Related papers: A Note on the Quickest Minimum Cost Transshipment …
In this paper we focus on a two-link swimmer called scallop which moves changing dynamics between two fluids regimes. We address and solve explicitly two optimal control problems, the minimum time one and the minimum quadratic cost needed…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
There are well-established connections between combinatorial optimization, optimal transport theory and Hydrodynamics, through the linear assignment problem in combinatorics, the Monge-Kantorovich problem in optimal transport theory and the…
In this paper, we consider a modified projected Gauss-Newton method for solving constrained nonlinear least-squares problems. We assume that the functional constraints are smooth and the the other constraints are represented by a simple…
This work explores the capability of simulating complex fluid flows by directly solving the Boltzmann equation. Due to the high-dimensionality of the governing equation, the substantial computational cost of solving the Boltzmann equation…
We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result by Kuwert and Sch\"atzle in 2002 and prove short time existence and uniqueness of the…
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
Let $D$ be a directed graph cellularly embedded in a surface together with non-negative cost on its arcs. Given any integer circulation in $D$, we study the problem of finding a minimum-cost non-negative integer circulation in $D$ that is…
We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one…
We show NP-hardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to Interference-plus-Noise Ratio (SINR), is above a…
Advancements in computational fluid mechanics have largely relied on Newtonian frameworks, particularly through the direct simulation of Navier-Stokes equations. In this work, we propose an alternative computational framework that employs…
In 2010s Fleiner introduced a notion of stable flows in directed networks and showed that such a flow always exists and can be found by use of a reduction to the stable allocation problem due to Baiou and Balinski. Recently Cseh and…
Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we…
Let $T=(V,E)$ be a tree with associated costs on its subtrees. A minmax $k$-partition of $T$ is a partition into $k$ subtrees, minimizing the maximum cost of a subtree over all possible partitions. In the centered version of the problem,…
We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…
The parametric shortest path problem is to find the shortest paths in graph where the edge costs are of the form w_ij+lambda where each w_ij is constant and lambda is a parameter that varies. The problem is to find shortest path trees for…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. We consider first a common generalization of these two concepts for…
Min cut is an important graph partitioning method. However, current solutions to the min cut problem suffer from slow speeds, difficulty in solving, and often converge to simple solutions. To address these issues, we relax the min cut…