider an off-line optimisation problem where $k$ robots must service $n$ requests on a single line. A request $i$ has weight $w_i$ and takes place at time $t_i$ at location $d_i$ on the line. A robot can service a request and collect…
We consider the CONGEST model on a network with $n$ nodes, $m$ edges, diameter $D$, and integer costs and capacities bounded by $\text{poly} n$. In this paper, we show how to find an exact solution to the minimum cost flow problem in…
The Traveling Salesman Problem (TSP) is one of the classic and hard problems in combinatorial optimization. We develop a new heuristic that uses a connection between Minimum Cost Flow Problems and the TSP to improve on a given suboptimal…
We introduce a new problem that combines the well known All Pairs Shortest Paths (APSP) problem and the All Pairs Bottleneck Paths (APBP) problem to compute the shortest paths for all pairs of vertices for all possible flow amounts. We call…
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…
Dynamic Flows were introduced by Ford and Fulkerson in 1958 to model flows over time. They define edge capacities to be the total amount of flow that can enter an edge {\em in one time unit}. Each edge also has a length, representing the…
Consider a simple finite graph and its nodes to represent identical water barrels (containing different amounts of water) on a level plane. Each edge corresponds to a (locked, water-filled) pipe connecting two barrels below the plane. We…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
In this article, we address the solution of advection-dominated flow problems by stabilised methods, by means of least-squares computed stabilised coefficients. As main methodological tool, we introduce a data-driven off-line/on-line…
T. Borrvall and J. Petersson [Topology optimization of fluids in Stokes flow, International Journal for Numerical Methods in Fluids 41 (1) (2003) 77--107] developed the first model for topology optimization of fluids in Stokes flow. They…
In this research, we examine the minsum flow problem in dynamic path networks where flows are represented as discrete and weighted sets. The minsum flow problem has been widely studied for its relevance in finding evacuation routes during…
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…
We combine the well known Shortest Paths (SP) problem and the Bottleneck Paths (BP) problem to introduce a new problem called the Shortest Paths for All Flows (SP-AF) problem that has relevance in real life applications. We first solve the…
Crossing minimization is one of the central problems in graph drawing. Recently, there has been an increased interest in the problem of minimizing crossings between paths in drawings of graphs. This is the metro-line crossing minimization…
In this paper, we derive a number of interesting properties and extensions of the convex flow problem from the perspective of convex geometry. We show that the sets of allowable flows always can be imbued with a downward closure property,…